Actual source code: ex69.c

  1: static char help[] = "The variable-viscosity Stokes Problem in 2d with finite elements.\n\
2: We solve the Stokes problem in a square domain\n\
3: and compare against exact solutions from Mirko Velic.\n\n\n";

5: /* We discretize the variable-viscosity Stokes problem using the finite element method on an unstructured mesh. The weak form equations are
6: \begin{align*}
7:   (\nabla v, \mu (\nabla u + {\nabla u}^T)) - (\nabla\cdot v, p) + (v, f) &= 0 \\
8:   (q, \nabla\cdot u)                                                      &= 0
9: \end{align*}
10: Free slip conditions for velocity are enforced on every wall. The pressure is constrained to have zero integral over the domain.

12: To produce nice output, use

14:   -dm_refine 3 -show_error -dm_view hdf5:sol1.h5 -error_vec_view hdf5:sol1.h5::append -sol_vec_view hdf5:sol1.h5::append -exact_vec_view hdf5:sol1.h5::append
15: */

17: #include <petscdmplex.h>
18: #include <petscsnes.h>
19: #include <petscds.h>
20: #include <petscbag.h>

22: typedef enum {
23:   SOLKX,
24:   SOLCX,
25:   NUM_SOL_TYPES
26: } SolutionType;
27: const char *solTypes[NUM_SOL_TYPES + 1] = {"solkx", "solcx", "unknown"};

29: typedef struct {
30:   PetscInt n, m; /* x- and y-wavelengths for variation across the domain */
31:   /* SolKx */
32:   PetscReal B; /* Exponential scale for viscosity variation */
33:   /* SolCx */
34:   PetscReal etaA, etaB; /* Two viscosities for discontinuous change */
35:   PetscReal xc;         /* The location of viscosity jump */
36: } Parameter;

38: typedef struct {
39:   SolutionType solType; /* The type of exact solution */
40:   PetscBag     bag;     /* Holds problem parameters */
41: } AppCtx;

43: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
44: {
45:   PetscInt c;
46:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
47:   return PETSC_SUCCESS;
48: }
49: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
50: {
51:   PetscInt c;
52:   for (c = 0; c < Nc; ++c) u[c] = 1.0;
53:   return PETSC_SUCCESS;
54: }

56: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
57: {
58:   f0[0] = 0.0;
59:   f0[1] = -PetscSinScalar(constants[1] * PETSC_PI * x[1]) * PetscCosScalar(constants[0] * PETSC_PI * x[0]);
60: }

62: static void stokes_momentum_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
63: {
64:   const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
65:   PetscInt        c, d;

67:   for (c = 0; c < dim; ++c) {
68:     for (d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
69:     f1[c * dim + c] -= u[dim];
70:   }
71: }

73: static void stokes_momentum_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
74: {
75:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
76:   PetscInt        c, d;

78:   for (c = 0; c < dim; ++c) {
79:     for (d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
80:     f1[c * dim + c] -= u[dim];
81:   }
82: }

84: static void stokes_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
85: {
86:   PetscInt d;
87:   f0[0] = 0.0;
88:   for (d = 0; d < dim; ++d) f0[0] -= u_x[d * dim + d];
89: }

91: static void f1_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
92: {
93:   PetscInt d;
94:   for (d = 0; d < dim * dim; ++d) f1[d] = 0.0;
95: }

97: /* < q, \nabla\cdot u >, J_{pu} */
98: static void stokes_mass_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
99: {
100:   PetscInt d;
101:   for (d = 0; d < dim; ++d) g1[d * dim + d] = -1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
102: }

104: /* -< \nabla\cdot v, p >, J_{up} */
105: static void stokes_momentum_pres_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
106: {
107:   PetscInt d;
108:   for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
109: }

111: /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu}
112:    This just gives \nabla u, give the perdiagonal for the transpose */
113: static void stokes_momentum_vel_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
114: {
115:   const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
116:   PetscInt        cI, d;

118:   for (cI = 0; cI < dim; ++cI) {
119:     for (d = 0; d < dim; ++d) {
120:       g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
121:       g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
122:     }
123:   }
124: }
125: static void stokes_momentum_vel_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
126: {
127:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
128:   PetscInt        cI, d;

130:   for (cI = 0; cI < dim; ++cI) {
131:     for (d = 0; d < dim; ++d) {
132:       g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
133:       g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
134:     }
135:   }
136: }

138: /* 1/mu < q, I q >, Jp_{pp} */
139: static void stokes_identity_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
140: {
141:   const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
142:   g0[0]              = 1.0 / mu;
143: }

145: static void stokes_identity_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
146: {
147:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
148:   g0[0]              = 1.0 / mu;
149: }

151: /*
152:   SolKxSolution - Exact Stokes solutions for exponentially varying viscosity

154:  Input Parameters:
155: + pos   - The (x,z) coordinate at which to evaluate the solution
156: . n     - The constant defining the x-dependence of the forcing function
157: . m     - The constant defining the z-dependence of the forcing function
158: - B     - The viscosity coefficient

160:   Output Parameters:
161: + vel   - The (x,z)-velocity at (x,z), or NULL
162: . p     - The pressure at (x,z), or NULL
163: . s     - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
164: . gamma - The strain rate, or NULL
165: - mu    - The viscosity at (x,z), or NULL

167:   Note:
168: .vb
169:   The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
170:   conditions everywhere. The forcing term f is given by

172:     fx = 0
173:     fz = sigma*sin(km*z)*cos(kn*x)

175:   where

177:     km = m*Pi (m may be non-integral)
178:     kn = n*Pi

180:   meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
181:   The viscosity eta is exp(2*B*x).
182: .ve

184: */
185: static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
186: {
187:   PetscReal sigma = 1.0;
188:   PetscReal Z;
189:   PetscReal u1, u2, u3, u4, u5, u6;
190:   PetscReal sum1, sum2, sum3, sum4, sum5, sum6;
191:   PetscReal kn, km, x, z;
192:   PetscReal _PC1, _PC2, _PC3, _PC4;
193:   PetscReal Rp, UU, VV;
194:   PetscReal a, b, r, _aa, _bb, AA, BB, Rm;
195:   PetscReal num1, num2, num3, num4, den1;

197:   PetscReal t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
198:   PetscReal t11, t12, t13, t14, t15, t16, t17, t18, t19, t20;
199:   PetscReal t21, t22, t23, t24, t25, t26, t27, t28, t29, t30;
200:   PetscReal t31, t32, t33, t34, t35, t36, t37, t38, t39, t40;
201:   PetscReal t41, t42, t43, t44, t45, t46, t47, t49, t51, t53;
202:   PetscReal t56, t58, t61, t62, t63, t64, t65, t66, t67, t68;
203:   PetscReal t69, t70, t71, t72, t73, t74, t75, t76, t77, t78;
204:   PetscReal t79, t80, t81, t82, t83, t84, t85, t86, t87, t88;
205:   PetscReal t89, t90, t91, t92, t93, t94, t95, t96, t97, t99;
206:   PetscReal t100, t101, t103, t104, t105, t106, t107, t108, t109, t110;
207:   PetscReal t111, t112, t113, t114, t115, t116, t117, t118, t119, t120;
208:   PetscReal t121, t124, t125, t126, t127, t129, t130, t132, t133, t135;
209:   PetscReal t136, t138, t140, t141, t142, t143, t152, t160, t162;

211:   PetscFunctionBegin;
212:   /*************************************************************************/
213:   /*************************************************************************/
214:   /* rho = -sin(km*z)*cos(kn*x) */
215:   x  = pos[0];
216:   z  = pos[1];
217:   Z  = PetscExpReal(2.0 * B * x);
218:   km = m * PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */
219:   kn = (PetscReal)n * PETSC_PI;
220:   /*************************************************************************/
221:   /*************************************************************************/
222:   a  = B * B + km * km;
223:   b  = 2.0 * km * B;
224:   r  = PetscSqrtReal(a * a + b * b);
225:   Rp = PetscSqrtReal((r + a) / 2.0);
226:   Rm = PetscSqrtReal((r - a) / 2.0);
227:   UU = Rp - B;
228:   VV = Rp + B;

230:   sum1 = 0.0;
231:   sum2 = 0.0;
232:   sum3 = 0.0;
233:   sum4 = 0.0;
234:   sum5 = 0.0;
235:   sum6 = 0.0;
236:   /*sum7=0.0;*/

238:   /*******************************************/
239:   /*         calculate the constants         */
240:   /*******************************************/

242:   t1  = kn * kn;
243:   t4  = km * km;
244:   t5  = t4 + t1;
245:   t6  = t5 * t5;
246:   t8  = pow(km + kn, 0.2e1);
247:   t9  = B * B;
248:   t16 = pow(km - kn, 0.2e1);
249:   _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9);

251:   t2  = km * km;
252:   t3  = kn * kn;
253:   t5  = pow(t2 + t3, 0.2e1);
254:   t6  = km - kn;
255:   t7  = km + kn;
256:   t9  = B * B;
257:   t13 = t7 * t7;
258:   t19 = t6 * t6;
259:   _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9);

261:   AA = _aa;
262:   BB = _bb;

264:   /*******************************************/
265:   /*       calculate the velocities etc      */
266:   /*******************************************/
267:   t1   = Rm * Rm;
268:   t2   = B - Rp;
269:   t4   = Rp + B;
270:   t6   = UU * x;
271:   t9   = PetscExpReal(t6 - 0.4e1 * Rp);
272:   t13  = B * B;
273:   t16  = Rp * t1;
274:   t18  = Rp * Rp;
275:   t19  = B * t18;
276:   t20  = t13 * Rp;
277:   t22  = kn * kn;
278:   t24  = B * t1;
279:   t32  = 0.8e1 * t13 * BB * kn * Rp;
280:   t34  = 0.2e1 * Rm;
281:   t35  = PetscCosReal(t34);
282:   t37  = Rp * Rm;
283:   t49  = PetscSinReal(t34);
284:   t63  = PetscExpReal(t6 - 0.2e1 * Rp);
285:   t65  = Rm * t2;
286:   t67  = 0.2e1 * B * kn;
287:   t68  = B * Rm;
288:   t69  = t67 + t68 + t37;
289:   t73  = 0.3e1 * t13;
290:   t75  = 0.2e1 * B * Rp;
291:   t76  = t73 - t75 + t1 - t22 - t18;
292:   t78  = t65 * t76 * BB;
293:   t80  = Rm - kn;
294:   t81  = PetscCosReal(t80);
295:   t83  = -t67 + t68 + t37;
296:   t88  = Rm + kn;
297:   t89  = PetscCosReal(t88);
298:   t92  = t65 * t76 * AA;
299:   t97  = PetscSinReal(t80);
300:   t103 = PetscSinReal(t88);
301:   t108 = PetscExpReal(t6 - 0.3e1 * Rp - B);
302:   t110 = Rm * t4;
303:   t111 = t67 + t68 - t37;
304:   t115 = t73 + t75 + t1 - t22 - t18;
305:   t117 = t110 * t115 * BB;
306:   t120 = -t67 + t68 - t37;
307:   t127 = t110 * t115 * AA;
308:   t140 = PetscExpReal(t6 - Rp - B);
309:   num1 = -0.4e1 * t1 * t2 * t4 * AA * t9 + ((0.2e1 * Rp * (0.3e1 * t13 * B - 0.2e1 * t16 - t19 - 0.2e1 * t20 - B * t22 - t24) * AA - t32) * t35 + (0.2e1 * t37 * (t1 + 0.5e1 * t13 - t22 - t18) * AA - 0.8e1 * B * BB * kn * Rm * Rp) * t49 - 0.2e1 * B * (0.3e1 * t20 - Rp * t22 - t18 * Rp - 0.2e1 * t19 - t16 - 0.2e1 * t24) * AA + t32) * t63 + ((0.2e1 * t65 * t69 * AA + t78) * t81 + (0.2e1 * t65 * t83 * AA - t78) * t89 + (t92 - 0.2e1 * t65 * t69 * BB) * t97 + (t92 + 0.2e1 * t65 * t83 * BB) * t103) * t108 + ((-0.2e1 * t110 * t111 * AA - t117) * t81 + (-0.2e1 * t110 * t120 * AA + t117) * t89 + (-t127 + 0.2e1 * t110 * t111 * BB) * t97 + (-t127 - 0.2e1 * t110 * t120 * BB) * t103) * t140;

311:   t1   = Rp + B;
312:   t2   = Rm * t1;
313:   t3   = B * B;
314:   t4   = 0.3e1 * t3;
315:   t5   = B * Rp;
316:   t7   = Rm * Rm;
317:   t8   = kn * kn;
318:   t9   = Rp * Rp;
319:   t10  = t4 + 0.2e1 * t5 + t7 - t8 - t9;
320:   t12  = t2 * t10 * AA;
321:   t14  = B * Rm;
322:   t20  = UU * x;
323:   t23  = PetscExpReal(t20 - 0.4e1 * Rp);
324:   t25  = Rp * Rm;
325:   t32  = Rm * kn;
326:   t37  = 0.2e1 * Rm;
327:   t38  = PetscCosReal(t37);
328:   t40  = t3 * B;
329:   t44  = B * t9;
330:   t45  = t3 * Rp;
331:   t53  = t3 * BB;
332:   t58  = PetscSinReal(t37);
333:   t69  = PetscExpReal(t20 - 0.2e1 * Rp);
334:   t72  = 0.3e1 * t40 * Rm;
335:   t73  = t9 * Rp;
336:   t74  = t73 * Rm;
337:   t75  = t7 * Rm;
338:   t76  = B * t75;
339:   t77  = t14 * t8;
340:   t78  = Rp * t75;
341:   t80  = 0.8e1 * t45 * kn;
342:   t81  = t25 * t8;
343:   t83  = 0.5e1 * t45 * Rm;
344:   t84  = t44 * Rm;
345:   t85  = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84;
346:   t88  = 0.2e1 * t9 * t3;
347:   t90  = 0.3e1 * t40 * Rp;
348:   t91  = t7 * t3;
349:   t93  = 0.2e1 * t5 * t32;
350:   t94  = t5 * t7;
351:   t95  = t5 * t8;
352:   t96  = B * t73;
353:   t97  = t7 * t9;
354:   t100 = 0.2e1 * t3 * Rm * kn;
355:   t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100;
356:   t105 = Rm - kn;
357:   t106 = PetscCosReal(t105);
358:   t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77;
359:   t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94;
360:   t114 = Rm + kn;
361:   t115 = PetscCosReal(t114);
362:   t121 = PetscSinReal(t105);
363:   t127 = PetscSinReal(t114);
364:   t132 = PetscExpReal(t20 - 0.3e1 * Rp - B);
365:   t135 = 0.2e1 * B * kn;
366:   t136 = t135 + t14 - t25;
367:   t142 = -t135 + t14 - t25;
368:   t152 = t2 * t10 * BB;
369:   t162 = PetscExpReal(t20 - Rp - B);
370:   num2 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t23 + ((-0.2e1 * t25 * (t7 + 0.5e1 * t3 - t8 - t9) * AA + 0.8e1 * B * BB * t32 * Rp) * t38 + (0.2e1 * Rp * (0.3e1 * t40 - 0.2e1 * Rp * t7 - t44 - 0.2e1 * t45 - B * t8 - B * t7) * AA - 0.8e1 * t53 * kn * Rp) * t58 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t53 * t32) * t69 + ((-t85 * AA - 0.2e1 * t101 * BB) * t106 + (-t108 * AA + 0.2e1 * t110 * BB) * t115 + (-0.2e1 * t101 * AA + t85 * BB) * t121 + (-0.2e1 * t110 * AA - t108 * BB) * t127) * t132 + ((t12 - 0.2e1 * t2 * t136 * BB) * t106 + (t12 + 0.2e1 * t2 * t142 * BB) * t115 + (-0.2e1 * t2 * t136 * AA - t152) * t121 + (-0.2e1 * t2 * t142 * AA + t152) * t127) * t162;

372:   t1   = Rm * Rm;
373:   t2   = B - Rp;
374:   t4   = Rp + B;
375:   t6   = VV * x;
376:   t7   = PetscExpReal(-t6);
377:   t11  = kn * kn;
378:   t13  = B * t1;
379:   t14  = Rp * Rp;
380:   t15  = B * t14;
381:   t16  = B * B;
382:   t17  = t16 * Rp;
383:   t21  = Rp * t1;
384:   t30  = 0.8e1 * t16 * BB * kn * Rp;
385:   t32  = 0.2e1 * Rm;
386:   t33  = PetscCosReal(t32);
387:   t35  = Rp * Rm;
388:   t47  = PetscSinReal(t32);
389:   t61  = PetscExpReal(-t6 - 0.2e1 * Rp);
390:   t63  = Rm * t2;
391:   t65  = 0.2e1 * B * kn;
392:   t66  = B * Rm;
393:   t67  = t65 + t66 + t35;
394:   t71  = 0.3e1 * t16;
395:   t73  = 0.2e1 * B * Rp;
396:   t74  = t71 - t73 + t1 - t11 - t14;
397:   t76  = t63 * t74 * BB;
398:   t78  = Rm - kn;
399:   t79  = PetscCosReal(t78);
400:   t81  = -t65 + t66 + t35;
401:   t86  = Rm + kn;
402:   t87  = PetscCosReal(t86);
403:   t90  = t63 * t74 * AA;
404:   t95  = PetscSinReal(t78);
405:   t101 = PetscSinReal(t86);
406:   t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B);
407:   t108 = Rm * t4;
408:   t109 = t65 + t66 - t35;
409:   t113 = t71 + t73 + t1 - t11 - t14;
410:   t115 = t108 * t113 * BB;
411:   t118 = -t65 + t66 - t35;
412:   t125 = t108 * t113 * AA;
413:   t138 = PetscExpReal(-t6 - Rp - B);
414:   num3 = -0.4e1 * t1 * t2 * t4 * AA * t7 + ((-0.2e1 * Rp * (-B * t11 - t13 - t15 + 0.2e1 * t17 + 0.3e1 * t16 * B + 0.2e1 * t21) * AA + t30) * t33 + (-0.2e1 * t35 * (t1 + 0.5e1 * t16 - t11 - t14) * AA + 0.8e1 * B * BB * kn * Rm * Rp) * t47 + 0.2e1 * B * (0.3e1 * t17 - t21 + 0.2e1 * t15 + 0.2e1 * t13 - Rp * t11 - t14 * Rp) * AA - t30) * t61 + ((-0.2e1 * t63 * t67 * AA - t76) * t79 + (-0.2e1 * t63 * t81 * AA + t76) * t87 + (-t90 + 0.2e1 * t63 * t67 * BB) * t95 + (-t90 - 0.2e1 * t63 * t81 * BB) * t101) * t106 + ((0.2e1 * t108 * t109 * AA + t115) * t79 + (0.2e1 * t108 * t118 * AA - t115) * t87 + (t125 - 0.2e1 * t108 * t109 * BB) * t95 + (t125 + 0.2e1 * t108 * t118 * BB) * t101) * t138;

416:   t1   = B - Rp;
417:   t2   = Rm * t1;
418:   t3   = B * B;
419:   t4   = 0.3e1 * t3;
420:   t5   = B * Rp;
421:   t7   = Rm * Rm;
422:   t8   = kn * kn;
423:   t9   = Rp * Rp;
424:   t10  = t4 - 0.2e1 * t5 + t7 - t8 - t9;
425:   t12  = t2 * t10 * AA;
426:   t14  = B * Rm;
427:   t20  = VV * x;
428:   t21  = PetscExpReal(-t20);
429:   t23  = Rp * Rm;
430:   t30  = Rm * kn;
431:   t35  = 0.2e1 * Rm;
432:   t36  = PetscCosReal(t35);
433:   t40  = B * t9;
434:   t41  = t3 * Rp;
435:   t43  = t3 * B;
436:   t51  = t3 * BB;
437:   t56  = PetscSinReal(t35);
438:   t67  = PetscExpReal(-t20 - 0.2e1 * Rp);
439:   t70  = 0.2e1 * B * kn;
440:   t71  = t70 + t14 + t23;
441:   t76  = Rm - kn;
442:   t77  = PetscCosReal(t76);
443:   t79  = -t70 + t14 + t23;
444:   t84  = Rm + kn;
445:   t85  = PetscCosReal(t84);
446:   t91  = t2 * t10 * BB;
447:   t93  = PetscSinReal(t76);
448:   t99  = PetscSinReal(t84);
449:   t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B);
450:   t107 = 0.3e1 * t43 * Rm;
451:   t108 = t9 * Rp;
452:   t109 = t108 * Rm;
453:   t110 = t7 * Rm;
454:   t111 = B * t110;
455:   t112 = t14 * t8;
456:   t113 = Rp * t110;
457:   t115 = 0.8e1 * t41 * kn;
458:   t116 = t23 * t8;
459:   t118 = 0.5e1 * t41 * Rm;
460:   t119 = t40 * Rm;
461:   t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119;
462:   t124 = 0.2e1 * t3 * Rm * kn;
463:   t125 = t5 * t8;
464:   t126 = B * t108;
465:   t127 = t7 * t9;
466:   t129 = 0.2e1 * t9 * t3;
467:   t130 = t5 * t7;
468:   t132 = 0.3e1 * t43 * Rp;
469:   t133 = t7 * t3;
470:   t135 = 0.2e1 * t5 * t30;
471:   t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135;
472:   t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112;
473:   t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135;
474:   t160 = PetscExpReal(-t20 - Rp - B);
475:   num4 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t21 + ((0.2e1 * t23 * (t7 + 0.5e1 * t3 - t8 - t9) * AA - 0.8e1 * B * BB * t30 * Rp) * t36 + (-0.2e1 * Rp * (-B * t8 - B * t7 - t40 + 0.2e1 * t41 + 0.3e1 * t43 + 0.2e1 * Rp * t7) * AA + 0.8e1 * t51 * kn * Rp) * t56 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t51 * t30) * t67 + ((t12 - 0.2e1 * t2 * t71 * BB) * t77 + (t12 + 0.2e1 * t2 * t79 * BB) * t85 + (-0.2e1 * t2 * t71 * AA - t91) * t93 + (-0.2e1 * t2 * t79 * AA + t91) * t99) * t104 + ((-t120 * AA + 0.2e1 * t136 * BB) * t77 + (-t141 * AA - 0.2e1 * t143 * BB) * t85 + (0.2e1 * t136 * AA + t120 * BB) * t93 + (0.2e1 * t143 * AA - t141 * BB) * t99) * t160;

477:   t1   = Rm * Rm;
478:   t2   = Rp * Rp;
479:   t3   = t1 * t2;
480:   t4   = B * B;
481:   t5   = t1 * t4;
482:   t9   = PetscExpReal(-0.4e1 * Rp);
483:   t15  = PetscCosReal(0.2e1 * Rm);
484:   t22  = PetscExpReal(-0.2e1 * Rp);
485:   den1 = (-0.4e1 * t3 + 0.4e1 * t5) * t9 + ((0.8e1 * t1 + 0.8e1 * t4) * t2 * t15 - 0.8e1 * t5 - 0.8e1 * t2 * t4) * t22 - 0.4e1 * t3 + 0.4e1 * t5;

487:   _PC1 = num1 / den1;
488:   _PC2 = num2 / den1;
489:   _PC3 = num3 / den1;
490:   _PC4 = num4 / den1;

492:   t1  = Rm * x;
493:   t2  = PetscCosReal(t1);
494:   t4  = PetscSinReal(t1);
495:   t10 = PetscExpReal(-0.2e1 * x * B);
496:   t12 = kn * x;
497:   t13 = PetscCosReal(t12);
498:   t16 = PetscSinReal(t12);
499:   u1  = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16);

501:   t2  = Rm * x;
502:   t3  = PetscCosReal(t2);
503:   t6  = PetscSinReal(t2);
504:   t22 = PetscExpReal(-0.2e1 * x * B);
505:   t23 = B * t22;
506:   t24 = kn * x;
507:   t25 = PetscCosReal(t24);
508:   t29 = PetscSinReal(t24);
509:   u2  = UU * _PC1 * t3 + UU * _PC2 * t6 - _PC1 * t6 * Rm + _PC2 * t3 * Rm - VV * _PC3 * t3 - VV * _PC4 * t6 - _PC3 * t6 * Rm + _PC4 * t3 * Rm - 0.2e1 * t23 * AA * t25 - 0.2e1 * t23 * BB * t29 - t22 * AA * t29 * kn + t22 * BB * t25 * kn;

511:   t3   = PetscExpReal(0.2e1 * x * B);
512:   t4   = t3 * B;
513:   t8   = km * km;
514:   t9   = t3 * t8;
515:   t11  = 0.3e1 * t9 * Rm;
516:   t12  = Rm * Rm;
517:   t14  = t3 * t12 * Rm;
518:   t15  = UU * UU;
519:   t19  = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm;
520:   t20  = Rm * x;
521:   t21  = PetscSinReal(t20);
522:   t27  = 0.2e1 * B * t9;
523:   t33  = 0.2e1 * t4 * t12;
524:   t36  = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU;
525:   t37  = PetscCosReal(t20);
526:   t49  = VV * VV;
527:   t53  = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14;
528:   t64  = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12;
529:   t76  = B * t8;
530:   t80  = kn * kn;
531:   t83  = B * B;
532:   t87  = t80 * kn;
533:   t90  = kn * x;
534:   t91  = PetscSinReal(t90);
535:   t106 = PetscCosReal(t90);
536:   u3 = -((t19 * t21 + t36 * t37) * _PC1 + (t36 * t21 - t19 * t37) * _PC2 + (t53 * t21 + t64 * t37) * _PC3 + (t64 * t21 - t53 * t37) * _PC4 + (-0.3e1 * t8 * AA * kn - 0.8e1 * t76 * BB - 0.4e1 * BB * B * t80 + 0.4e1 * AA * t83 * kn - AA * t87) * t91 + (-0.4e1 * AA * t80 * B - 0.4e1 * t83 * BB * kn + 0.3e1 * t8 * BB * kn - sigma + BB * t87 - 0.8e1 * t76 * AA) * t106) / km;

538:   t3  = PetscExpReal(0.2e1 * x * B);
539:   t4  = km * km;
540:   t5  = t3 * t4;
541:   t6  = Rm * x;
542:   t7  = PetscCosReal(t6);
543:   t8  = _PC1 * t7;
544:   t10 = PetscSinReal(t6);
545:   t11 = _PC2 * t10;
546:   t13 = _PC3 * t7;
547:   t15 = _PC4 * t10;
548:   t18 = kn * x;
549:   t19 = PetscCosReal(t18);
550:   t22 = PetscSinReal(t18);
551:   t24 = UU * UU;
552:   t25 = t3 * t24;
553:   t28 = t3 * UU;
554:   t38 = Rm * Rm;
555:   t39 = t7 * t38;
556:   t42 = t10 * t38;
557:   t44 = t5 * t8 + t5 * t11 + t5 * t13 + t5 * t15 + t4 * AA * t19 + t4 * BB * t22 + t25 * t8 + t25 * t11 - 0.2e1 * t28 * _PC1 * t10 * Rm + 0.2e1 * t28 * _PC2 * t7 * Rm - t3 * _PC1 * t39 - t3 * _PC2 * t42;
558:   t45 = VV * VV;
559:   t46 = t3 * t45;
560:   t49 = t3 * VV;
561:   t62 = B * B;
562:   t78 = kn * kn;
563:   t82 = t46 * t13 + t46 * t15 + 0.2e1 * t49 * _PC3 * t10 * Rm - 0.2e1 * t49 * _PC4 * t7 * Rm - t3 * _PC3 * t39 - t3 * _PC4 * t42 + 0.4e1 * t62 * AA * t19 + 0.4e1 * t62 * BB * t22 + 0.4e1 * B * AA * t22 * kn - 0.4e1 * B * BB * t19 * kn - AA * t19 * t78 - BB * t22 * t78;
564:   u4 = t44 + t82;

566:   t3   = PetscExpReal(0.2e1 * x * B);
567:   t4   = t3 * B;
568:   t8   = km * km;
569:   t9   = t3 * t8;
570:   t10  = t9 * Rm;
571:   t11  = Rm * Rm;
572:   t13  = t3 * t11 * Rm;
573:   t14  = UU * UU;
574:   t18  = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm;
575:   t19  = Rm * x;
576:   t20  = PetscSinReal(t19);
577:   t26  = 0.2e1 * B * t9;
578:   t31  = 0.2e1 * t4 * t11;
579:   t34  = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU;
580:   t35  = PetscCosReal(t19);
581:   t47  = VV * VV;
582:   t51  = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13;
583:   t61  = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11;
584:   t72  = B * t8;
585:   t76  = kn * kn;
586:   t79  = B * B;
587:   t83  = t76 * kn;
588:   t86  = kn * x;
589:   t87  = PetscSinReal(t86);
590:   t101 = PetscCosReal(t86);
591:   u5 = ((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-t8 * AA * kn - 0.4e1 * t72 * BB - 0.4e1 * BB * B * t76 + 0.4e1 * AA * t79 * kn - AA * t83) * t87 + (-0.4e1 * AA * t76 * B - 0.4e1 * t79 * BB * kn + t8 * BB * kn - sigma + BB * t83 - 0.4e1 * t72 * AA) * t101) / km;

593:   t3  = PetscExpReal(0.2e1 * x * B);
594:   t4  = UU * UU;
595:   t8  = km * km;
596:   t9  = t3 * t8;
597:   t10 = t9 * Rm;
598:   t11 = Rm * Rm;
599:   t13 = t3 * t11 * Rm;
600:   t14 = t3 * B;
601:   t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm;
602:   t19 = Rm * x;
603:   t20 = PetscSinReal(t19);
604:   t28 = 0.2e1 * B * t9;
605:   t33 = 0.2e1 * t14 * t11;
606:   t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33;
607:   t35 = PetscCosReal(t19);
608:   t47 = VV * VV;
609:   t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm;
610:   t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28;
611:   t71 = kn * kn;
612:   t74 = B * B;
613:   t80 = t71 * kn;
614:   t83 = kn * x;
615:   t84 = PetscSinReal(t83);
616:   t96 = PetscCosReal(t83);
617:   u6 = -((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-0.4e1 * BB * B * t71 + 0.4e1 * AA * t74 * kn + t8 * AA * kn - AA * t80) * t84 + (-0.4e1 * AA * t71 * B - t8 * BB * kn - 0.4e1 * t74 * BB * kn - sigma + BB * t80) * t96) / km;

619:   /* SS = sin(km*z)*(exp(UU*x)*(_PC1*cos(Rm*x)+_PC2*sin(Rm*x)) + exp(-VV*x)*(_PC3*cos(Rm*x)+_PC4*sin(Rm*x)) + exp(-2*x*B)*(AA*cos(kn*x)+BB*sin(kn*x))); */

621:   /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */

623:   sum5 += u5 * PetscCosReal(km * z); /* pressure */
624:   sum6 += u6 * PetscCosReal(km * z); /* zz total stress */

626:   u1 *= PetscCosReal(km * z); /* x velocity */
627:   sum1 += u1;
628:   u2 *= PetscSinReal(km * z); /* z velocity */
629:   sum2 += u2;

631:   u3 *= PetscCosReal(km * z); /* xx total stress */
632:   sum3 += u3;
633:   u4 *= PetscSinReal(km * z); /* zx stress */
634:   sum4 += u4;

636:   /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */
637:   /* sum7 += rho; */

639:   /* Output */
640:   if (mu) *mu = Z;
641:   if (vel) {
642:     vel[0] = sum1;
643:     vel[1] = sum2;
644:   }
645:   if (p) (*p) = sum5;
646:   if (s) {
647:     s[0] = sum3;
648:     s[1] = sum4;
649:     s[2] = sum6;
650:   }
651:   if (gamma) {
652:     /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
653:     gamma[0] = (sum3 + sum5) / (2.0 * Z);
654:     gamma[1] = (sum4) / (2.0 * Z);
655:     gamma[2] = (sum6 + sum5) / (2.0 * Z);
656:   }
657:   PetscFunctionReturn(PETSC_SUCCESS);
658: }

660: static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
661: {
662:   Parameter *s = (Parameter *)ctx;

664:   PetscFunctionBegin;
665:   PetscCall(SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL));
666:   PetscFunctionReturn(PETSC_SUCCESS);
667: }

669: static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
670: {
671:   Parameter *s = (Parameter *)ctx;

673:   PetscFunctionBegin;
674:   PetscCall(SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL));
675:   PetscFunctionReturn(PETSC_SUCCESS);
676: }

678: /*
679:   SolCxSolution - Exact Stokes solutions for discontinuous viscosity

681:  Input Parameters:
682: + pos   - The (x,z) coordinate at which to evaluate the solution
683: . n     - The constant defining the x-dependence of the forcing function
684: . m     - The constant defining the z-dependence of the forcing function
685: . xc    - The x coordinate at which the viscosity is discontinuous
686: . etaA  - The viscosity coefficient for x < xc
687: - etaB  - The viscosity coefficient for x > xc

689:   Output Parameters:
690: + vel   - The (x,z)-velocity at (x,z), or NULL
691: . p     - The pressure at (x,z), or NULL
692: . s     - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
693: . gamma - The strain rate, or NULL
694: - mu    - The viscosity at (x,z), or NULL

696:   Note:
697: .vb
698:   The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
699:   conditions everywhere. The forcing term f is given by

701:     fx = 0
702:     fz = sigma*sin(km*z)*cos(kn*x)

704:   where

706:     km = m*Pi (m may be non-integral)
707:     kn = n*Pi

709:   meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
710:   The viscosity eta jumps from etaA to etaB at x = xc.
711: .ve
712: */
713: static PetscErrorCode SolCxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal xc, PetscReal etaA, PetscReal etaB, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
714: {
715:   PetscReal _PC1A, _PC2A, _PC3A, _PC4A, _PC1B, _PC2B, _PC3B, _PC4B, _PC1, _PC2, _PC3, _PC4;
716:   PetscReal t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21, t22, t23, t24, t25, t26, t27, t28, t29, t30, t31, t32, t33, t34, t35, t36, t37, t38, t39, t40;
717:   PetscReal t41, t42, t43, t44, t45, t46, t47, t48, t49, t50, t51, t52, t53, t54, t55, t56, t57, t58, t59, t60, t61, t62, t63, t64, t65, t66, t67, t68, t69, t70, t71, t72, t73, t74, t75, t76, t77, t78, t79, t80;
718:   PetscReal t81, t82, t83, t84, t85, t86, t87, t88, t89, t90, t91, t92, t93, t94, t95, t96, t97, t98, t99, t100, t101, t102, t103, t104, t105, t106, t107, t108, t109, t110, t111, t112, t113, t115, t116, t117, t118, t119, t120;
719:   PetscReal t121, t122, t123, t124, t125, t126, t127, t128, t129, t130, t131, t132, t133, t134, t135, t136, t137, t138, t139, t140, t141, t142, t143, t144, t145, t146, t147, t148, t149, t150, t151, t152, t153, t154, t155, t156, t157, t158, t159, t160;
720:   PetscReal t161, t162, t163, t164, t165, t166, t167, t168, t169, t170, t171, t172, t173, t174, t175, t176, t177, t178, t179, t180, t181, t182, t183, t184, t186, t187, t188, t189, t190, t191, t192, t193, t194, t195, t196, t197, t198, t199;
721:   PetscReal t201, t202, t203, t204, t206, t207, t208, t209, t210, t211, t212, t213, t215, t216, t217, t218, t219, t220, t221, t222, t223, t224, t225, t226, t227, t228, t229, t230, t231, t232, t233, t234, t235, t236, t237, t238, t239, t240;
722:   PetscReal t241, t242, t243, t244, t245, t246, t247, t248, t249, t250, t251, t252, t253, t254, t255, t256, t257, t258, t259, t260, t261, t262, t263, t264, t265, t267, t268, t269, t270, t272, t273, t274, t275, t276, t277, t278, t279, t280;
723:   PetscReal t281, t282, t283, t284, t285, t286, t288, t289, t290, t291, t292, t295, t296, t297, t298, t299, t300, t301, t303, t304, t305, t307, t308, t310, t311, t312, t313, t314, t315, t316, t317, t318, t319, t320;
724:   PetscReal t321, t322, t323, t324, t325, t326, t327, t328, t329, t330, t331, t332, t334, t335, t336, t337, t338, t339, t340, t341, t342, t344, t345, t346, t347, t348, t349, t350, t351, t352, t353, t354, t355, t356, t358, t359, t360;
725:   PetscReal t361, t362, t363, t364, t365, t366, t367, t368, t369, t370, t371, t372, t373, t374, t375, t376, t377, t378, t379, t380, t381, t382, t383, t384, t385, t386, t387, t389, t390, t391, t393, t394, t395, t396, t397, t398;
726:   PetscReal t401, t402, t403, t404, t405, t406, t407, t408, t409, t410, t411, t412, t413, t414, t415, t416, t417, t418, t419, t421, t422, t423, t424, t425, t426, t427, t428, t429, t430, t431, t432, t433, t434, t436, t437, t438, t439, t440;
727:   PetscReal t441, t442, t443, t444, t445, t446, t447, t448, t450, t451, t453, t454, t455, t456, t457, t458, t459, t461, t462, t463, t464, t465, t466, t468, t469, t470, t471, t474, t475, t478, t480;
728:   PetscReal t482, t483, t484, t485, t488, t489, t490, t492, t493, t495, t497, t498, t499, t501, t502, t503, t504, t505, t507, t508, t509, t510, t511, t512, t513, t515, t518, t520;
729:   PetscReal t522, t525, t527, t528, t529, t530, t532, t533, t534, t535, t536, t538, t539, t541, t542, t544, t545, t546, t547, t548, t549, t550, t551, t552, t553, t554, t555, t556, t557, t560;
730:   PetscReal t561, t562, t563, t564, t567, t568, t571, t573, t575, t576, t578, t579, t583, t590, t591, t594, t595, t596, t597, t598, t600;
731:   PetscReal t601, t602, t604, t606, t607, t608, t611, t613, t615, t616, t617, t619, t621, t623, t624, t625, t626, t627, t629, t630, t632, t633, t634, t638, t639, t640;
732:   PetscReal t641, t642, t643, t644, t645, t647, t648, t649, t650, t651, t652, t653, t654, t655, t656, t657, t658, t659, t660, t662, t663, t665, t666, t667, t668, t670, t671, t672, t673, t674, t675, t676, t679, t680;
733:   PetscReal t682, t683, t684, t685, t686, t688, t689, t690, t691, t693, t694, t695, t696, t697, t698, t699, t700, t701, t702, t704, t705, t708, t709, t711, t712, t713, t714, t717, t718, t719;
734:   PetscReal t721, t722, t723, t726, t727, t728, t730, t733, t734, t735, t736, t737, t738, t739, t740, t741, t744, t745, t746, t749, t750, t752, t753, t754, t755, t757, t758, t759, t760;
735:   PetscReal t761, t762, t763, t764, t766, t767, t768, t770, t771, t772, t773, t774, t775, t776, t777, t778, t780, t781, t782, t785, t786, t789, t790, t791, t792, t793, t794, t795, t796, t797, t798, t800;
736:   PetscReal t801, t806, t807, t808, t809, t811, t812, t817, t818, t819, t821, t822, t824, t827, t828, t830, t834, t835, t837, t840;
737:   PetscReal t842, t843, t844, t845, t846, t849, t850, t853, t854, t855, t857, t858, t859, t860, t863, t864, t867, t868, t869, t873, t874, t877, t878, t879, t880;
738:   PetscReal t884, t888, t891, t894, t900, t901, t903, t904, t907, t908, t909, t911, t914, t915, t916, t919, t920;
739:   PetscReal t923, t924, t925, t926, t927, t929, t932, t935, t937, t939, t942, t943, t944, t945, t947, t948, t949, t950, t952, t953, t954, t955, t956, t957;
740:   PetscReal t961, t964, t965, t966, t967, t968, t969, t971, t972, t974, t977, t978, t981, t983, t987, t988, t992, t993, t994, t997, t998;
741:   PetscReal t1001, t1003, t1005, t1006, t1009, t1010, t1012, t1013, t1015, t1016, t1017, t1018, t1020, t1021, t1029, t1031, t1032, t1033, t1040;
742:   PetscReal t1041, t1042, t1044, t1047, t1050, t1054, t1055, t1057, t1058, t1063, t1068, t1069, t1070, t1079, t1080;
743:   PetscReal t1088, t1089, t1091, t1092, t1094, t1096, t1101, t1102, t1103, t1104, t1105, t1108, t1112, t1113, t1118, t1119, t1120;
744:   PetscReal t1121, t1122, t1123, t1124, t1125, t1126, t1127, t1128, t1129, t1130, t1132, t1133, t1134, t1135, t1138, t1139, t1140, t1141, t1142, t1145, t1146, t1148, t1149, t1150, t1153, t1154, t1156, t1157, t1158, t1159;
745:   PetscReal t1161, t1162, t1165, t1166, t1170, t1171, t1172, t1173, t1175, t1176, t1178, t1180, t1181, t1182, t1185, t1189, t1192, t1193, t1195, t1196, t1199;
746:   PetscReal t1201, t1203, t1209, t1210, t1211, t1213, t1214, t1218, t1221, t1224, t1225, t1226, t1228, t1233, t1234, t1235, t1236, t1237, t1240;
747:   PetscReal t1241, t1242, t1243, t1244, t1245, t1248, t1251, t1252, t1257, t1258, t1259, t1260, t1263, t1268, t1269, t1272, t1280;
748:   PetscReal t1282, t1283, t1284, t1285, t1287, t1288, t1289, t1292, t1293, t1296, t1297, t1300, t1304, t1307, t1310, t1311, t1312, t1316, t1317, t1320;
749:   PetscReal t1321, t1323, t1328, t1330, t1331, t1332, t1333, t1336, t1338, t1343, t1344, t1346, t1349, t1350, t1354;
750:   PetscReal t1366, t1369, t1370, t1371, t1376, t1378, t1380, t1383, t1386, t1387, t1388, t1391, t1393, t1399;
751:   PetscReal t1411, t1412, t1420, t1427;
752:   PetscReal t1450, t1456, t1468, t1472, t1474, t1478;
753:   PetscReal t1504, t1511;
754:   PetscReal t1545;
755:   PetscReal t1564, t1583;

757:   PetscReal sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, sum6 = 0.0;
758:   PetscReal ZA = etaA, ZB = etaB;
759:   PetscInt  nz = m, nx = n;
760:   PetscReal u1, u2, u3, u4, u5, u6, Z, x = pos[0], z = pos[1];

762:   PetscFunctionBegin;
763:   /* Note that there is no Fourier sum here. */
764:   /****************************************************************************************/
765:   _PC1A = 0;
766:   /****************************************************************************************/
767:   t1   = nx * 0.3141592654e1;
768:   t2   = PetscSinReal(t1);
769:   t3   = nx * t2;
770:   t4   = nz * nz;
771:   t5   = t4 * t4;
772:   t6   = 0.3141592654e1 * 0.3141592654e1;
773:   t8   = t3 * t5 * t6;
774:   t9   = ZA * xc;
775:   t12  = PetscExpReal(xc * nz * 0.3141592654e1);
776:   t13  = t12 * t12;
777:   t15  = nz * 0.3141592654e1;
778:   t16  = PetscExpReal(t15);
779:   t17  = t16 * t16;
780:   t18  = t17 * t16;
781:   t19  = ZB * t13 * t18;
782:   t20  = t9 * t19;
783:   t23  = ZA * ZA;
784:   t24  = nx * nx;
785:   t25  = t24 * nx;
786:   t26  = t23 * t25;
787:   t28  = t13 * t13;
788:   t29  = t28 * t13;
789:   t33  = nx * ZB;
790:   t34  = t1 * xc;
791:   t35  = PetscSinReal(t34);
792:   t36  = t4 * nz;
793:   t37  = t35 * t36;
794:   t38  = t33 * t37;
795:   t39  = 0.3141592654e1 * ZA;
796:   t40  = t13 * t12;
797:   t41  = t17 * t40;
798:   t45  = ZB * ZB;
799:   t46  = t45 * t24;
800:   t47  = t46 * t4;
801:   t48  = 0.3141592654e1 * xc;
802:   t49  = t13 * t17;
803:   t53  = xc * xc;
804:   t54  = t36 * t53;
805:   t56  = t54 * t6 * t45;
806:   t57  = PetscCosReal(t34);
807:   t58  = t57 * t24;
808:   t59  = t28 * t12;
809:   t60  = t17 * t59;
810:   t61  = t58 * t60;
811:   t64  = t25 * t2;
812:   t65  = t64 * t15;
813:   t72  = nx * t23;
814:   t74  = t72 * t2 * t5;
815:   t75  = t6 * t53;
816:   t76  = t16 * t29;
817:   t80  = t23 * nz;
818:   t81  = t80 * 0.3141592654e1;
819:   t82  = t18 * t28;
820:   t86  = nx * t5;
821:   t87  = t23 * t6;
822:   t89  = xc * t2;
823:   t90  = t13 * t18;
824:   t91  = t89 * t90;
825:   t94  = t28 * t28;
826:   t96  = t24 * nz;
827:   t98  = t4 * t45;
828:   t99  = t98 * 0.3141592654e1;
829:   t100 = t58 * t41;
830:   t104 = 0.3141592654e1 * t25;
831:   t105 = ZA * nz * t104;
832:   t106 = t2 * ZB;
833:   t110 = t17 * t17;
834:   t111 = ZA * t110;
835:   t116 = nz * t28;
836:   t122 = t64 * t4 * t6;
837:   t126 = t23 * t29 * t4;
838:   t128 = t24 * xc;
839:   t132 = t36 * t23;
840:   t133 = t6 * t57;
841:   t135 = t128 * t41;
842:   t138 = t6 * xc;
843:   t142 = t72 * t2;
844:   t147 = 0.4e1 * t8 * t20 - 0.2e1 * t26 * t2 * t16 * t29 - 0.8e1 * t38 * t39 * t41 + 0.4e1 * t47 * t48 * t49 - 0.8e1 * t56 * t61 - 0.4e1 * t65 * t20 + 0.2e1 * t26 * t2 * t18 * t28 - 0.4e1 * t74 * t75 * t76 - 0.2e1 * t81 * t64 * t82 - 0.4e1 * t86 * t87 * t91 - t23 * t94 * t96 + 0.8e1 * t99 * t100 - 0.2e1 * t105 * t106 * t82 - 0.4e1 * t38 * t48 * t111 * t12 + 0.2e1 * t116 * ZB * t111 * t24 + 0.4e1 * t122 * t20 + 0.4e1 * t126 * 0.3141592654e1 * t17 * t128 + 0.8e1 * t132 * t133 * t135 + 0.4e1 * t74 * t138 * t76 - 0.2e1 * t142 * t4 * t18 * t28;
845:   t149 = ZA * t25 * t2;
846:   t150 = ZB * t28;
847:   t154 = t35 * t5;
848:   t155 = t72 * t154;
849:   t156 = t75 * t41;
850:   t159 = nx * ZA;
851:   t160 = t2 * t36;
852:   t161 = t159 * t160;
853:   t162 = 0.3141592654e1 * ZB;
854:   t163 = t28 * t16;
855:   t167 = t23 * t57;
856:   t168 = t167 * t24;
857:   t169 = nz * t110;
858:   t170 = t169 * t40;
859:   t173 = ZA * ZB;
860:   t174 = t173 * t90;
861:   t177 = t36 * 0.3141592654e1;
862:   t181 = t80 * t104;
863:   t184 = nz * t17;
864:   t188 = t17 * t29;
865:   t190 = t4 * 0.3141592654e1;
866:   t191 = t190 * t24;
867:   t206 = t138 * t60;
868:   t209 = t23 * t4;
869:   t211 = t209 * t6 * t25;
870:   t212 = t89 * t76;
871:   t216 = ZB * t16 * t29;
872:   t217 = t9 * t216;
873:   t220 = ZB * t110;
874:   t221 = ZA * t24;
875:   t222 = t221 * nz;
876:   t225 = t132 * t75;
877:   t232 = t45 * t28;
878:   t233 = t110 * t24;
879:   t234 = t233 * nz;
880:   t236 = t209 * 0.3141592654e1;
881:   t237 = t17 * xc;
882:   t239 = t237 * t13 * t24;
883:   t242 = -0.2e1 * t149 * t150 * t16 - 0.8e1 * t155 * t156 - 0.2e1 * t161 * t162 * t163 + 0.2e1 * t168 * t170 + 0.2e1 * t65 * t174 - 0.2e1 * t142 * t177 * t76 + 0.4e1 * t181 * t91 - 0.4e1 * t168 * t184 * t59 - 0.4e1 * t188 * t23 * t191 + 0.4e1 * t38 * t48 * ZA * t17 * t40 + 0.4e1 * t49 * t23 * t191 + 0.2e1 * t26 * t2 * t13 * t18 - 0.8e1 * t155 * t206 + 0.4e1 * t211 * t212 - 0.4e1 * t8 * t217 + 0.2e1 * t220 * t222 - 0.8e1 * t225 * t100 + 0.2e1 * t142 * t4 * t16 * t29 + t232 * t234 - 0.4e1 * t236 * t239;
884:   t244 = nx * t45;
885:   t245 = t244 * t37;
886:   t246 = t110 * t40;
887:   t251 = t237 * t59;
888:   t256 = t64 * t90;
889:   t260 = t36 * t45 * t133;
890:   t263 = t45 * t57;
891:   t264 = t263 * t24;
892:   t265 = t169 * t12;
893:   t269 = t6 * t36;
894:   t270 = t17 * t24;
895:   t274 = t110 * t13;
896:   t276 = t190 * t128;
897:   t279 = nx * t36;
898:   t281 = t28 * t40;
899:   t282 = t281 * t35;
900:   t286 = t138 * t41;
901:   t289 = t75 * t60;
902:   t296 = t190 * t173;
903:   t305 = t86 * t45 * t35;
904:   t312 = t33 * t154;
905:   t313 = t6 * ZA;
906:   t324 = t232 * t270;
907:   t327 = -0.2e1 * t245 * t48 * t246 + 0.4e1 * t159 * t37 * t162 * t251 + 0.4e1 * t209 * t75 * t256 + 0.8e1 * t260 * t135 + 0.2e1 * t264 * t265 + 0.32e2 * t9 * t150 * t269 * t270 + 0.4e1 * t274 * t23 * t276 + 0.2e1 * t279 * t45 * t282 * t48 + 0.8e1 * t155 * t286 + 0.8e1 * t155 * t289 - 0.8e1 * t150 * ZA * t96 * t17 + 0.8e1 * t296 * t61 - 0.2e1 * t105 * t106 * t163 - 0.2e1 * t81 * t256 - 0.8e1 * t305 * t156 - 0.4e1 * t33 * t282 * t177 * t9 - 0.16e2 * t312 * t313 * t237 * t40 - 0.4e1 * t168 * t184 * t40 + 0.2e1 * t168 * t265 + 0.16e2 * t269 * t53 * t324;
908:   t328 = t3 * t4;
909:   t331 = t72 * t37;
910:   t332 = t48 * t60;
911:   t335 = nz * t94;
912:   t345 = t72 * t35;
913:   t349 = t173 * t57;
914:   t355 = t53 * t17;
915:   t364 = t54 * t6 * ZB;
916:   t365 = t28 * t17;
917:   t369 = xc * ZB;
918:   t370 = t269 * t369;
919:   t371 = ZA * t57;
920:   t373 = t371 * t270 * t40;
921:   t385 = nx * t35;
922:   t396 = t4 * xc;
923:   t397 = t396 * t162;
924:   t415 = t37 * t48;
925:   t418 = -0.32e2 * t364 * t365 * t221 - 0.16e2 * t370 * t373 - 0.4e1 * t331 * t48 * t41 + 0.4e1 * t86 * t23 * t53 * t6 * t2 * t90 + 0.2e1 * t385 * t177 * t23 * xc * t246 + 0.16e2 * t132 * t53 * t6 * t28 * t270 - 0.4e1 * t397 * t371 * t233 * t12 - 0.12e2 * t173 * t58 * t190 * t251 + 0.2e1 * t385 * t36 * 0.3141592654e1 * t23 * xc * t59 - 0.8e1 * t99 * t61 - 0.2e1 * t244 * t59 * t415;
926:   t427 = t371 * t270 * t59;
927:   t439 = t209 * t48;
928:   t440 = t110 * t12;
929:   t441 = t58 * t440;
930:   t447 = t36 * xc;
931:   t455 = t48 * t440;
932:   t471 = ZB * t17;
933:   t492 = 0.12e2 * t397 * t373 - 0.4e1 * t122 * t217 + 0.16e2 * t364 * t427 + 0.16e2 * t312 * t313 * t355 * t40 - 0.8e1 * t279 * t39 * t35 * ZB * t60 + 0.2e1 * t439 * t441 - 0.2e1 * t81 * t64 * t163 + 0.8e1 * t447 * t87 * t61 + 0.2e1 * t23 * t59 * t57 * t276 + 0.2e1 * t245 * t455 - 0.4e1 * t349 * t96 * t440 - 0.16e2 * t370 * t427 + 0.4e1 * t181 * t212 - 0.16e2 * t365 * t23 * t269 * t128 + 0.16e2 * t86 * t138 * ZA * t35 * t471 * t59 + 0.8e1 * t305 * t289 - 0.4e1 * t439 * t100 + 0.2e1 * ZB * t25 * t2 * ZA * t18 * t28 + 0.2e1 * t142 * t4 * t28 * t16 - 0.8e1 * t56 * t100;
934:   t499 = ZA * t53 * t19;
935:   t505 = t396 * 0.3141592654e1;
936:   t518 = t173 * t53 * t16 * t29;
937:   t533 = t23 * t28;
938:   t535 = t188 * t45;
939:   t538 = t24 * t4;
940:   t545 = t3 * t177;
941:   t546 = t173 * t76;
942:   t555 = t45 * t110;
943:   t557 = t72 * t160;
944:   t561 = -0.8e1 * t225 * t61 - 0.2e1 * t161 * t162 * t82 + t533 * t234 + 0.4e1 * t535 * t191 + 0.4e1 * t167 * t538 * t332 + 0.4e1 * t349 * t96 * t60 + 0.2e1 * t545 * t546 - 0.2e1 * t264 * t170 + 0.4e1 * t397 * t281 * ZA * t58 - t555 * t96 - 0.4e1 * t557 * t48 * t76;
945:   t567 = t396 * 0.3141592654e1 * t45;
946:   t568 = t58 * t246;
947:   t597 = t58 * nz;
948:   t615 = t13 * t45;
949:   t616 = t615 * t233;
950:   t619 = t94 * t45;
951:   t621 = t45 * t59;
952:   t625 = 0.2e1 * t149 * t216 + 0.2e1 * t567 * t568 - 0.16e2 * t269 * xc * t324 - 0.2e1 * t236 * xc * t281 * t58 - 0.2e1 * t142 * t177 * t90 - 0.8e1 * t567 * t100 + 0.2e1 * t65 * t546 - 0.8e1 * t305 * t206 + 0.2e1 * nz * t45 * t281 * t57 * t24 - t23 * t110 * t96 - 0.8e1 * t296 * t100 + 0.2e1 * t23 * t281 * t597 + 0.4e1 * t545 * t20 + 0.2e1 * t159 * t2 * t4 * ZB * t163 - 0.4e1 * t557 * t48 * t90 + 0.4e1 * t122 * t518 + 0.8e1 * t263 * t538 * t332 - 0.4e1 * t505 * t616 - t619 * t96 - 0.2e1 * t621 * t57 * t276;
953:   t626 = t49 * t45;
954:   t660 = t29 * t45;
955:   t685 = 0.2e1 * t545 * t174 - 0.4e1 * t126 * 0.3141592654e1 * t24 * xc - 0.4e1 * t47 * t48 * t188 + 0.4e1 * t505 * t660 * t24 - 0.2e1 * t142 * t177 * t163 - 0.2e1 * t142 * t4 * t13 * t18 + 0.8e1 * t260 * t128 * t60 - 0.2e1 * t328 * t546 - 0.2e1 * t26 * t2 * t28 * t16 + 0.4e1 * t545 * t217 - 0.4e1 * t209 * t138 * t256;
956:   t690 = t6 * 0.3141592654e1;
957:   t691 = ZA * t690;
958:   t693 = t24 * t24;
959:   t694 = t693 * xc;
960:   t695 = t188 * t694;
961:   t698 = t23 * ZA;
962:   t699 = t698 * t690;
963:   t700 = t699 * t5;
964:   t704 = t5 * t4;
965:   t705 = t691 * t704;
966:   t709 = t691 * t5;
967:   t713 = t5 * nz;
968:   t714 = t713 * ZB;
969:   t718 = t698 * t6;
970:   t719 = t713 * t28;
971:   t722 = t699 * t704;
972:   t726 = t713 * t94;
973:   t733 = t713 * t45;
974:   t736 = t87 * t36;
975:   t740 = -0.4e1 * t691 * t98 * t695 + 0.8e1 * t700 * t270 * t13 + 0.4e1 * t705 * t660 * xc + 0.8e1 * t709 * t660 * t128 + 0.2e1 * t87 * t714 * t110 + t718 * t719 * t110 - 0.4e1 * t722 * t237 * t13 - t313 * t726 * t45 - 0.4e1 * t699 * t704 * xc * t29 + t313 * t733 * t28 + 0.4e1 * t736 * t150 * t233;
976:   t746 = t313 * t36;
977:   t752 = t6 * t6;
978:   t753 = t23 * t752;
979:   t759 = t698 * t752;
980:   t760 = t759 * t36;
981:   t761 = t17 * t693;
982:   t762 = xc * t28;
983:   t763 = t761 * t762;
984:   t766 = t87 * t713;
985:   t773 = t699 * t4;
986:   t774 = t110 * t693;
987:   t775 = xc * t13;
988:   t785 = t704 * t17;
989:   t789 = -0.16e2 * t736 * t150 * t270 + t718 * t116 * t693 - 0.2e1 * t746 * t555 * t24 + 0.4e1 * t705 * t535 + 0.64e2 * t753 * t713 * t17 * t150 * t128 - 0.16e2 * t760 * t763 + 0.2e1 * t766 * t150 * t110 + 0.4e1 * t722 * t274 * xc + 0.4e1 * t773 * t774 * t775 - 0.8e1 * t766 * t150 * t17 + 0.8e1 * t700 * t233 * t775 + 0.4e1 * t699 * t785 * t13;
990:   t791 = t691 * t4;
991:   t792 = t45 * t693;
992:   t793 = t49 * t792;
993:   t796 = t759 * t713;
994:   t797 = t53 * t28;
995:   t798 = t270 * t797;
996:   t801 = t87 * nz;
997:   t818 = t5 * t36;
998:   t819 = t753 * t818;
999:   t827 = t753 * t36 * ZB;
1000:   t830 = xc * t45;
1001:   t834 = -0.4e1 * t791 * t793 + 0.32e2 * t796 * t798 + 0.2e1 * t801 * ZB * t693 * t110 + 0.2e1 * t718 * t36 * t28 * t24 - 0.8e1 * t700 * t128 * t29 - 0.8e1 * t700 * t239 - 0.8e1 * t801 * t150 * t761 + 0.32e2 * t819 * t365 * t369 - 0.64e2 * t753 * t714 * t798 + 0.32e2 * t827 * t763 + 0.4e1 * t705 * t830 * t49;
1002:   t842 = xc * t29;
1003:   t843 = t270 * t842;
1004:   t849 = t759 * t818;
1005:   t853 = t691 * t396;
1006:   t857 = t691 * t5 * t45;
1007:   t869 = t313 * nz;
1008:   t874 = -0.2e1 * t718 * t36 * t94 * t24 - 0.4e1 * t773 * t761 * t29 + 0.8e1 * t700 * t843 + 0.2e1 * t87 * t726 * ZB + 0.16e2 * t849 * t797 * t17 + 0.4e1 * t853 * t793 + 0.8e1 * t857 * t239 + 0.2e1 * t801 * t150 * t693 - 0.8e1 * t700 * t270 * t29 - 0.8e1 * t709 * t49 * t46 - t869 * t619 * t693 + t869 * t232 * t693;
1009:   t877 = ZA * t752;
1010:   t878 = t877 * t818;
1011:   t911 = 0.16e2 * t878 * t53 * t45 * t365 - 0.4e1 * t699 * t785 * t29 - 0.4e1 * t705 * t188 * t830 + 0.2e1 * t801 * t94 * t693 * ZB - 0.8e1 * t857 * t843 - t718 * t726 + 0.4e1 * t773 * t761 * t13 - 0.4e1 * t705 * t775 * t555 + 0.2e1 * t746 * t232 * t233 - 0.16e2 * t878 * t830 * t365 - 0.2e1 * t746 * t619 * t24;
1012:   t916 = t110 * t28;
1013:   t945 = t28 * t693 * t45 * t17;
1014:   t948 = 0.32e2 * t877 * t733 * t798 + 0.2e1 * t718 * t36 * t916 * t24 - 0.4e1 * t705 * t626 + t718 * nz * t916 * t693 - t869 * t792 * t110 - 0.4e1 * t773 * t761 * t775 + t718 * t719 + 0.2e1 * t746 * t232 * t24 - 0.16e2 * t849 * t365 * xc - t718 * t713 * t110 - 0.4e1 * t773 * t694 * t29 + 0.16e2 * t877 * t54 * t945;
1015:   t974 = t761 * t797;
1016:   t987 = 0.4e1 * t773 * t695 + 0.4e1 * t736 * t150 * t24 + 0.4e1 * t722 * t842 * t17 - 0.16e2 * t877 * t447 * t945 + 0.2e1 * t87 * t714 * t28 + t313 * t713 * t916 * t45 - 0.4e1 * t853 * t615 * t774 - 0.32e2 * t877 * t713 * xc * t324 + 0.16e2 * t760 * t974 + 0.4e1 * t736 * t94 * t24 * ZB + t869 * t792 * t916 - 0.8e1 * t691 * t5 * xc * t616;
1017:   t1021 = -t718 * t169 * t693 - 0.32e2 * t827 * t974 + 0.2e1 * t801 * t150 * t774 + 0.4e1 * t791 * t188 * t792 + 0.4e1 * t736 * t220 * t24 + 0.4e1 * t791 * t842 * t792 + 0.8e1 * t709 * t660 * t270 - t718 * t335 * t693 - 0.2e1 * t718 * t36 * t110 * t24 - 0.32e2 * t819 * t797 * t471 - t313 * t733 * t110 - 0.32e2 * t796 * t270 * t762;

1019:   _PC2A = (t147 - 0.4e1 * t65 * t217 + t418 + 0.2e1 * t150 * t222 + t327 - 0.2e1 * t149 * t19 + 0.2e1 * t335 * ZB * t24 * ZA - 0.16e2 * t312 * t313 * t355 * t59 - 0.4e1 * t281 * ZB * ZA * t597 - 0.2e1 * t505 * t45 * t281 * t58 - 0.4e1 * t211 * t2 * t53 * t76 + 0.8e1 * t305 * t286 - 0.4e1 * t122 * t499 - 0.4e1 * t331 * t332 + 0.8e1 * t345 * t177 * t60 - 0.2e1 * t142 * t177 * t82 + 0.2e1 * t72 * t281 * t415 + 0.4e1 * t349 * t96 * t41 - 0.2e1 * t81 * t64 * t76 + 0.2e1 * t58 * t80 * t59 + 0.8e1 * t345 * t177 * t41 - 0.4e1 * t8 * t499 + t242 + 0.4e1 * t8 * t518 + t625 + t685 + 0.2e1 * t328 * t174 + 0.2e1 * t331 * t455 - 0.2e1 * t33 * t2 * t4 * ZA * t82 - 0.4e1 * t626 * t191 + 0.16e2 * t364 * t373 - 0.2e1 * t621 * t597 - 0.2e1 * t439 * t568 + t492 + t533 * t96 + t232 * t96 + 0.2e1 * t567 * t441 + t561) / (t740 + t789 + t834 + t874 + t911 + t948 + t987 + t1021);
1020:   /****************************************************************************************/
1021:   t1   = nz * nz;
1022:   t2   = t1 * nz;
1023:   t3   = t2 * 0.3141592654e1;
1024:   t4   = t3 * xc;
1025:   t5   = ZB * ZB;
1026:   t7   = PetscExpReal(nz * 0.3141592654e1);
1027:   t8   = t7 * t7;
1028:   t9   = t5 * t8;
1029:   t12  = PetscExpReal(xc * nz * 0.3141592654e1);
1030:   t13  = t12 * t12;
1031:   t14  = t13 * t13;
1032:   t15  = t14 * t13;
1033:   t19  = nx * nx;
1034:   t21  = nx * 0.3141592654e1;
1035:   t22  = PetscSinReal(t21);
1036:   t23  = t19 * nx * t22;
1037:   t24  = t23 * 0.3141592654e1;
1038:   t25  = ZA * ZB;
1039:   t26  = t7 * t15;
1040:   t27  = t25 * t26;
1041:   t30  = t21 * xc;
1042:   t31  = PetscSinReal(t30);
1043:   t32  = t31 * nx;
1044:   t33  = t32 * nz;
1045:   t34  = ZA * ZA;
1046:   t35  = t8 * t8;
1047:   t36  = t34 * t35;
1048:   t40  = t2 * t34;
1049:   t41  = 0.3141592654e1 * t8;
1050:   t42  = t41 * t15;
1051:   t45  = t1 * t5;
1052:   t46  = t14 * t14;
1053:   t49  = t19 * t5;
1054:   t51  = t19 * t46;
1055:   t53  = t19 * t34;
1056:   t55  = t8 * t7;
1057:   t56  = t13 * t55;
1058:   t57  = t25 * t56;
1059:   t60  = t2 * nx;
1060:   t61  = 0.3141592654e1 * 0.3141592654e1;
1061:   t63  = t60 * t31 * t61;
1062:   t64  = xc * xc;
1063:   t65  = ZA * t64;
1064:   t66  = ZB * t8;
1065:   t67  = t14 * t12;
1066:   t68  = t66 * t67;
1067:   t69  = t65 * t68;
1068:   t72  = -0.4e1 * t4 * t9 * t15 + 0.4e1 * t24 * t27 + 0.4e1 * t33 * t36 * t12 - 0.4e1 * t40 * t42 - t45 * t46 + t45 * t14 - t49 * t14 + t51 * t5 - t53 * t14 + 0.4e1 * t24 * t57 + 0.32e2 * t63 * t69;
1069:   t73  = t1 * nx;
1070:   t75  = t73 * t31 * 0.3141592654e1;
1071:   t76  = t8 * t67;
1072:   t77  = t25 * t76;
1073:   t80  = t1 * t1;
1074:   t81  = t80 * t34;
1075:   t83  = t61 * t14;
1076:   t87  = t1 * t19;
1077:   t88  = PetscCosReal(t30);
1078:   t90  = t87 * t88 * t61;
1079:   t91  = t5 * t64;
1080:   t92  = t13 * t12;
1081:   t93  = t8 * t92;
1082:   t94  = t91 * t93;
1083:   t100 = ZB * t64 * ZA * t8 * t92;
1084:   t103 = nz * t19;
1085:   t105 = t103 * t88 * 0.3141592654e1;
1086:   t106 = ZA * xc;
1087:   t107 = ZB * t35;
1088:   t109 = t106 * t107 * t12;
1089:   t112 = t34 * xc;
1090:   t113 = t112 * t93;
1091:   t116 = t35 * t14;
1092:   t118 = t1 * ZA;
1093:   t119 = ZB * t14;
1094:   t122 = t1 * t46;
1095:   t125 = t19 * ZB;
1096:   t126 = t35 * ZA;
1097:   t127 = t125 * t126;
1098:   t129 = t1 * ZB;
1099:   t132 = -0.16e2 * t75 * t77 + 0.16e2 * t81 * t64 * t83 * t8 + 0.16e2 * t90 * t94 - 0.32e2 * t90 * t100 + 0.8e1 * t105 * t109 - 0.8e1 * t75 * t113 + t45 * t116 + 0.2e1 * t118 * t119 + 0.2e1 * t122 * t25 - 0.2e1 * t127 + 0.2e1 * t129 * t126;
1100:   t134 = t1 * t34;
1101:   t136 = t34 * t64;
1102:   t137 = t136 * t76;
1103:   t141 = t91 * t76;
1104:   t145 = t103 * t34;
1105:   t146 = 0.3141592654e1 * xc;
1106:   t147 = t8 * t13;
1107:   t153 = t14 * ZA;
1108:   t156 = xc * t5;
1109:   t157 = t156 * t93;
1110:   t160 = t103 * t5;
1111:   t162 = t146 * t8 * t15;
1112:   t166 = t34 * t7 * t15;
1113:   t169 = t134 * t116 - 0.16e2 * t63 * t137 - t49 * t116 - 0.16e2 * t63 * t141 - t53 * t116 + 0.4e1 * t145 * t146 * t147 - 0.2e1 * t51 * t25 - 0.2e1 * t125 * t153 - 0.16e2 * t75 * t157 + 0.4e1 * t160 * t162 - 0.4e1 * t24 * t166;
1114:   t170 = t106 * t68;
1115:   t177 = t35 * t92;
1116:   t178 = t112 * t177;
1117:   t181 = t156 * t76;
1118:   t186 = t35 * t12;
1119:   t187 = t112 * t186;
1120:   t193 = t5 * 0.3141592654e1;
1121:   t206 = t34 * t14;
1122:   t207 = t206 * t7;
1123:   t210 = -0.32e2 * t63 * t170 + 0.32e2 * t90 * t170 + 0.8e1 * t75 * t109 + 0.4e1 * t105 * t178 - 0.16e2 * t75 * t181 - 0.16e2 * t90 * t113 - 0.4e1 * t75 * t187 + 0.16e2 * t90 * t141 - 0.4e1 * t103 * t15 * t193 * xc + 0.16e2 * t73 * t22 * t34 * t146 * t26 + 0.4e1 * t32 * nz * t34 * t67 + 0.4e1 * t24 * t207;
1124:   t217 = t106 * t66 * t92;
1125:   t226 = t88 * t19 * nz;
1126:   t227 = 0.3141592654e1 * t34;
1127:   t229 = t227 * xc * t67;
1128:   t232 = t73 * t31;
1129:   t234 = t146 * t5 * t67;
1130:   t238 = t61 * ZB;
1131:   t239 = t14 * t8;
1132:   t240 = t238 * t239;
1133:   t243 = t136 * t93;
1134:   t246 = -0.8e1 * t33 * t25 * t186 + 0.32e2 * t90 * t217 - t45 * t35 + t53 * t35 - t134 * t35 - t134 * t46 + t134 * t14 - 0.4e1 * t226 * t229 + 0.4e1 * t232 * t234 + 0.32e2 * t87 * t65 * t240 + 0.16e2 * t63 * t243;
1135:   t247 = t14 * t92;
1136:   t249 = t227 * t247 * xc;
1137:   t254 = t73 * t22;
1138:   t259 = t60 * t22 * t61;
1139:   t260 = t112 * t26;
1140:   t264 = t146 * t247 * t5;
1141:   t268 = xc * t14;
1142:   t274 = t5 * t14;
1143:   t275 = t274 * t8;
1144:   t280 = nz * nx;
1145:   t281 = t280 * t22;
1146:   t282 = t55 * t14;
1147:   t283 = t25 * t282;
1148:   t290 = ZA * t247 * xc * ZB;
1149:   t295 = t22 * nx * t1 * 0.3141592654e1;
1150:   t298 = -0.4e1 * t232 * t249 + 0.8e1 * t105 * t217 - 0.4e1 * t254 * t227 * t26 - 0.8e1 * t259 * t260 - 0.4e1 * t232 * t264 - 0.16e2 * t81 * t61 * t268 * t8 + 0.16e2 * t80 * t64 * t61 * t275 - 0.4e1 * t232 * t229 + 0.8e1 * t281 * t283 - 0.4e1 * t105 * t187 + 0.8e1 * t75 * t290 + 0.4e1 * t295 * t27;
1151:   t301 = t61 * t5;
1152:   t307 = t87 * t34;
1153:   t312 = t61 * xc;
1154:   t313 = t312 * t239;
1155:   t317 = t34 * t55 * t14;
1156:   t329 = ZB * t13 * t55;
1157:   t330 = t65 * t329;
1158:   t337 = -0.16e2 * t87 * t64 * t301 * t239 - 0.32e2 * t90 * t69 - 0.16e2 * t307 * t64 * t61 * t239 + 0.16e2 * t307 * t313 + 0.4e1 * t24 * t317 + t53 * t46 + t49 * t35 - 0.32e2 * t63 * t100 - 0.4e1 * t280 * t31 * t34 * t247 + 0.8e1 * t259 * t330 - 0.4e1 * t280 * t31 * t247 * t5;
1159:   t340 = t5 * t35;
1160:   t344 = t25 * t93;
1161:   t356 = t41 * t13;
1162:   t360 = t23 * nz * t61;
1163:   t363 = t25 * t64 * t7 * t15;
1164:   t366 = t156 * t177;
1165:   t369 = t14 * t7;
1166:   t370 = t25 * t369;
1167:   t373 = t156 * t186;
1168:   t378 = 0.4e1 * t24 * t283 + 0.4e1 * t33 * t340 * t12 - 0.16e2 * t75 * t344 - 0.4e1 * t280 * t31 * t5 * t67 + 0.8e1 * t33 * t25 * t247 + 0.32e2 * t63 * t217 + 0.4e1 * t40 * t356 - 0.8e1 * t360 * t363 + 0.4e1 * t75 * t366 + 0.4e1 * t295 * t370 - 0.4e1 * t75 * t373 - 0.4e1 * t105 * t366;
1169:   t382 = t112 * t76;
1170:   t387 = t80 * t61;
1171:   t391 = t136 * t26;
1172:   t409 = 0.16e2 * t63 * t382 + 0.4e1 * t226 * t234 - 0.16e2 * t387 * xc * t275 + 0.8e1 * t259 * t391 - 0.16e2 * t105 * t344 + 0.4e1 * t226 * t264 - 0.8e1 * t105 * t170 + 0.16e2 * t232 * t193 * t76 + 0.8e1 * t360 * t330 - 0.8e1 * t105 * t290 + 0.16e2 * t90 * t243;
1173:   t423 = t153 * t8;
1174:   t426 = t34 * t13;
1175:   t427 = t426 * t55;
1176:   t430 = t34 * t8;
1177:   t437 = t80 * ZA;
1178:   t441 = 0.4e1 * t145 * t42 - 0.16e2 * t90 * t157 + 0.24e2 * t75 * t217 + 0.4e1 * t226 * t249 + 0.4e1 * t254 * t227 * t282 + 0.4e1 * t160 * t356 - 0.8e1 * t129 * t423 - 0.8e1 * t281 * t427 - 0.8e1 * t33 * t430 * t67 + 0.8e1 * t33 * t430 * t92 + 0.32e2 * t437 * ZB * t313;
1179:   t453 = t106 * ZB * t7 * t15;
1180:   t456 = t2 * t5;
1181:   t459 = t112 * t56;
1182:   t462 = t126 * t14;
1183:   t474 = t40 * 0.3141592654e1;
1184:   t475 = xc * t8;
1185:   t480 = t146 * t13 * t35;
1186:   t483 = -0.4e1 * t103 * xc * t193 * t147 + 0.16e2 * t87 * t61 * t156 * t239 + 0.8e1 * t259 * t453 - 0.4e1 * t456 * t356 + 0.8e1 * t259 * t459 - 0.2e1 * t125 * t462 - 0.8e1 * t281 * t207 + 0.16e2 * t295 * t459 - 0.8e1 * t60 * t22 * ZA * t312 * t329 + 0.4e1 * t474 * t475 * t15 + 0.4e1 * t160 * t480;
1187:   t497 = t136 * t56;
1188:   t504 = t9 * t13;
1189:   t509 = t475 * t13;
1190:   t512 = -0.8e1 * t105 * t113 - 0.4e1 * t254 * t227 * t56 + 0.8e1 * t281 * t57 + 0.4e1 * t295 * t283 + 0.2e1 * t129 * t462 + 0.4e1 * t24 * t370 - 0.8e1 * t360 * t497 - 0.4e1 * t24 * t427 - 0.4e1 * t145 * t162 + 0.4e1 * t4 * t504 - 0.8e1 * t281 * t370 - 0.4e1 * t474 * t509;
1191:   t528 = t5 * t13;
1192:   t529 = t528 * t35;
1193:   t532 = t106 * t329;
1194:   t542 = -0.16e2 * t295 * t453 - 0.32e2 * t437 * t64 * t240 + 0.8e1 * t281 * t317 + 0.24e2 * t75 * t170 - 0.4e1 * t75 * t178 + 0.8e1 * t360 * t453 - 0.4e1 * t4 * t529 - 0.16e2 * t295 * t532 - 0.8e1 * t33 * t344 - 0.16e2 * t90 * t181 + 0.4e1 * t33 * t340 * t92;
1195:   t557 = t146 * t15;
1196:   t562 = xc * t15;
1197:   t563 = t562 * t5;
1198:   t573 = 0.16e2 * t232 * t193 * t93 - 0.8e1 * t259 * t363 - 0.8e1 * t259 * t497 + 0.8e1 * t33 * t77 + 0.8e1 * t360 * t391 + 0.4e1 * t254 * t227 * t369 + 0.4e1 * t145 * t557 + 0.8e1 * t281 * t166 + 0.4e1 * t3 * t563 + 0.8e1 * t105 * t382 - 0.4e1 * t145 * t480 - 0.4e1 * t33 * t36 * t92;
1199:   t600 = 0.4e1 * t456 * t42 - 0.8e1 * t360 * t260 - 0.4e1 * t40 * t557 - 0.4e1 * t105 * t373 + 0.16e2 * t226 * t227 * t93 - 0.16e2 * t90 * t382 - 0.4e1 * t145 * t356 - 0.16e2 * t63 * t157 - 0.32e2 * t87 * t25 * t313 - 0.16e2 * t226 * t227 * t76 - 0.16e2 * t63 * t113;
1200:   t623 = xc * t13;
1201:   t627 = 0.8e1 * t125 * t423 - 0.8e1 * t360 * t532 + 0.16e2 * t90 * t137 - 0.4e1 * t160 * t42 + 0.16e2 * t63 * t94 + 0.16e2 * t63 * t181 - 0.8e1 * t281 * t27 - 0.8e1 * t75 * t382 + 0.8e1 * t360 * t459 + 0.4e1 * t295 * t57 + 0.16e2 * t105 * t77 + 0.4e1 * t474 * t623 * t35;
1202:   t632 = t61 * 0.3141592654e1;
1203:   t633 = t632 * t8;
1204:   t634 = t80 * nz;
1205:   t638 = t632 * t634;
1206:   t639 = t638 * xc;
1207:   t642 = t61 * t34;
1208:   t643 = t122 * t19;
1209:   t649 = t61 * t61;
1210:   t650 = t649 * t1;
1211:   t652 = t19 * t19;
1212:   t653 = t14 * t652;
1213:   t654 = t653 * t9;
1214:   t657 = t14 * t1;
1215:   t658 = t657 * t19;
1216:   t665 = t632 * t34;
1217:   t666 = t665 * t2;
1218:   t667 = t8 * t19;
1219:   t668 = t667 * t623;
1220:   t674 = t665 * nz;
1221:   t675 = t652 * xc;
1222:   t682 = 0.8e1 * t633 * t426 * t634 - 0.8e1 * t639 * t529 - 0.4e1 * t642 * t643 + 0.2e1 * t642 * t116 * t80 + 0.32e2 * t650 * t64 * t654 + 0.4e1 * t301 * t658 + 0.4e1 * t387 * t46 * ZA * ZB - 0.16e2 * t666 * t668 - 0.16e2 * t666 * t667 * t15 - 0.8e1 * t674 * t675 * t15 + 0.4e1 * t238 * t153 * t80;
1223:   t683 = t46 * t652;
1224:   t686 = t633 * t15;
1225:   t691 = t35 * t80;
1226:   t698 = t35 * t652;
1227:   t705 = t14 * t80;
1228:   t708 = t61 * t35;
1229:   t717 = -0.2e1 * t642 * t683 - 0.8e1 * t686 * t5 * t634 * xc - 0.2e1 * t301 * t691 + 0.8e1 * t638 * t563 - 0.2e1 * t642 * t691 - 0.2e1 * t642 * t698 - 0.2e1 * t301 * t698 - 0.2e1 * t301 * t683 + 0.2e1 * t642 * t705 + 0.2e1 * t708 * t274 * t80 + 0.2e1 * t301 * t653 - 0.2e1 * t642 * t80 * t46;
1230:   t727 = t61 * t46;
1231:   t737 = t649 * t34;
1232:   t738 = t737 * t1;
1233:   t739 = t8 * t652;
1234:   t740 = t739 * t268;
1235:   t746 = t61 * ZA;
1236:   t754 = t632 * nz * xc;
1237:   t758 = 0.2e1 * t301 * t705 + 0.2e1 * t642 * t653 - 0.8e1 * t665 * xc * t634 * t15 - 0.2e1 * t727 * t5 * t80 - 0.32e2 * t650 * xc * t654 + 0.2e1 * t301 * t698 * t14 - 0.32e2 * t738 * t740 + 0.8e1 * t674 * t739 * t562 + 0.4e1 * t746 * t119 * t652 + 0.8e1 * t674 * t698 * t623 - 0.8e1 * t754 * t528 * t698;
1238:   t762 = t633 * t13;
1239:   t764 = t5 * nz * t652;
1240:   t767 = t80 * t1;
1241:   t768 = t649 * t767;
1242:   t772 = t649 * ZA;
1243:   t773 = t772 * t129;
1244:   t777 = t35 * t1 * t19;
1245:   t780 = t632 * t5;
1246:   t781 = t780 * t15;
1247:   t786 = t698 * ZA;
1248:   t790 = t64 * t14;
1249:   t800 = t649 * t8;
1250:   t809 = 0.4e1 * t238 * t126 * t80 - 0.8e1 * t762 * t764 - 0.32e2 * t768 * xc * t275 + 0.64e2 * t773 * t740 - 0.4e1 * t301 * t777 - 0.8e1 * t781 * nz * t8 * t675 + 0.4e1 * t238 * t786 + 0.32e2 * t768 * t34 * t790 * t8 - 0.8e1 * t633 * t528 * t634 + 0.8e1 * t754 * t528 * t739 + 0.128e3 * t800 * t119 * t80 * t19 * t106 + 0.8e1 * t674 * t739 * t13;
1251:   t812 = t649 * t80;
1252:   t817 = t83 * ZB;
1253:   t824 = t746 * ZB;
1254:   t828 = t800 * t14;
1255:   t855 = -0.64e2 * t812 * xc * t274 * t667 + 0.4e1 * t817 * t786 + 0.4e1 * t727 * ZA * t652 * ZB - 0.32e2 * t824 * t657 * t667 - 0.32e2 * t828 * t34 * t767 * xc - 0.8e1 * t633 * t15 * t34 * t634 - 0.8e1 * t674 * t739 * t15 + 0.32e2 * t768 * t64 * t275 + 0.4e1 * t708 * t14 * t307 + 0.2e1 * t708 * t206 * t652 + 0.8e1 * t632 * t35 * t13 * t34 * t634 * xc;
1256:   t858 = t35 * t19;
1257:   t873 = t2 * t8;
1258:   t878 = t61 * t1;
1259:   t901 = -0.16e2 * t632 * t2 * xc * t528 * t858 + 0.8e1 * t824 * t658 + 0.4e1 * t301 * t14 * t777 - 0.8e1 * t665 * t634 * t509 - 0.8e1 * t674 * t739 * t623 - 0.16e2 * t781 * t873 * t19 * xc + 0.8e1 * t878 * t14 * t127 + 0.8e1 * t878 * ZA * t51 * ZB + 0.8e1 * t686 * t764 + 0.8e1 * t665 * xc * t634 * t15 * t8 + 0.8e1 * t633 * t15 * t5 * t634 + 0.4e1 * t387 * t14 * t107 * ZA;
1260:   t903 = t739 * t790;
1261:   t923 = t737 * t80;
1262:   t924 = t667 * t790;
1263:   t927 = t780 * t2;
1264:   t937 = t15 * t19 * xc;
1265:   t943 = 0.32e2 * t738 * t903 + 0.16e2 * t781 * t873 * t19 + 0.8e1 * t754 * t15 * t652 * t5 + 0.16e2 * t666 * t858 * t623 + 0.64e2 * t828 * t25 * t767 * xc - 0.16e2 * t762 * t456 * t19 + 0.64e2 * t923 * t924 + 0.16e2 * t927 * t668 - 0.64e2 * t768 * ZA * t790 * t66 - 0.64e2 * t773 * t903 + 0.16e2 * t927 * t937 + 0.16e2 * t666 * t667 * t562;
1266:   t977 = 0.64e2 * t812 * t5 * t924 + 0.8e1 * t639 * t504 + 0.8e1 * t238 * t35 * t118 * t19 + 0.4e1 * t642 * t658 - 0.16e2 * t817 * t437 * t8 - 0.128e3 * t772 * ZB * t80 * t924 + 0.16e2 * t666 * t667 * t13 - 0.4e1 * t301 * t643 - 0.16e2 * t824 * t653 * t8 - 0.4e1 * t642 * t777 - 0.64e2 * t923 * t667 * t268 - 0.16e2 * t666 * t937;

1268:   _PC3A = (t72 + t132 + t169 + t210 + t246 + t298 + t337 + t378 + t409 + t441 + t483 + t512 + t542 + t573 + t600 + t627) / (t682 + t717 + t758 + t809 + t855 + t901 + t943 + t977);
1269:   /****************************************************************************************/
1270:   _PC4A = 0;
1271:   /****************************************************************************************/
1272:   t1   = nx * 0.3141592654e1;
1273:   t2   = t1 * xc;
1274:   t3   = PetscCosReal(t2);
1275:   t4   = nx * nx;
1276:   t6   = nz * 0.3141592654e1;
1277:   t7   = t3 * t4 * t6;
1278:   t8   = ZA * ZB;
1279:   t9   = PetscExpReal(t6);
1280:   t10  = t9 * t9;
1281:   t11  = xc * nz;
1282:   t13  = PetscExpReal(t11 * 0.3141592654e1);
1283:   t14  = t13 * t13;
1284:   t15  = t14 * t13;
1285:   t16  = t14 * t14;
1286:   t17  = t16 * t15;
1287:   t18  = t10 * t17;
1288:   t19  = t8 * t18;
1289:   t22  = PetscSinReal(t2);
1290:   t23  = nx * t22;
1291:   t24  = t23 * nz;
1292:   t25  = ZB * ZB;
1293:   t30  = nz * nz;
1294:   t31  = t30 * nz;
1295:   t32  = t31 * nx;
1296:   t33  = 0.3141592654e1 * 0.3141592654e1;
1297:   t35  = t32 * t22 * t33;
1298:   t36  = ZA * ZA;
1299:   t37  = t36 * xc;
1300:   t38  = t16 * t13;
1301:   t39  = t10 * t38;
1302:   t40  = t37 * t39;
1303:   t43  = PetscSinReal(t1);
1304:   t44  = nx * t43;
1305:   t45  = t30 * 0.3141592654e1;
1306:   t46  = t44 * t45;
1307:   t47  = ZA * xc;
1308:   t49  = ZB * t16 * t9;
1309:   t54  = t4 * nx * t43;
1310:   t55  = xc * xc;
1311:   t57  = t54 * t30 * t55;
1312:   t58  = t33 * 0.3141592654e1;
1313:   t59  = t58 * t25;
1314:   t60  = t16 * t9;
1315:   t61  = t59 * t60;
1316:   t64  = xc * t25;
1317:   t65  = t14 * t9;
1318:   t66  = t64 * t65;
1319:   t70  = t44 * t31 * t33;
1320:   t71  = t37 * t65;
1321:   t74  = t10 * t15;
1322:   t75  = t64 * t74;
1323:   t78  = t25 * t10;
1324:   t83  = t54 * nz * t33;
1325:   t84  = t55 * t25;
1326:   t85  = t10 * t9;
1327:   t86  = t14 * t85;
1328:   t87  = t84 * t86;
1329:   t90  = t30 * t30;
1330:   t92  = t44 * t90 * t58;
1331:   t93  = t55 * xc;
1332:   t94  = t93 * t25;
1333:   t95  = t85 * t16;
1334:   t96  = t94 * t95;
1335:   t102 = t23 * t45;
1336:   t103 = t10 * t10;
1337:   t104 = ZB * t103;
1338:   t106 = t47 * t104 * t15;
1339:   t111 = t54 * 0.3141592654e1;
1340:   t112 = t25 * t85;
1341:   t113 = t112 * t16;
1342:   t115 = t8 * t39;
1343:   t118 = t16 * t14;
1344:   t119 = t85 * t118;
1345:   t120 = t37 * t119;
1346:   t123 = t16 * t16;
1347:   t124 = t36 * t123;
1348:   t125 = t124 * t9;
1349:   t127 = -0.8e1 * t7 * t19 + 0.2e1 * t24 * t25 * t13 * t10 - 0.16e2 * t35 * t40 - 0.16e2 * t46 * t47 * t49 - 0.8e1 * t57 * t61 + 0.4e1 * t46 * t66 + 0.2e1 * t70 * t71 - 0.16e2 * t35 * t75 + 0.6e1 * t24 * t78 * t38 - 0.2e1 * t83 * t87 - 0.8e1 * t92 * t96 - 0.8e1 * t46 * t37 * t95 - 0.12e2 * t102 * t106 + 0.2e1 * t83 * t71 + t111 * t113 + 0.8e1 * t7 * t115 + 0.2e1 * t83 * t120 + t111 * t125;
1350:   t128 = t37 * t74;
1351:   t131 = t44 * nz;
1352:   t133 = t25 * t9 * t118;
1353:   t136 = t36 * t14;
1354:   t137 = t136 * t9;
1355:   t140 = t30 * t4;
1356:   t142 = t140 * t3 * t33;
1357:   t143 = t64 * t39;
1358:   t147 = t30 * nx * t43;
1359:   t148 = 0.3141592654e1 * t36;
1360:   t149 = t9 * t118;
1361:   t153 = t44 * t31 * ZA;
1362:   t154 = t33 * xc;
1363:   t155 = t154 * t49;
1364:   t160 = ZA * t17 * xc * ZB;
1365:   t163 = t103 * t13;
1366:   t164 = t64 * t163;
1367:   t170 = t44 * t90 * t55;
1368:   t171 = t58 * ZB;
1369:   t172 = ZA * t16;
1370:   t174 = t171 * t172 * t9;
1371:   t177 = t36 * t55;
1372:   t178 = t177 * t149;
1373:   t181 = t54 * t11;
1374:   t182 = t33 * t25;
1375:   t186 = t25 * t14;
1376:   t187 = t186 * t9;
1377:   t193 = t186 * t85;
1378:   t198 = ZB * t55;
1379:   t199 = ZA * t103;
1380:   t201 = t198 * t199 * t15;
1381:   t204 = 0.2e1 * t7 * t128 - 0.2e1 * t131 * t133 - 0.2e1 * t131 * t137 + 0.16e2 * t142 * t143 - t147 * t148 * t149 + 0.8e1 * t153 * t155 - 0.4e1 * t7 * t160 + 0.2e1 * t7 * t164 + 0.10e2 * t102 * t40 + 0.16e2 * t170 * t174 + 0.2e1 * t83 * t178 - 0.2e1 * t181 * t182 * t65 - t111 * t187 - 0.2e1 * t70 * t87 + 0.4e1 * t102 * t160 - 0.2e1 * t131 * t193 - 0.16e2 * t142 * t75 + 0.16e2 * t35 * t201;
1382:   t210 = t32 * t22;
1383:   t211 = t33 * t55;
1384:   t212 = t25 * t38;
1385:   t213 = t211 * t212;
1386:   t216 = nz * nx;
1387:   t217 = t22 * t25;
1388:   t222 = ZB * t85 * t16;
1389:   t226 = t23 * t30;
1390:   t227 = t13 * t10;
1391:   t228 = t148 * t227;
1392:   t233 = t37 * t163;
1393:   t237 = nz * t4 * t3;
1394:   t238 = t148 * t74;
1395:   t241 = t64 * t86;
1396:   t245 = t148 * xc * t15;
1397:   t248 = t112 * t118;
1398:   t250 = t22 * t36;
1399:   t256 = 0.3141592654e1 * t25;
1400:   t257 = t256 * t39;
1401:   t262 = t38 * t103;
1402:   t263 = t37 * t262;
1403:   t267 = t148 * t17 * xc;
1404:   t270 = -0.6e1 * t7 * t143 - 0.4e1 * t24 * t19 - 0.8e1 * t210 * t213 - 0.2e1 * t216 * t217 * t15 - 0.32e2 * t153 * t211 * t222 + 0.4e1 * t226 * t228 + 0.16e2 * t142 * t201 + 0.2e1 * t7 * t233 - 0.4e1 * t237 * t238 - 0.2e1 * t83 * t241 - 0.2e1 * t237 * t245 + t111 * t248 + 0.2e1 * t216 * t250 * t15 - 0.2e1 * t131 * t125 - 0.4e1 * t226 * t257 + t147 * t148 * t95 - 0.2e1 * t102 * t263 + 0.2e1 * t237 * t267;
1405:   t273 = t37 * t149;
1406:   t277 = t47 * t104 * t13;
1407:   t285 = t31 * t36;
1408:   t286 = t44 * t285;
1409:   t291 = t25 * t123 * t9;
1410:   t304 = 0.3141592654e1 * xc;
1411:   t305 = t304 * t212;
1412:   t312 = t256 * t18;
1413:   t315 = t8 * t60;
1414:   t319 = t54 * t30 * t58;
1415:   t323 = t90 * t36;
1416:   t324 = t44 * t323;
1417:   t325 = t55 * t58;
1418:   t326 = t325 * t60;
1419:   t329 = 0.2e1 * t102 * t164 + 0.2e1 * t83 * t273 - 0.4e1 * t102 * t277 - 0.2e1 * t7 * t263 + 0.4e1 * t24 * t8 * t17 - 0.4e1 * t286 * t154 * t60 - 0.2e1 * t131 * t291 - t147 * t148 * t119 + 0.2e1 * t24 * t78 * t17 + 0.2e1 * t54 * t85 * 0.3141592654e1 * ZA * ZB - 0.4e1 * t226 * t305 - 0.2e1 * t70 * t66 + t147 * t256 * t95 + 0.4e1 * t237 * t312 + 0.2e1 * t111 * t315 - 0.8e1 * t319 * t96 - t111 * t193 - 0.8e1 * t324 * t326;
1420:   t332 = t8 * t95;
1421:   t335 = t136 * t85;
1422:   t337 = t256 * t227;
1423:   t340 = t177 * t119;
1424:   t346 = t37 * t86;
1425:   t351 = t103 * t15;
1426:   t352 = t177 * t351;
1427:   t355 = t64 * t119;
1428:   t358 = t8 * t227;
1429:   t361 = t85 * 0.3141592654e1;
1430:   t365 = t84 * t39;
1431:   t372 = ZB * t10;
1432:   t373 = t372 * t38;
1433:   t374 = t47 * t373;
1434:   t379 = t177 * t39;
1435:   t384 = -0.2e1 * t46 * t332 + t111 * t335 + 0.4e1 * t237 * t337 - 0.2e1 * t83 * t340 + 0.16e2 * t286 * t211 * t95 + 0.2e1 * t70 * t346 - 0.8e1 * t170 * t61 - 0.8e1 * t142 * t352 - 0.2e1 * t83 * t355 - 0.4e1 * t24 * t358 + 0.2e1 * t147 * t361 * t8 + 0.8e1 * t35 * t365 - 0.2e1 * t226 * t267 + 0.8e1 * t102 * t115 - 0.12e2 * t102 * t374 + 0.16e2 * t142 * t40 - 0.8e1 * t142 * t379 + 0.4e1 * t237 * t228;
1436:   t386 = t54 * t30 * t93;
1437:   t387 = ZA * t85;
1438:   t389 = t171 * t387 * t16;
1439:   t394 = t64 * t60;
1440:   t398 = t304 * t25 * t15;
1441:   t401 = t361 * t25;
1442:   t405 = t84 * t65;
1443:   t410 = t148 * t18;
1444:   t414 = t25 * t16 * t9;
1445:   t417 = t84 * t74;
1446:   t422 = t177 * t86;
1447:   t428 = ZB * t38;
1448:   t429 = t47 * t428;
1449:   t432 = t148 * t39;
1450:   t439 = 0.16e2 * t386 * t389 - 0.16e2 * t386 * t174 + 0.8e1 * t46 * t394 + 0.2e1 * t237 * t398 - t147 * t401 + 0.4e1 * t7 * t374 + 0.2e1 * t83 * t405 - 0.4e1 * t46 * t241 - 0.4e1 * t226 * t410 + 0.2e1 * t131 * t414 + 0.8e1 * t35 * t417 - 0.8e1 * t142 * t365 + 0.2e1 * t70 * t422 - 0.4e1 * t181 * t182 * t60 + 0.12e2 * t102 * t429 - 0.4e1 * t226 * t432 + 0.32e2 * t35 * t374 - 0.4e1 * t7 * t106;
1451:   t442 = t36 * t9 * t118;
1452:   t444 = t123 * t9;
1453:   t445 = t8 * t444;
1454:   t448 = t361 * t36;
1455:   t451 = t47 * t372 * t17;
1456:   t454 = t94 * t60;
1457:   t457 = t25 * t103;
1458:   t465 = t47 * t372 * t15;
1459:   t468 = t36 * t85;
1460:   t469 = t468 * t16;
1461:   t474 = t43 * t85;
1462:   t478 = t8 * t74;
1463:   t484 = t256 * t74;
1464:   t489 = t198 * ZA * t10 * t15;
1465:   t501 = -t111 * t442 + 0.4e1 * t131 * t445 - t147 * t448 + 0.4e1 * t7 * t451 + 0.8e1 * t92 * t454 - 0.2e1 * t24 * t457 * t13 - 0.2e1 * t286 * t211 * t65 + 0.4e1 * t7 * t465 + t111 * t469 - 0.2e1 * t216 * t250 * t17 - 0.2e1 * t216 * t474 * t25 - 0.4e1 * t24 * t478 + 0.4e1 * t24 * t8 * t38 + 0.4e1 * t226 * t484 - 0.16e2 * t142 * t489 - 0.2e1 * t24 * t212 * t103 - 0.2e1 * t216 * t22 * t17 * t25 + 0.2e1 * t70 * t120;
1466:   t504 = t33 * t36 * t55 * t38;
1467:   t507 = t37 * t18;
1468:   t512 = t47 * ZB * t13 * t10;
1469:   t518 = t59 * t95;
1470:   t530 = t84 * t351;
1471:   t534 = t37 * t227;
1472:   t549 = -0.8e1 * t210 * t504 + 0.2e1 * t102 * t507 + 0.4e1 * t7 * t512 + t111 * t133 - 0.16e2 * t35 * t489 + 0.8e1 * t170 * t518 + 0.2e1 * t24 * t36 * t13 * t10 + 0.4e1 * t131 * t387 * ZB + 0.12e2 * t102 * t465 - 0.8e1 * t142 * t530 + t111 * t291 - 0.2e1 * t102 * t534 - 0.4e1 * t70 * t394 - 0.10e2 * t102 * t128 + 0.4e1 * t237 * t305 + 0.8e1 * t102 * t19 + 0.2e1 * t83 * t346 - 0.16e2 * t35 * t128;
1473:   t557 = t468 * t118;
1474:   t562 = t93 * t58;
1475:   t563 = t562 * t60;
1476:   t567 = t44 * t90 * t93;
1477:   t575 = ZA * t55;
1478:   t576 = t575 * t428;
1479:   t583 = t37 * t60;
1480:   t590 = t140 * t3;
1481:   t601 = -0.2e1 * t226 * t398 - 0.2e1 * t70 * t340 - 0.2e1 * t131 * t557 - 0.4e1 * t24 * t115 + 0.8e1 * t324 * t563 + 0.16e2 * t567 * t389 + 0.16e2 * t70 * t84 * t95 + 0.2e1 * t70 * t178 - 0.16e2 * t142 * t576 - 0.4e1 * t237 * t257 - 0.4e1 * t226 * t312 + 0.8e1 * t46 * t583 + 0.2e1 * t24 * t36 * t38 * t103 + 0.8e1 * t590 * t213 + 0.2e1 * t102 * t143 - 0.16e2 * t35 * t143 + 0.2e1 * t131 * t248 + 0.4e1 * t46 * t346;
1482:   t604 = nz * t36;
1483:   t606 = t154 * t95;
1484:   t625 = t36 * t103;
1485:   t640 = t30 * t36;
1486:   t641 = t54 * t640;
1487:   t642 = t325 * t95;
1488:   t647 = -0.4e1 * t131 * t315 - 0.4e1 * t54 * t604 * t606 - t147 * t148 * t60 + 0.16e2 * t35 * t576 - 0.8e1 * t102 * t478 + 0.32e2 * t142 * t465 - 0.4e1 * t237 * t484 - 0.2e1 * t70 * t355 + 0.2e1 * t70 * t273 + 0.2e1 * t102 * t233 - 0.2e1 * t24 * t625 * t13 - 0.8e1 * t7 * t358 - 0.2e1 * t111 * t445 - 0.4e1 * t7 * t429 + 0.16e2 * t46 * t47 * t222 + 0.2e1 * t131 * t113 + 0.8e1 * t641 * t642 - 0.2e1 * t7 * t534;
1489:   t652 = t36 * t16;
1490:   t653 = t652 * t9;
1491:   t655 = t64 * t227;
1492:   t658 = t182 * t95;
1493:   t663 = t562 * t95;
1494:   t684 = t64 * t351;
1495:   t689 = t36 * t10;
1496:   t695 = t154 * t222;
1497:   t698 = -0.4e1 * t216 * t217 * t38 - t111 * t653 - 0.2e1 * t7 * t655 - 0.4e1 * t181 * t658 + 0.2e1 * t131 * t469 - 0.8e1 * t641 * t663 - 0.4e1 * t83 * t583 - 0.2e1 * t83 * t177 * t65 - 0.4e1 * t24 * t457 * t15 + 0.16e2 * t70 * t84 * t60 + 0.8e1 * t57 * t518 - 0.32e2 * t142 * t374 + 0.4e1 * t24 * t8 * t351 + 0.4e1 * t102 * t684 - t147 * t256 * t86 - 0.2e1 * t24 * t689 * t15 - 0.2e1 * t70 * t241 + 0.8e1 * t153 * t695;
1498:   t711 = t575 * t373;
1499:   t717 = t304 * t17 * t25;
1500:   t736 = t177 * t74;
1501:   t739 = 0.2e1 * t226 * t245 - 0.8e1 * t102 * t358 - 0.16e2 * t57 * t389 - 0.2e1 * t102 * t655 + 0.8e1 * t590 * t504 - 0.8e1 * t641 * t326 - 0.16e2 * t35 * t711 - t111 * t557 + t111 * t137 - 0.2e1 * t226 * t717 + 0.8e1 * t102 * t37 * t351 + 0.2e1 * t131 * t335 - 0.4e1 * t131 * t332 - 0.2e1 * t216 * t474 * t36 - 0.2e1 * t111 * t332 + 0.16e2 * t142 * t711 - t147 * t256 * t60 + 0.8e1 * t142 * t736;
1502:   t750 = t64 * t262;
1503:   t763 = t44 * t640;
1504:   t770 = t84 * t119;
1505:   t782 = 0.4e1 * t102 * t512 + 0.8e1 * t142 * t417 + 0.8e1 * t641 * t563 - 0.2e1 * t7 * t507 + 0.2e1 * t7 * t750 - 0.8e1 * t35 * t352 + 0.4e1 * t237 * t410 + 0.4e1 * t7 * t684 - 0.2e1 * t46 * t445 + t147 * t148 * t65 + 0.4e1 * t763 * t304 * t119 + 0.16e2 * t70 * t177 * t60 + 0.2e1 * t70 * t770 - t111 * t414 - 0.16e2 * t567 * t174 - 0.4e1 * t46 * t71 - 0.4e1 * t46 * t355 - 0.4e1 * t7 * t277;
1506:   t797 = t64 * t149;
1507:   t821 = -t54 * t448 + 0.2e1 * t131 * t442 + 0.8e1 * t7 * t478 + 0.8e1 * t35 * t379 - 0.2e1 * t181 * t182 * t149 + 0.2e1 * t70 * t405 + 0.2e1 * t83 * t770 - 0.2e1 * t70 * t797 - 0.6e1 * t7 * t75 - 0.4e1 * t286 * t606 - 0.4e1 * t237 * t432 + t147 * t256 * t149 - 0.4e1 * t763 * t304 * t149 - 0.2e1 * t102 * t75 + 0.2e1 * t237 * t717 + 0.8e1 * t324 * t642 - 0.16e2 * t170 * t389 + 0.2e1 * t83 * t422;
1508:   t827 = t84 * t149;
1509:   t846 = t54 * nz * ZA;
1510:   t854 = t64 * t18;
1511:   t867 = -0.16e2 * t142 * t128 + 0.32e2 * t35 * t465 - 0.2e1 * t83 * t827 + 0.2e1 * t46 * t315 + t147 * t148 * t86 - 0.4e1 * t102 * t451 - 0.8e1 * t226 * t148 * xc * t38 - 0.2e1 * t24 * t689 * t38 + 0.2e1 * t131 * t187 + 0.8e1 * t846 * t155 + 0.8e1 * t35 * t736 + 0.2e1 * t24 * t689 * t17 - 0.2e1 * t7 * t854 + t147 * t256 * t119 + 0.2e1 * t102 * t854 - 0.8e1 * t35 * t530 + 0.4e1 * t46 * t797 + 0.2e1 * t102 * t750;
1512:   t909 = -0.8e1 * t324 * t663 + t147 * t256 * t444 - t147 * t256 * t65 + 0.4e1 * t226 * t238 + 0.2e1 * t7 * t40 - t54 * t401 + 0.16e2 * t57 * t174 + 0.4e1 * t226 * t337 + 0.4e1 * t24 * t8 * t163 + 0.8e1 * t846 * t695 + 0.8e1 * t319 * t454 + 0.2e1 * t131 * t653 - 0.8e1 * t46 * t64 * t95 + 0.6e1 * t24 * t78 * t15 - 0.4e1 * t44 * t31 * xc * t658 - 0.32e2 * t153 * t211 * t49 - 0.2e1 * t70 * t827 + t147 * t148 * t444;
1513:   t914 = t25 * ZB;
1514:   t915 = t33 * t914;
1515:   t919 = t4 * t4;
1516:   t920 = t16 * t919;
1517:   t929 = t123 * t90;
1518:   t932 = t919 * t103;
1519:   t935 = t33 * ZB;
1520:   t939 = t652 * t919;
1521:   t942 = t16 * t30;
1522:   t943 = t942 * t4;
1523:   t949 = t103 * t16;
1524:   t950 = t949 * t90;
1525:   t953 = -0.2e1 * t915 * t103 * t90 + 0.2e1 * t915 * t920 - 0.2e1 * t915 * t123 * t919 + 0.2e1 * t915 * t16 * t90 - 0.2e1 * t915 * t929 - 0.2e1 * t915 * t932 - 0.2e1 * t935 * t323 * t123 + 0.2e1 * t935 * t939 + 0.4e1 * t915 * t943 + 0.4e1 * t182 * t172 * t90 + 0.2e1 * t915 * t950;
1526:   t954  = t171 * t36;
1527:   t955  = t90 * nz;
1528:   t956  = xc * t955;
1529:   t957  = t118 * t10;
1530:   t964  = t33 * t33;
1531:   t965  = t964 * ZB;
1532:   t966  = t965 * t640;
1533:   t967  = t10 * t919;
1534:   t968  = t55 * t16;
1535:   t969  = t967 * t968;
1536:   t972  = t935 * t36;
1537:   t974  = t103 * t30 * t4;
1538:   t977  = xc * t16;
1539:   t978  = t967 * t977;
1540:   t981  = t90 * t30;
1541:   t983  = t16 * t10;
1542:   t987  = t182 * ZA;
1543:   t988  = t4 * t10;
1544:   t992  = t171 * t604;
1545:   t993  = xc * t14;
1546:   t994  = t932 * t993;
1547:   t997  = t182 * t30;
1548:   t1005 = t171 * t285;
1549:   t1006 = t988 * t993;
1550:   t1009 = t58 * t914;
1551:   t1010 = t1009 * t31;
1552:   t1013 = 0.8e1 * t954 * t956 * t957 + 0.2e1 * t915 * t932 * t16 + 0.32e2 * t966 * t969 - 0.4e1 * t972 * t974 - 0.32e2 * t966 * t978 + 0.32e2 * t965 * t981 * t177 * t983 - 0.32e2 * t987 * t942 * t988 + 0.8e1 * t992 * t994 + 0.8e1 * t997 * t949 * ZA * t4 - 0.2e1 * t935 * t124 * t919 - 0.16e2 * t1005 * t1006 + 0.16e2 * t1010 * t1006;
1553:   t1015 = t964 * t25;
1554:   t1016 = ZA * t30;
1555:   t1017 = t1015 * t1016;
1556:   t1020 = t967 * t993;
1557:   t1031 = t1009 * t118;
1558:   t1032 = t31 * t10;
1559:   t1040 = t964 * t914;
1560:   t1041 = t1040 * t90;
1561:   t1044 = t55 * t10 * t4 * t16;
1562:   t1047 = t1040 * t30;
1563:   t1050 = t123 * ZA;
1564:   t1054 = t977 * t988;
1565:   t1057 = 0.64e2 * t1017 * t978 - 0.8e1 * t992 * t1020 + 0.2e1 * t972 * t950 + 0.4e1 * t182 * t929 * ZA + 0.4e1 * t182 * t199 * t90 - 0.16e2 * t1031 * t1032 * t4 * xc + 0.4e1 * t182 * t172 * t919 + 0.64e2 * t1041 * t1044 + 0.32e2 * t1047 * t969 + 0.4e1 * t182 * t1050 * t919 - 0.64e2 * t1041 * t1054;
1566:   t1058 = t1009 * nz;
1567:   t1063 = t932 * ZA;
1568:   t1069 = t123 * t30 * t4;
1569:   t1080 = t993 * t103 * t4;
1570:   t1088 = t935 * t103;
1571:   t1094 = -0.8e1 * t1058 * t994 - 0.32e2 * t1047 * t978 + 0.4e1 * t182 * t1063 - 0.4e1 * t915 * t974 - 0.4e1 * t915 * t1069 - 0.2e1 * t935 * t625 * t90 - 0.8e1 * t1009 * t10 * t14 * t955 - 0.16e2 * t1010 * t1080 - 0.2e1 * t935 * t625 * t919 - 0.64e2 * t1017 * t969 + 0.2e1 * t1088 * t939 + 0.8e1 * t1009 * t957 * t955;
1572:   t1113 = t955 * t118 * xc;
1573:   t1120 = t4 * t118;
1574:   t1125 = t981 * xc;
1575:   t1133 = nz * t10;
1576:   t1140 = -0.8e1 * t954 * t955 * t10 * t993 + 0.2e1 * t935 * t652 * t90 - 0.64e2 * t1015 * t981 * t575 * t983 + 0.8e1 * t182 * t103 * t1016 * t4 + 0.8e1 * t1009 * t1113 + 0.16e2 * t954 * t1032 * t4 * t14 - 0.16e2 * t954 * t1032 * t1120 + 0.64e2 * t1015 * t10 * t172 * t1125 + 0.8e1 * t171 * t103 * t136 * t956 - 0.8e1 * t1031 * t1133 * t919 * xc + 0.8e1 * t1058 * t1020;
1577:   t1153 = xc * t118;
1578:   t1165 = t182 * t16;
1579:   t1170 = t171 * t10;
1580:   t1178 = ZA * t90;
1581:   t1182 = 0.4e1 * t1088 * t652 * t140 + 0.8e1 * t954 * t1133 * t919 * t14 + 0.4e1 * t972 * t943 - 0.4e1 * t972 * t1069 - 0.16e2 * t954 * t31 * t4 * t1153 - 0.8e1 * t954 * nz * t919 * t1153 - 0.8e1 * t954 * t1133 * t919 * t118 + 0.4e1 * t1165 * t1063 + 0.16e2 * t1005 * t1080 - 0.8e1 * t1170 * t118 * t36 * t955 - 0.16e2 * t987 * t920 * t10 - 0.16e2 * t1165 * t1178 * t10;
1582:   t1195 = t1040 * t981;
1583:   t1199 = t1009 * t955;
1584:   t1203 = t1009 * t10;
1585:   t1211 = t965 * t323;
1586:   t1225 = -0.32e2 * t965 * t10 * t652 * t1125 + 0.4e1 * t915 * t16 * t974 + 0.4e1 * t182 * t90 * t949 * ZA + 0.32e2 * t1195 * t968 * t10 - 0.8e1 * t1199 * t993 * t103 + 0.8e1 * t1203 * t118 * nz * t919 + 0.8e1 * t1170 * t136 * t955 + 0.64e2 * t1211 * t1044 + 0.16e2 * t1031 * t1032 * t4 + 0.8e1 * t987 * t943 + 0.8e1 * t1199 * t993 * t10 + 0.8e1 * t997 * t1050 * t4;
1587:   t1263 = -0.128e3 * t1015 * t1178 * t1044 + 0.16e2 * t1005 * t988 * t1153 + 0.8e1 * t1058 * t1153 * t919 + 0.16e2 * t1010 * t1120 * xc - 0.8e1 * t954 * t1113 - 0.8e1 * t1203 * t14 * nz * t919 - 0.16e2 * t1203 * t14 * t31 * t4 - 0.8e1 * t1203 * t1113 - 0.32e2 * t1195 * t977 * t10 - 0.64e2 * t1211 * t1054 + 0.8e1 * t992 * t967 * t1153 + 0.128e3 * t1015 * t983 * t90 * t4 * t47;

1589:   _PC1B = (t127 + t204 + t270 + t329 + t384 + t439 + t501 + t549 + t601 + t647 + t698 + t739 + t782 + t821 + t867 + t909) / (t953 + t1013 + t1057 + t1094 + t1140 + t1182 + t1225 + t1263);
1590:   /****************************************************************************************/
1591:   t1   = nz * nz;
1592:   t2   = t1 * nz;
1593:   t3   = nx * t2;
1594:   t4   = 0.3141592654e1 * ZA;
1595:   t5   = t3 * t4;
1596:   t6   = nx * 0.3141592654e1;
1597:   t7   = t6 * xc;
1598:   t8   = PetscSinReal(t7);
1599:   t9   = t8 * ZB;
1600:   t10  = nz * 0.3141592654e1;
1601:   t11  = PetscExpReal(t10);
1602:   t12  = t11 * t11;
1603:   t15  = PetscExpReal(xc * nz * 0.3141592654e1);
1604:   t16  = t15 * t15;
1605:   t17  = t16 * t16;
1606:   t18  = t17 * t15;
1607:   t19  = t12 * t18;
1608:   t23  = t1 * t1;
1609:   t24  = nx * t23;
1610:   t25  = ZB * ZB;
1611:   t27  = t18 * t8;
1612:   t28  = 0.3141592654e1 * 0.3141592654e1;
1613:   t29  = xc * xc;
1614:   t30  = t28 * t29;
1615:   t34  = t1 * xc;
1616:   t35  = 0.3141592654e1 * ZB;
1617:   t36  = t34 * t35;
1618:   t37  = PetscCosReal(t7);
1619:   t38  = ZA * t37;
1620:   t39  = nx * nx;
1621:   t40  = t39 * t12;
1622:   t41  = t16 * t15;
1623:   t43  = t38 * t40 * t41;
1624:   t46  = t25 * nz;
1625:   t47  = t46 * 0.3141592654e1;
1626:   t48  = t39 * nx;
1627:   t49  = PetscSinReal(t6);
1628:   t50  = t48 * t49;
1629:   t51  = t12 * t11;
1630:   t52  = t51 * t17;
1631:   t53  = t50 * t52;
1632:   t56  = t34 * 0.3141592654e1 * t25;
1633:   t57  = t37 * t39;
1634:   t58  = t17 * t41;
1635:   t59  = t12 * t58;
1636:   t60  = t57 * t59;
1637:   t63  = t25 * t18;
1638:   t64  = t57 * nz;
1639:   t67  = ZA * ZA;
1640:   t68  = t67 * nz;
1641:   t69  = 0.3141592654e1 * t48;
1642:   t70  = t68 * t69;
1643:   t71  = t49 * xc;
1644:   t72  = t17 * t16;
1645:   t73  = t11 * t72;
1646:   t74  = t71 * t73;
1647:   t77  = t1 * t67;
1648:   t78  = t77 * 0.3141592654e1;
1649:   t81  = nx * t25;
1650:   t82  = t81 * t49;
1651:   t83  = t17 * t17;
1652:   t85  = t1 * t83 * t11;
1653:   t87  = nx * ZB;
1654:   t88  = t8 * t2;
1655:   t89  = t87 * t88;
1656:   t90  = 0.3141592654e1 * xc;
1657:   t91  = t12 * t12;
1658:   t92  = ZA * t91;
1659:   t97  = ZB * ZA;
1660:   t98  = t97 * t37;
1661:   t99  = t39 * nz;
1662:   t100 = t12 * t41;
1663:   t104 = 0.8e1 * t5 * t9 * t19 + 0.8e1 * t24 * t25 * t27 * t30 + 0.12e2 * t36 * t43 - t47 * t53 - 0.2e1 * t56 * t60 - 0.4e1 * t63 * t64 + 0.6e1 * t70 * t74 + 0.4e1 * t78 * t60 - t82 * t85 + 0.4e1 * t89 * t90 * t92 * t41 + 0.4e1 * t98 * t99 * t100;
1664:   t105 = t67 * t48;
1665:   t106 = t49 * t51;
1666:   t107 = t106 * t72;
1667:   t109 = t1 * 0.3141592654e1;
1668:   t110 = t109 * xc;
1669:   t115 = nx * t67;
1670:   t116 = t115 * t49;
1671:   t117 = t1 * t16;
1672:   t118 = t117 * t11;
1673:   t120 = t2 * t25;
1674:   t121 = t28 * 0.3141592654e1;
1675:   t122 = t121 * t29;
1676:   t123 = t120 * t122;
1677:   t129 = t1 * ZB;
1678:   t130 = t129 * t4;
1679:   t131 = t57 * t100;
1680:   t134 = t12 * t16;
1681:   t136 = t109 * t39;
1682:   t139 = ZB * t18;
1683:   t141 = t39 * t1;
1684:   t142 = t141 * t90;
1685:   t145 = t77 * t90;
1686:   t146 = t91 * t41;
1687:   t147 = t57 * t146;
1688:   t151 = t25 * t39 * t1;
1689:   t152 = t72 * t12;
1690:   t156 = t49 * t2;
1691:   t158 = t83 * t11;
1692:   t162 = -t105 * t107 + 0.8e1 * t110 * t72 * t25 * t39 - t116 * t118 + 0.8e1 * t123 * t53 + 0.8e1 * t5 * t9 * t59 - 0.8e1 * t130 * t131 - 0.8e1 * t134 * t25 * t136 - 0.12e2 * t139 * t38 * t142 - 0.8e1 * t145 * t147 - 0.8e1 * t151 * t90 * t152 - 0.2e1 * t87 * t156 * t4 * t158;
1693:   t164 = t115 * t88;
1694:   t165 = t90 * t19;
1695:   t168 = t25 * t48;
1696:   t169 = t49 * t16;
1697:   t170 = t169 * t11;
1698:   t174 = ZA * nz * t69;
1699:   t175 = ZB * t51;
1700:   t176 = t175 * t17;
1701:   t177 = t71 * t176;
1702:   t180 = t1 * t29;
1703:   t181 = t28 * t25;
1704:   t182 = t180 * t181;
1705:   t183 = t50 * t73;
1706:   t186 = ZA * t1;
1707:   t187 = t28 * t48;
1708:   t188 = t186 * t187;
1709:   t189 = ZB * t17;
1710:   t190 = t189 * t11;
1711:   t191 = t71 * t190;
1712:   t194 = t50 * t158;
1713:   t196 = t115 * t156;
1714:   t197 = t90 * t73;
1715:   t201 = t49 * t17 * t11;
1716:   t204 = t88 * t90;
1717:   t207 = t68 * 0.3141592654e1;
1718:   t208 = t17 * t11;
1719:   t209 = t50 * t208;
1720:   t211 = -0.2e1 * t164 * t165 - t168 * t170 + t168 * t107 + 0.8e1 * t174 * t177 + 0.2e1 * t182 * t183 + 0.8e1 * t188 * t191 + t47 * t194 - 0.6e1 * t196 * t197 - t168 * t201 - 0.4e1 * t81 * t18 * t204 - t207 * t209;
1721:   t212 = t2 * 0.3141592654e1;
1722:   t213 = t212 * t52;
1723:   t215 = t81 * t8;
1724:   t216 = t212 * t59;
1725:   t219 = t3 * t90;
1726:   t220 = t25 * t8;
1727:   t221 = t18 * t91;
1728:   t225 = t71 * t52;
1729:   t231 = t16 * t51;
1730:   t232 = t50 * t231;
1731:   t237 = ZA * t12;
1732:   t243 = t67 * t28;
1733:   t244 = t24 * t243;
1734:   t245 = t71 * t231;
1735:   t249 = -t116 * t213 - 0.4e1 * t215 * t216 + 0.2e1 * t219 * t220 * t221 - 0.4e1 * t70 * t225 + 0.4e1 * t98 * t99 * t146 + t47 * t232 - 0.2e1 * t145 * t57 * t221 + 0.4e1 * t89 * t90 * t237 * t41 - t105 * t201 - 0.6e1 * t244 * t245 + t105 * t170;
1736:   t252 = t25 * t37;
1737:   t253 = t252 * t39;
1738:   t255 = nz * t15 * t12;
1739:   t258 = t2 * t29;
1740:   t259 = ZB * t28;
1741:   t260 = t258 * t259;
1742:   t263 = t106 * t17;
1743:   t265 = xc * t25;
1744:   t269 = t25 * t49;
1745:   t270 = t269 * t52;
1746:   t273 = t1 * t25;
1747:   t274 = t273 * 0.3141592654e1;
1748:   t275 = t57 * t19;
1749:   t278 = t24 * t30;
1750:   t288 = t1 * t11 * t72;
1751:   t290 = t212 * t208;
1752:   t292 = t2 * xc;
1753:   t296 = 0.2e1 * t253 * t255 + 0.16e2 * t260 * t43 + t105 * t263 - 0.4e1 * t10 * t265 * t53 + 0.4e1 * t219 * t270 - 0.12e2 * t274 * t275 + 0.8e1 * t278 * t270 - 0.2e1 * ZB * nz * t69 * t49 * ZA * t158 - t82 * t288 - t116 * t290 + 0.16e2 * t292 * t243 * t275;
1754:   t301 = t50 * t176;
1755:   t304 = t51 * t72;
1756:   t305 = t71 * t304;
1757:   t308 = t25 * t41;
1758:   t311 = ZA * t48;
1759:   t312 = t311 * t49;
1760:   t317 = t91 * t15;
1761:   t318 = t57 * t317;
1762:   t321 = t81 * t88;
1763:   t322 = t90 * t59;
1764:   t325 = t212 * t231;
1765:   t327 = t15 * t12;
1766:   t328 = t57 * t327;
1767:   t331 = t77 * t187;
1768:   t334 = t2 * ZA;
1769:   t335 = t334 * t122;
1770:   t336 = t50 * t190;
1771:   t339 = 0.8e1 * t151 * t90 * t134 + 0.16e2 * t186 * t30 * t301 - 0.2e1 * t70 * t305 + 0.2e1 * t308 * t64 - 0.2e1 * t312 * ZB * t83 * t11 + 0.2e1 * t56 * t318 + 0.2e1 * t321 * t322 - t116 * t325 - 0.4e1 * t274 * t328 + 0.2e1 * t331 * t305 - 0.16e2 * t335 * t336;
1772:   t341 = t169 * t51;
1773:   t344 = t49 * t11 * t72;
1774:   t346 = t77 * t30;
1775:   t347 = t50 * t304;
1776:   t350 = t25 * t51;
1777:   t352 = nx * ZA;
1778:   t353 = t49 * t23;
1779:   t354 = t352 * t353;
1780:   t355 = t28 * xc;
1781:   t362 = t25 * t91;
1782:   t365 = t23 * nz;
1783:   t366 = nx * t365;
1784:   t367 = t366 * t122;
1785:   t368 = ZB * t49;
1786:   t369 = ZA * t51;
1787:   t370 = t369 * t17;
1788:   t371 = t368 * t370;
1789:   t374 = t115 * t353;
1790:   t375 = t355 * t73;
1791:   t381 = t105 * t341 - t105 * t344 - 0.2e1 * t346 * t347 - t350 * t50 - 0.8e1 * t354 * t355 * t176 - 0.4e1 * t98 * t99 * t317 - 0.2e1 * t362 * t99 - 0.16e2 * t367 * t371 + 0.6e1 * t374 * t375 - 0.8e1 * t182 * t53 - t82 * t290;
1792:   t382 = t71 * t208;
1793:   t394 = t2 * t67;
1794:   t395 = t394 * t122;
1795:   t398 = t352 * t156;
1796:   t402 = t17 * t12;
1797:   t403 = t39 * ZA;
1798:   t404 = t402 * t403;
1799:   t407 = t269 * t208;
1800:   t411 = t49 * t83 * t11;
1801:   t413 = t46 * t69;
1802:   t419 = -0.4e1 * t331 * t382 + 0.2e1 * t115 * t58 * t204 - 0.2e1 * t145 * t60 + 0.12e2 * t274 * t131 + 0.2e1 * t346 * t232 + 0.8e1 * t395 * t53 - 0.8e1 * t398 * t90 * t176 - 0.64e2 * t260 * t404 + 0.4e1 * t219 * t407 + t168 * t411 - 0.6e1 * t413 * t74 - 0.2e1 * t110 * t308 * t57;
1803:   t424 = t16 * t11;
1804:   t425 = t212 * t424;
1805:   t427 = t258 * t181;
1806:   t430 = t67 * t29;
1807:   t431 = t366 * t430;
1808:   t432 = t121 * t49;
1809:   t433 = t432 * t52;
1810:   t436 = nz * t12;
1811:   t437 = t436 * t18;
1812:   t440 = t29 * xc;
1813:   t441 = t440 * t121;
1814:   t442 = t394 * t441;
1815:   t445 = t67 * t37;
1816:   t446 = t445 * t39;
1817:   t448 = nz * t18 * t91;
1818:   t453 = t352 * t49;
1819:   t458 = t8 * t23;
1820:   t462 = t81 * t458;
1821:   t463 = t30 * t19;
1822:   t466 = -t47 * t209 + t116 * t425 - 0.8e1 * t427 * t275 + 0.8e1 * t431 * t433 - 0.2e1 * t253 * t437 - 0.8e1 * t442 * t53 - 0.2e1 * t446 * t448 + 0.2e1 * t175 * t312 + 0.6e1 * t453 * t129 * t208 + 0.8e1 * t115 * t18 * t458 * t30 + 0.8e1 * t462 * t463;
1823:   t470 = t436 * t58;
1824:   t475 = t2 * t121 * t440 * t25;
1825:   t485 = t212 * t73;
1826:   t488 = t67 * t72 * t1;
1827:   t490 = t39 * xc;
1828:   t501 = 0.4e1 * t374 * t355 * t52 + 0.2e1 * t446 * t470 - 0.8e1 * t475 * t53 - 0.2e1 * t446 * t437 - 0.4e1 * t36 * t38 * t39 * t15 * t12 - t116 * t485 + 0.8e1 * t488 * 0.3141592654e1 * t12 * t490 - t207 * t183 - 0.2e1 * t182 * t232 - 0.6e1 * t413 * t245 - 0.4e1 * t413 * t382;
1829:   t503 = t115 * t8;
1830:   t510 = t355 * t19;
1831:   t513 = t432 * t208;
1832:   t525 = t38 * t40 * t18;
1833:   t533 = -0.4e1 * t503 * t216 - 0.4e1 * t89 * t90 * t92 * t15 - 0.16e2 * t462 * t510 + 0.8e1 * t431 * t513 - 0.4e1 * t78 * t131 + t47 * t183 - 0.2e1 * t67 * t83 * t99 + 0.4e1 * t331 * t225 + 0.16e2 * t260 * t525 - 0.4e1 * t89 * t90 * t237 * t58 - t207 * t53;
1834:   t536 = t28 * t37;
1835:   t538 = t490 * t100;
1836:   t541 = t334 * t441;
1837:   t547 = t394 * t30;
1838:   t550 = t212 * t19;
1839:   t553 = t366 * t441;
1840:   t556 = nz * t17;
1841:   t571 = -0.8e1 * t427 * t131 + 0.16e2 * t394 * t536 * t538 + 0.16e2 * t541 * t336 + 0.2e1 * t453 * t129 * t158 - 0.8e1 * t547 * t147 + 0.4e1 * t503 * t550 - 0.8e1 * t553 * t270 + 0.4e1 * t556 * ZB * t92 * t39 - 0.2e1 * t67 * t91 * t99 - t82 * t425 + 0.4e1 * t78 * t275 + 0.2e1 * t78 * xc * t41 * t57;
1842:   t583 = t90 * t317;
1843:   t594 = t212 * t158;
1844:   t596 = t152 * t67;
1845:   t602 = t67 * t17;
1846:   t607 = 0.8e1 * t367 * t407 - 0.4e1 * t98 * t99 * t59 + 0.16e2 * t260 * t18 * ZA * t57 + 0.2e1 * t321 * t583 - 0.6e1 * t174 * t368 * t52 - 0.4e1 * t89 * t90 * ZA * t15 * t12 + t116 * t594 - 0.8e1 * t596 * t136 - 0.4e1 * t98 * t99 * t327 + 0.2e1 * t602 * t99 + 0.2e1 * t164 * t583;
1847:   t613 = t83 * t25;
1848:   t616 = t81 * t156;
1849:   t627 = t90 * t231;
1850:   t630 = t91 * t16;
1851:   t638 = 0.4e1 * t196 * t90 * t208 - 0.8e1 * t130 * t60 - 0.2e1 * t613 * t99 + 0.6e1 * t616 * t197 - 0.8e1 * t547 * t131 + 0.8e1 * t67 * t18 * t37 * t142 + 0.2e1 * t145 * t328 - 0.6e1 * t196 * t627 + 0.8e1 * t630 * t67 * t142 - 0.8e1 * t547 * t275 + 0.8e1 * t395 * t209;
1852:   t643 = t77 * t355;
1853:   t648 = t115 * t458;
1854:   t651 = t134 * t67;
1855:   t657 = t30 * t304;
1856:   t660 = t30 * t146;
1857:   t665 = t25 * t17;
1858:   t668 = t50 * t424;
1859:   t671 = -0.4e1 * t321 * t90 * t146 - 0.6e1 * t643 * t232 + 0.8e1 * t182 * t209 - 0.16e2 * t648 * t510 + 0.8e1 * t651 * t136 + 0.8e1 * t89 * t4 * t100 - 0.2e1 * t374 * t657 - 0.8e1 * t648 * t660 + 0.8e1 * t130 * t328 + 0.2e1 * t665 * t99 + 0.2e1 * t346 * t668;
1860:   t672 = t90 * t424;
1861:   t676 = t120 * t536;
1862:   t680 = t436 * t41;
1863:   t688 = t366 * t67 * t440;
1864:   t696 = xc * t12;
1865:   t697 = t696 * t18;
1866:   t701 = t252 * t141;
1867:   t702 = t90 * t221;
1868:   t705 = 0.2e1 * t196 * t672 - t47 * t347 + 0.16e2 * t676 * t538 - t116 * t85 - 0.2e1 * t253 * t680 + t207 * t194 + 0.4e1 * t98 * t99 * t19 - 0.8e1 * t688 * t433 + 0.16e2 * t541 * t301 - 0.6e1 * t312 * t190 + 0.4e1 * t352 * t88 * t35 * t697 + 0.2e1 * t701 * t702;
1869:   t712 = t24 * t430;
1870:   t713 = t28 * t49;
1871:   t721 = t1 * t17 * t11;
1872:   t726 = ZB * xc;
1873:   t737 = nz * t91;
1874:   t741 = 0.8e1 * t346 * t209 + 0.2e1 * t712 * t713 * t424 + 0.8e1 * t130 * t275 - t47 * t668 + t116 * t721 - 0.8e1 * t688 * t513 + 0.4e1 * t352 * t27 * t212 * t726 + 0.8e1 * t648 * t463 + 0.4e1 * t274 * t60 - 0.4e1 * t374 * t355 * t208 - 0.4e1 * t253 * t737 * t41;
1875:   t745 = t269 * t231;
1876:   t749 = t1 * t28 * t265;
1877:   t757 = t16 * t39;
1878:   t758 = t696 * t757;
1879:   t762 = t69 * t49;
1880:   t772 = t355 * t100;
1881:   t775 = t81 * t353;
1882:   t778 = -0.8e1 * t398 * t90 * t190 - 0.2e1 * t278 * t745 + 0.4e1 * t749 * t53 + 0.32e2 * t394 * t29 * t28 * t17 * t40 - 0.8e1 * t78 * t758 + t350 * nz * t762 - 0.6e1 * t87 * t49 * t186 * t52 - 0.8e1 * t553 * t407 - 0.4e1 * t749 * t209 + 0.16e2 * t648 * t772 - 0.6e1 * t775 * t375;
1883:   t790 = t212 * t304;
1884:   t793 = t156 * 0.3141592654e1;
1885:   t795 = t355 * t304;
1886:   t800 = t91 * t39;
1887:   t801 = t800 * nz;
1888:   t807 = t2 * t28;
1889:   t808 = t807 * t726;
1890:   t811 = -0.2e1 * t616 * t672 - 0.2e1 * t446 * t680 - 0.2e1 * t78 * xc * t58 * t57 + 0.8e1 * t367 * t270 - t82 * t790 + t115 * t51 * t793 - 0.2e1 * t775 * t795 + 0.8e1 * t123 * t209 + 0.2e1 * t665 * t801 - 0.2e1 * t67 * t41 * t64 - 0.32e2 * t808 * t43;
1891:   t812 = t117 * t51;
1892:   t821 = t24 * t355;
1893:   t827 = t90 * t304;
1894:   t840 = t800 * t41;
1895:   t844 = -t116 * t812 - 0.2e1 * t110 * t25 * t58 * t57 - 0.4e1 * t78 * t328 + t82 * t485 - 0.4e1 * t821 * t407 + 0.4e1 * t196 * t90 * t52 + 0.2e1 * t196 * t827 + t82 * t325 + 0.2e1 * t253 * t448 - 0.32e2 * t402 * t67 * t807 * t490 - t207 * t232 + 0.12e2 * t186 * t90 * ZB * t37 * t840;
1896:   t849 = t1 * t51;
1897:   t850 = t849 * t17;
1898:   t860 = t269 * t424;
1899:   t863 = t273 * t187;
1900:   t874 = 0.16e2 * t462 * t772 - t116 * t850 + 0.16e2 * t553 * t371 + t116 * t288 - 0.12e2 * t97 * t57 * t109 * t697 + t82 * t594 - 0.2e1 * t278 * t860 - 0.2e1 * t863 * t305 - 0.16e2 * t180 * t259 * t311 * t201 - 0.6e1 * t863 * t74 + 0.8e1 * t174 * t191;
1901:   t879 = xc * ZA;
1902:   t888 = t67 * t51;
1903:   t901 = ZA * t17;
1904:   t903 = t368 * t901 * t11;
1905:   t908 = -0.2e1 * t352 * t51 * t156 * t35 + 0.64e2 * t879 * t189 * t807 * t40 + 0.2e1 * t46 * t58 * t37 * t39 - t888 * t50 + t105 * t411 - 0.16e2 * t335 * t301 + 0.8e1 * t152 * t25 * t136 - 0.8e1 * t278 * t407 + 0.2e1 * t712 * t713 * t231 - 0.16e2 * t367 * t903 + 0.2e1 * t145 * t318;
1906:   t923 = t71 * t424;
1907:   t926 = t87 * t458;
1908:   t927 = t28 * ZA;
1909:   t944 = 0.8e1 * t354 * t355 * t190 - 0.8e1 * t110 * t16 * t25 * t800 - 0.2e1 * t374 * t30 * t73 - 0.16e2 * t354 * t30 * t176 - 0.2e1 * t244 * t923 - 0.32e2 * t926 * t927 * t696 * t41 - 0.32e2 * t808 * t525 + 0.6e1 * t749 * t232 - 0.8e1 * t188 * t177 + 0.4e1 * t36 * t58 * ZA * t57 + 0.4e1 * t821 * t270;
1910:   t948 = t90 * t327;
1911:   t961 = t30 * t100;
1912:   t964 = t29 * t49;
1913:   t981 = t106 * t1;
1914:   t983 = -0.2e1 * t219 * t220 * t100 + 0.2e1 * t321 * t948 - 0.16e2 * t189 * ZA * t99 * t12 - 0.2e1 * t369 * nz * t69 * t368 + 0.2e1 * t374 * t795 - 0.8e1 * t462 * t961 - 0.8e1 * t244 * t964 * t208 + 0.2e1 * t413 * t923 + 0.4e1 * t36 * t38 * t40 * t58 - 0.2e1 * t87 * t51 * t49 * t1 * ZA + t888 * nz * t762 + t115 * t981;
1915:   t1012 = 0.6e1 * t616 * t627 - t82 * t213 + 0.2e1 * t775 * t657 - 0.12e2 * t215 * t550 - 0.6e1 * t145 * t131 + 0.2e1 * t81 * t41 * t204 + 0.6e1 * ZB * t48 * t49 * t370 - 0.4e1 * t70 * t382 + 0.2e1 * t446 * t255 + 0.8e1 * t89 * t4 * t327 - 0.4e1 * t56 * t147;
1916:   t1018 = t212 * t100;
1917:   t1029 = t212 * t327;
1918:   t1040 = 0.6e1 * t70 * t245 + 0.2e1 * t56 * t328 + t207 * t668 + 0.4e1 * t503 * t1018 + 0.2e1 * t253 * t470 - 0.6e1 * t398 * t35 * t208 - 0.8e1 * t331 * t964 * t52 - 0.4e1 * t503 * t1029 + 0.6e1 * t821 * t745 + 0.4e1 * t63 * t37 * t142 + 0.16e2 * t260 * t38 * t840;
1919:   t1068 = t207 * t347 - 0.2e1 * t164 * t702 - 0.2e1 * t331 * t964 * t73 + 0.8e1 * t374 * t30 * t52 + 0.16e2 * t278 * t903 + 0.2e1 * t863 * t923 + 0.6e1 * t445 * t141 * t165 - 0.2e1 * t164 * t90 * t100 + 0.6e1 * t331 * t74 - 0.2e1 * t182 * t668 - 0.2e1 * t115 * t41 * t204;
1920:   t1079 = t58 * t8;
1921:   t1091 = t807 * t29;
1922:   t1092 = t665 * t40;
1923:   t1101 = ZB * t91;
1924:   t1102 = t403 * nz;
1925:   t1105 = -0.4e1 * t58 * ZB * ZA * t64 - t82 * t850 + 0.2e1 * t821 * t860 + t81 * t51 * t793 + 0.2e1 * t3 * t25 * t1079 * t90 + t82 * t721 - 0.2e1 * t643 * t668 + 0.16e2 * t926 * t927 * t29 * t91 * t41 + 0.32e2 * t1091 * t1092 - 0.2e1 * t219 * t220 * t19 + 0.4e1 * t139 * ZA * t64 + 0.4e1 * t1101 * t1102;
1926:   t1108 = t849 * t72;
1927:   t1121 = t737 * t15;
1928:   t1124 = t29 * t12;
1929:   t1133 = t116 * t1108 - 0.8e1 * t475 * t209 - 0.32e2 * t807 * xc * t1092 + 0.2e1 * t278 * t269 * t73 + t82 * t812 - 0.6e1 * t56 * t131 + 0.2e1 * t253 * t1121 + 0.16e2 * t926 * t927 * t1124 * t41 + t168 * t263 - 0.2e1 * t616 * t827 + t81 * t981;
1930:   t1134 = t394 * t28;
1931:   t1159 = -0.8e1 * t1134 * t29 * t18 * t57 + t82 * t118 - 0.12e2 * t215 * t1018 + 0.2e1 * t602 * t801 - t168 * t341 + 0.2e1 * t67 * t58 * t64 + t168 * t344 - 0.6e1 * t174 * t368 * t208 + 0.16e2 * t553 * t903 + t116 * t790 - 0.4e1 * t36 * t38 * t800 * t15;
1932:   t1161 = nz * t83;
1933:   t1173 = ZB * t12;
1934:   t1196 = 0.4e1 * t1161 * ZB * t39 * ZA - 0.4e1 * t215 * t1029 - 0.8e1 * t488 * 0.3141592654e1 * t39 * xc + 0.32e2 * t821 * ZA * t8 * t1173 * t18 - 0.8e1 * t427 * t147 + 0.6e1 * t701 * t165 - 0.16e2 * t926 * t927 * t1124 * t18 - 0.8e1 * t1091 * t63 * t57 - 0.8e1 * t442 * t209 - 0.8e1 * t462 * t660 - 0.6e1 * t398 * t35 * t52;
1935:   t1228 = 0.2e1 * t413 * t305 - 0.8e1 * t648 * t961 - 0.16e2 * t87 * t27 * t23 * t28 * ZA * t29 + 0.4e1 * t189 * t1102 - 0.4e1 * t87 * t1079 * t212 * t879 + 0.2e1 * t164 * t948 - 0.2e1 * t70 * t923 + 0.2e1 * t164 * t322 + 0.2e1 * t446 * t1121 + 0.2e1 * t863 * t964 * t304 - t82 * t1108 + 0.16e2 * t676 * t490 * t19;
1936:   t1234 = t25 * ZB;
1937:   t1235 = t1234 * t28;
1938:   t1236 = t365 * t91;
1939:   t1240 = ZB * t121;
1940:   t1241 = t1240 * t77;
1941:   t1242 = t39 * t39;
1942:   t1243 = t12 * t1242;
1943:   t1244 = xc * t72;
1944:   t1245 = t1243 * t1244;
1945:   t1248 = t365 * t25;
1946:   t1252 = t243 * nz;
1947:   t1257 = t23 * t1;
1948:   t1258 = t1240 * t1257;
1949:   t1259 = t67 * t12;
1950:   t1260 = xc * t16;
1951:   t1268 = t1234 * t121;
1952:   t1269 = t1268 * t23;
1953:   t1272 = t1242 * t91;
1954:   t1280 = t67 * xc;
1955:   t1284 = t28 * t28;
1956:   t1285 = t67 * t1284;
1957:   t1287 = t1285 * t2 * ZB;
1958:   t1288 = t17 * xc;
1959:   t1289 = t1243 * t1288;
1960:   t1292 = 0.2e1 * t1235 * t1236 * t17 + 0.8e1 * t1241 * t1245 + 0.4e1 * t927 * t1248 * t91 - 0.2e1 * t1252 * ZB * t1242 * t91 - 0.8e1 * t1258 * t1259 * t1260 - 0.4e1 * t1235 * t2 * t83 * t39 + 0.16e2 * t1269 * t758 + 0.2e1 * t1252 * t189 * t1272 - 0.2e1 * t1252 * t83 * t1242 * ZB + 0.8e1 * t1258 * t630 * t1280 - 0.32e2 * t1287 * t1289;
1961:   t1293 = t365 * t83;
1962:   t1300 = ZA * t1284;
1963:   t1304 = t17 * t1242 * t25 * t12;
1964:   t1307 = t927 * t2;
1965:   t1311 = t23 * t2;
1966:   t1312 = t1300 * t1311;
1967:   t1316 = t1234 * t1284;
1968:   t1317 = t1316 * t1311;
1969:   t1321 = t1240 * t23;
1970:   t1331 = t1240 * t23 * t67;
1971:   t1332 = t40 * t1244;
1972:   t1338 = t1243 * t1260;
1973:   t1344 = -0.2e1 * t1235 * t1293 - 0.16e2 * t181 * t365 * t901 * t12 - 0.64e2 * t1300 * t258 * t1304 + 0.8e1 * t1307 * t613 * t39 + 0.64e2 * t1312 * t265 * t402 - 0.32e2 * t1317 * t1288 * t12 - 0.16e2 * t1321 * t67 * t39 * t1244 + 0.2e1 * t1235 * nz * t1272 * t17 + 0.16e2 * t1331 * t1332 + 0.64e2 * t1300 * t292 * t1304 - 0.8e1 * t1241 * t1338 - 0.2e1 * t243 * t1293 * ZB;
1974:   t1346 = t1316 * t2;
1975:   t1349 = t927 * nz;
1976:   t1350 = t25 * t1242;
1977:   t1354 = t1268 * t1257;
1978:   t1366 = t1268 * t1;
1979:   t1370 = t29 * t17;
1980:   t1371 = t1243 * t1370;
1981:   t1386 = -0.32e2 * t1346 * t1289 + 0.4e1 * t1349 * t1350 * t91 + 0.8e1 * t1354 * t1260 * t12 - 0.16e2 * t181 * nz * t901 * t1243 - 0.4e1 * t1235 * t2 * t91 * t39 + 0.8e1 * t1366 * t152 * t1242 + 0.32e2 * t1287 * t1371 + 0.8e1 * t1258 * t1280 * t152 - 0.8e1 * t1354 * t1260 * t91 + 0.128e3 * t1300 * t365 * xc * t1092 + 0.8e1 * t1366 * t1338;
1982:   t1387 = t1257 * t12;
1983:   t1391 = t1240 * t1;
1984:   t1399 = t1272 * t1260;
1985:   t1412 = t1285 * t1311;
1986:   t1427 = -0.8e1 * t1268 * t1387 * t16 - 0.8e1 * t1391 * t67 * t1242 * t1244 - 0.4e1 * t1134 * t1101 * t39 + 0.8e1 * t1241 * t1399 - 0.8e1 * t1258 * t596 + 0.4e1 * t927 * t1293 * t25 - 0.16e2 * t1331 * t758 + 0.8e1 * t1307 * t665 * t39 + 0.32e2 * t1412 * t1370 * t1173 + 0.8e1 * t1307 * t665 * t800 + 0.8e1 * t1391 * t1259 * t1242 * t16 - 0.8e1 * t1391 * t1259 * t1242 * t72;
1987:   t1456 = t365 * ZB;
1988:   t1468 = 0.4e1 * t927 * t1248 * t17 - 0.2e1 * t1235 * nz * t1242 * t91 + 0.8e1 * t1366 * t1244 * t1242 - 0.16e2 * t1269 * t134 * t39 + 0.8e1 * t1268 * t1257 * t72 * xc + 0.16e2 * t1321 * t1259 * t757 + 0.32e2 * t1317 * t1370 * t12 + 0.4e1 * t1349 * t613 * t1242 + 0.2e1 * t243 * t1456 * t17 - 0.64e2 * t1285 * t365 * t12 * t189 * t490 - 0.8e1 * t1354 * t152 * xc;
1989:   t1472 = t1316 * t365;
1990:   t1474 = t1124 * t39 * t17;
1991:   t1478 = t17 * t91;
1992:   t1504 = t72 * t39;
1993:   t1511 = 0.4e1 * t1134 * t189 * t800 + 0.64e2 * t1472 * t1474 + 0.4e1 * t1235 * t2 * t1478 * t39 + 0.4e1 * t1349 * t665 * t1242 - 0.8e1 * t1258 * t1280 * t72 + 0.2e1 * t1252 * t189 * t1242 + 0.2e1 * t243 * t365 * t189 * t91 + 0.4e1 * t927 * t365 * t1478 * t25 - 0.128e3 * t1300 * t1248 * t1474 - 0.2e1 * t1235 * t1236 + 0.16e2 * t1269 * t1504 * xc + 0.2e1 * t1235 * t365 * t17;
1994:   t1545 = -0.2e1 * t1235 * t1161 * t1242 + 0.4e1 * t1349 * t1350 * t1478 - 0.8e1 * t1366 * t1245 + 0.2e1 * t1235 * t556 * t1242 - 0.32e2 * t1412 * t402 * t726 - 0.8e1 * t1366 * t1399 + 0.8e1 * t1258 * t651 - 0.2e1 * t243 * t1456 * t91 + 0.8e1 * t1268 * t1387 * t72 - 0.16e2 * t1269 * t1332 + 0.4e1 * t1134 * t189 * t39 + 0.16e2 * t1269 * t152 * t39;
1995:   t1564 = t1260 * t800;
1996:   t1583 = 0.64e2 * t1285 * t1456 * t1474 - 0.64e2 * t1472 * t1288 * t40 - 0.8e1 * t1366 * t134 * t1242 + 0.8e1 * t1307 * t362 * t39 + 0.4e1 * t1235 * t2 * t17 * t39 + 0.32e2 * t1346 * t1371 - 0.16e2 * t1269 * t1564 - 0.16e2 * t1321 * t1259 * t1504 + 0.16e2 * t1331 * t1564 - 0.64e2 * t1312 * t29 * t25 * t402 - 0.4e1 * t1134 * t83 * t39 * ZB - 0.32e2 * t181 * t2 * t404;

1998:   _PC2B = (t1133 + t1196 + t1068 + t811 + t466 + t1012 + t381 + t162 + t249 + t533 + t844 + t104 + t1159 + t571 + t211 + t874 + t607 + t339 + t296 + t638 + t908 + t671 + t419 + t983 + t705 + t1105 + t501 + t778 + t1040 + t1228 + t741 + t944) / (t1292 + t1344 + t1386 + t1427 + t1468 + t1511 + t1545 + t1583);
1999:   /****************************************************************************************/
2000:   t1   = nz * nz;
2001:   t2   = t1 * nz;
2002:   t3   = t2 * nx;
2003:   t4   = nx * 0.3141592654e1;
2004:   t5   = t4 * xc;
2005:   t6   = PetscSinReal(t5);
2006:   t7   = 0.3141592654e1 * 0.3141592654e1;
2007:   t9   = t3 * t6 * t7;
2008:   t10  = xc * xc;
2009:   t11  = ZA * ZA;
2010:   t12  = t10 * t11;
2011:   t13  = nz * 0.3141592654e1;
2012:   t14  = PetscExpReal(t13);
2013:   t15  = t14 * t14;
2014:   t16  = xc * nz;
2015:   t18  = PetscExpReal(t16 * 0.3141592654e1);
2016:   t19  = t18 * t18;
2017:   t20  = t19 * t18;
2018:   t21  = t15 * t20;
2019:   t22  = t12 * t21;
2020:   t25  = nx * t6;
2021:   t26  = t1 * 0.3141592654e1;
2022:   t27  = t25 * t26;
2023:   t28  = ZA * ZB;
2024:   t29  = t18 * t15;
2025:   t30  = t28 * t29;
2026:   t33  = t25 * nz;
2027:   t34  = t11 * t15;
2028:   t35  = t19 * t19;
2029:   t36  = t35 * t18;
2030:   t40  = t25 * t1;
2031:   t41  = 0.3141592654e1 * t11;
2032:   t42  = t15 * t36;
2033:   t43  = t41 * t42;
2034:   t46  = nx * nx;
2035:   t47  = t1 * t46;
2036:   t48  = t47 * t11;
2037:   t49  = t7 * xc;
2038:   t50  = t35 * t15;
2039:   t51  = t49 * t50;
2040:   t55  = PetscSinReal(t4);
2041:   t56  = t46 * nx * t55;
2042:   t58  = t56 * nz * t7;
2043:   t59  = ZB * ZB;
2044:   t60  = t10 * t59;
2045:   t61  = t15 * t14;
2046:   t62  = t19 * t61;
2047:   t63  = t60 * t62;
2048:   t66  = t19 * t14;
2049:   t67  = t60 * t66;
2050:   t70  = t28 * t42;
2051:   t73  = PetscCosReal(t5);
2052:   t74  = t47 * t73;
2053:   t75  = t7 * t11;
2054:   t77  = t75 * t10 * t36;
2055:   t80  = t73 * t46;
2056:   t81  = t80 * nz;
2057:   t82  = 0.3141592654e1 * t59;
2058:   t83  = t82 * t42;
2059:   t87  = xc * t11;
2060:   t88  = t87 * t62;
2061:   t91  = nz * nx;
2062:   t92  = t55 * t61;
2063:   t96  = nx * t55;
2064:   t98  = t96 * t2 * t7;
2065:   t101 = xc * t59;
2066:   t102 = t101 * t62;
2067:   t108 = t1 * t1;
2068:   t109 = t108 * t7;
2069:   t111 = t59 * t35;
2070:   t112 = t111 * t15;
2071:   t115 = t35 * t20;
2072:   t123 = t1 * nx * t55;
2073:   t124 = t61 * t35;
2074:   t127 = t35 * t19;
2075:   t128 = t61 * t127;
2076:   t129 = t60 * t128;
2077:   t132 = t56 * t16;
2078:   t133 = t7 * t59;
2079:   t134 = t133 * t124;
2080:   t137 = 0.6e1 * t58 * t88 - 0.2e1 * t91 * t92 * t11 + 0.2e1 * t98 * t63 - 0.6e1 * t58 * t102 - 0.2e1 * t91 * t92 * t59 - 0.16e2 * t109 * xc * t112 - 0.2e1 * t91 * t6 * t115 * t59 + 0.12e2 * t40 * t83 + t123 * t41 * t124 - 0.2e1 * t58 * t129 + 0.4e1 * t132 * t134;
2081:   t139 = t56 * 0.3141592654e1;
2082:   t140 = t111 * t14;
2083:   t144 = t49 * t124;
2084:   t147 = t91 * t55;
2085:   t148 = t61 * ZA;
2086:   t154 = ZA * t115 * xc * ZB;
2087:   t157 = t7 * 0.3141592654e1;
2088:   t159 = t96 * t108 * t157;
2089:   t160 = t10 * xc;
2090:   t161 = t160 * t59;
2091:   t162 = t35 * t14;
2092:   t163 = t161 * t162;
2093:   t166 = t28 * t162;
2094:   t169 = t80 * t13;
2095:   t170 = t101 * t42;
2096:   t173 = t2 * t11;
2097:   t174 = t96 * t173;
2098:   t175 = t7 * t10;
2099:   t179 = t59 * t15;
2100:   t184 = t15 * t15;
2101:   t193 = t139 * t140 + 0.4e1 * t56 * nz * t11 * t144 + 0.4e1 * t147 * t148 * ZB + 0.4e1 * t27 * t154 + 0.8e1 * t159 * t163 - 0.12e2 * t147 * t166 + 0.2e1 * t169 * t170 - 0.16e2 * t174 * t175 * t124 + 0.2e1 * t33 * t179 * t20 - 0.2e1 * t33 * t11 * t36 * t184 + 0.2e1 * t56 * t61 * 0.3141592654e1 * ZA * ZB;
2102:   t194 = t173 * 0.3141592654e1;
2103:   t195 = xc * t15;
2104:   t196 = t195 * t19;
2105:   t202 = t15 * t115;
2106:   t203 = t28 * t202;
2107:   t206 = t96 * t26;
2108:   t207 = t14 * t127;
2109:   t208 = t101 * t207;
2110:   t211 = t12 * t128;
2111:   t218 = t11 * t61;
2112:   t219 = t218 * t35;
2113:   t221 = t108 * ZA;
2114:   t223 = t7 * ZB;
2115:   t224 = t223 * t50;
2116:   t227 = ZA * xc;
2117:   t228 = ZB * t15;
2118:   t229 = t228 * t36;
2119:   t230 = t227 * t229;
2120:   t233 = t87 * t207;
2121:   t236 = t6 * t11;
2122:   t240 = -0.4e1 * t194 * t196 + 0.4e1 * t194 * t195 * t127 + 0.4e1 * t33 * t203 - 0.12e2 * t206 * t208 + 0.2e1 * t58 * t211 - 0.16e2 * t47 * t10 * t133 * t50 + t139 * t219 - 0.32e2 * t221 * t10 * t224 - 0.4e1 * t169 * t230 - 0.6e1 * t98 * t233 + 0.2e1 * t91 * t236 * t20;
2123:   t244 = t227 * t228 * t20;
2124:   t252 = t184 * t18;
2125:   t253 = t101 * t252;
2126:   t256 = t35 * t35;
2127:   t257 = t256 * t14;
2128:   t258 = t28 * t257;
2129:   t261 = t108 * t11;
2130:   t263 = t7 * t35;
2131:   t268 = ZB * t61 * t35;
2132:   t273 = t96 * t108 * t160;
2133:   t274 = t157 * ZB;
2134:   t276 = t274 * t148 * t35;
2135:   t279 = t101 * t21;
2136:   t282 = 0.3141592654e1 * xc;
2137:   t283 = t59 * t36;
2138:   t284 = t282 * t283;
2139:   t289 = 0.4e1 * t169 * t244 - 0.4e1 * t132 * t133 * t162 - 0.2e1 * t147 * t140 - 0.2e1 * t27 * t253 + 0.2e1 * t139 * t258 + 0.16e2 * t261 * t10 * t263 * t15 - 0.16e2 * t206 * t227 * t268 - 0.16e2 * t273 * t276 - 0.6e1 * t27 * t279 - 0.4e1 * t40 * t284 - 0.32e2 * t9 * t230;
2140:   t290 = t1 * t11;
2141:   t291 = t96 * t290;
2142:   t297 = t59 * t61;
2143:   t298 = t297 * t127;
2144:   t300 = ZB * t36;
2145:   t301 = t227 * t300;
2146:   t304 = t1 * t59;
2147:   t305 = t184 * t35;
2148:   t310 = t46 * ZB;
2149:   t311 = t184 * ZA;
2150:   t312 = t310 * t311;
2151:   t314 = t60 * t21;
2152:   t317 = t1 * ZA;
2153:   t318 = ZB * t35;
2154:   t321 = t1 * t256;
2155:   t324 = t96 * t261;
2156:   t325 = t10 * t157;
2157:   t326 = t325 * t124;
2158:   t329 = -0.4e1 * t291 * t282 * t128 + t123 * t82 * t62 - t139 * t298 + 0.12e2 * t27 * t301 + t304 * t305 - 0.2e1 * t58 * t12 * t66 - 0.2e1 * t312 + 0.8e1 * t9 * t314 + 0.2e1 * t317 * t318 + 0.2e1 * t321 * t28 - 0.8e1 * t324 * t326;
2159:   t331 = t28 * t124;
2160:   t334 = 0.3141592654e1 * t15;
2161:   t335 = t334 * t127;
2162:   t338 = t35 * ZA;
2163:   t341 = t46 * t256;
2164:   t344 = t46 * t11;
2165:   t346 = t46 * t59;
2166:   t348 = t297 * t35;
2167:   t351 = ZA * t10;
2168:   t352 = t351 * t300;
2169:   t355 = t1 * ZB;
2170:   t362 = 0.12e2 * t147 * t331 - 0.4e1 * t173 * t335 - 0.2e1 * t310 * t338 - 0.2e1 * t341 * t28 - t344 * t305 - t346 * t305 + 0.2e1 * t147 * t348 + 0.16e2 * t9 * t352 + 0.2e1 * t355 * t311 + t290 * t305 + 0.2e1 * t33 * t34 * t20;
2171:   t363 = t36 * t184;
2172:   t364 = t87 * t363;
2173:   t368 = t47 * t73 * t7;
2174:   t373 = t160 * t157;
2175:   t374 = t373 * t124;
2176:   t377 = t311 * t35;
2177:   t380 = t12 * t62;
2178:   t386 = ZB * t10 * ZA * t15 * t20;
2179:   t389 = t87 * t66;
2180:   t393 = t56 * t1 * t10;
2181:   t401 = 0.2e1 * t27 * t364 - 0.16e2 * t368 * t279 - t123 * t41 * t257 + 0.8e1 * t324 * t374 + 0.2e1 * t355 * t377 - 0.2e1 * t98 * t380 - 0.16e2 * t9 * t386 + 0.2e1 * t58 * t389 + 0.16e2 * t393 * t276 + t123 * t82 * t162 - 0.2e1 * t33 * t179 * t36;
2182:   t412 = t11 * t14 * t127;
2183:   t416 = t11 * t19;
2184:   t417 = t416 * t61;
2185:   t421 = t96 * t2 * ZA;
2186:   t426 = t56 * nz * ZA;
2187:   t427 = t318 * t14;
2188:   t428 = t49 * t427;
2189:   t431 = t82 * t29;
2190:   t434 = t87 * t21;
2191:   t442 = 0.2e1 * t33 * t11 * t184 * t18 + 0.4e1 * t81 * t284 - t139 * t412 + 0.2e1 * t147 * t219 - 0.2e1 * t147 * t417 + 0.32e2 * t421 * t175 * t268 + 0.8e1 * t426 * t428 + 0.4e1 * t81 * t431 - 0.2e1 * t169 * t434 - 0.2e1 * t98 * t129 - 0.32e2 * t47 * t28 * t51;
2192:   t443 = t184 * t20;
2193:   t447 = t61 * 0.3141592654e1;
2194:   t448 = t447 * t11;
2195:   t450 = t49 * t268;
2196:   t453 = t60 * t42;
2197:   t456 = t41 * t202;
2198:   t463 = t101 * t443;
2199:   t469 = t41 * xc * t20;
2200:   t474 = -0.8e1 * t27 * t87 * t443 - t56 * t448 - 0.8e1 * t426 * t450 + 0.8e1 * t368 * t453 + 0.4e1 * t40 * t456 + 0.4e1 * t40 * t431 - 0.4e1 * t81 * t456 - 0.4e1 * t27 * t463 + 0.6e1 * t139 * t331 + 0.2e1 * t40 * t469 - 0.16e2 * t9 * t434;
2201:   t482 = t108 * t10;
2202:   t492 = nz * t46;
2203:   t493 = t492 * t11;
2204:   t495 = t282 * t19 * t184;
2205:   t498 = t56 * t290;
2206:   t499 = t325 * t162;
2207:   t502 = t416 * t14;
2208:   t504 = t60 * t207;
2209:   t507 = -t123 * t82 * t257 - 0.4e1 * t169 * t301 + t123 * t41 * t162 + 0.16e2 * t482 * t7 * t112 - 0.12e2 * t206 * t102 - t123 * t82 * t66 - 0.4e1 * t147 * t258 - 0.4e1 * t493 * t495 - 0.8e1 * t498 * t499 + t139 * t502 - 0.2e1 * t98 * t504;
2210:   t508 = t101 * t162;
2211:   t512 = t41 * t115 * xc;
2212:   t515 = t87 * t42;
2213:   t520 = ZB * t184;
2214:   t522 = t227 * t520 * t18;
2215:   t525 = t492 * t59;
2216:   t528 = t6 * t59;
2217:   t532 = t520 * t20;
2218:   t533 = t351 * t532;
2219:   t539 = t447 * t59;
2220:   t544 = 0.8e1 * t206 * t508 - 0.2e1 * t40 * t512 - 0.16e2 * t368 * t515 + 0.12e2 * t206 * t88 + 0.4e1 * t27 * t522 + 0.4e1 * t525 * t495 - 0.4e1 * t91 * t528 * t36 - 0.16e2 * t368 * t533 - 0.16e2 * t206 * t227 * t427 - t56 * t539 - 0.2e1 * t132 * t133 * t66;
2221:   t551 = t87 * t162;
2222:   t554 = t351 * t229;
2223:   t560 = t59 * t19;
2224:   t561 = t560 * t14;
2225:   t564 = t101 * t202;
2226:   t567 = t87 * t252;
2227:   t573 = t227 * t228 * t115;
2228:   t578 = 0.4e1 * t33 * t70 + 0.4e1 * t493 * t335 - 0.4e1 * t58 * t551 + 0.16e2 * t9 * t554 - 0.4e1 * t33 * t28 * t252 + 0.2e1 * t147 * t561 + 0.2e1 * t169 * t564 - 0.2e1 * t27 * t567 - 0.8e1 * t324 * t499 - 0.4e1 * t169 * t573 + 0.12e2 * t27 * t244;
2229:   t579 = t82 * t202;
2230:   t591 = t282 * t115 * t59;
2231:   t598 = t101 * t66;
2232:   t606 = -0.4e1 * t81 * t579 - 0.2e1 * t169 * t567 - 0.6e1 * t27 * t170 + 0.8e1 * t169 * t203 + 0.2e1 * t98 * t67 + 0.2e1 * t81 * t591 + 0.32e2 * t368 * t244 - 0.2e1 * t27 * t564 + 0.4e1 * t206 * t598 + 0.16e2 * t9 * t170 + 0.2e1 * t33 * t283 * t184;
2233:   t608 = t373 * t162;
2234:   t611 = t59 * t184;
2235:   t617 = t101 * t29;
2236:   t624 = t227 * ZB * t18 * t15;
2237:   t629 = t157 * t59;
2238:   t630 = t629 * t124;
2239:   t633 = t3 * t6;
2240:   t634 = t175 * t283;
2241:   t644 = 0.8e1 * t498 * t608 + 0.2e1 * t33 * t611 * t18 - 0.4e1 * t206 * t389 - 0.2e1 * t27 * t617 - 0.4e1 * t169 * t154 + 0.4e1 * t27 * t624 + 0.12e2 * t27 * t230 - 0.8e1 * t393 * t630 - 0.8e1 * t633 * t634 + 0.16e2 * t47 * t7 * t101 * t50 + 0.2e1 * t123 * t447 * t28;
2242:   t645 = t41 * t29;
2243:   t648 = t2 * 0.3141592654e1;
2244:   t649 = t648 * xc;
2245:   t650 = t560 * t184;
2246:   t656 = t56 * t1 * t157;
2247:   t659 = t87 * t128;
2248:   t662 = t96 * t482;
2249:   t663 = t629 * t162;
2250:   t671 = t161 * t124;
2251:   t674 = t218 * t127;
2252:   t679 = 0.4e1 * t81 * t645 - 0.4e1 * t649 * t650 - 0.8e1 * t169 * t70 + 0.8e1 * t656 * t163 - 0.2e1 * t98 * t659 - 0.8e1 * t662 * t663 - 0.32e2 * t421 * t175 * t427 - 0.2e1 * t147 * t502 + 0.8e1 * t656 * t671 + 0.2e1 * t147 * t674 - 0.16e2 * t368 * t386;
2253:   t714 = t334 * t19;
2254:   t719 = t12 * t42;
2255:   t722 = t304 * t35 - t346 * t35 + t341 * t59 - t344 * t35 + t344 * t256 + t346 * t184 - 0.16e2 * t368 * t554 - 0.16e2 * t48 * t175 * t50 + 0.4e1 * t525 * t714 - 0.2e1 * t58 * t659 + 0.8e1 * t368 * t719;
2256:   t730 = xc * t19;
2257:   t735 = t59 * t256 * t14;
2258:   t752 = 0.4e1 * t173 * t714 - 0.6e1 * t27 * t515 - 0.16e2 * t9 * t279 + 0.4e1 * t194 * t730 * t184 - t139 * t735 - 0.4e1 * t492 * t127 * t82 * xc - 0.4e1 * t98 * t508 - t123 * t41 * t207 - 0.2e1 * t147 * t298 + 0.8e1 * t368 * t314 + 0.6e1 * t132 * t133 * t207;
2259:   t755 = t28 * t21;
2260:   t759 = t274 * t338 * t14;
2261:   t767 = t11 * t35;
2262:   t768 = t767 * t14;
2263:   t778 = t560 * t61;
2264:   t781 = -0.2e1 * t58 * t504 - 0.8e1 * t27 * t755 + 0.16e2 * t662 * t759 + 0.12e2 * t291 * t282 * t207 - 0.6e1 * t27 * t434 + t139 * t768 - 0.8e1 * t498 * t326 + 0.4e1 * t33 * t611 * t20 + 0.2e1 * t81 * t512 - t139 * t561 + 0.2e1 * t147 * t778;
2265:   t786 = t12 * t443;
2266:   t790 = t282 * t59 * t20;
2267:   t796 = t59 * t14 * t127;
2268:   t806 = t41 * t21;
2269:   t811 = -0.8e1 * t393 * t663 + 0.8e1 * t368 * t786 + 0.2e1 * t81 * t790 + 0.4e1 * t169 * t624 + t139 * t796 + 0.2e1 * t206 * t258 - 0.2e1 * t40 * t591 - 0.8e1 * t662 * t630 - 0.4e1 * t33 * t30 - 0.4e1 * t40 * t806 + 0.8e1 * t9 * t786;
2270:   t819 = t282 * t15 * t127;
2271:   t822 = t101 * t363;
2272:   t830 = t11 * t256 * t14;
2273:   t835 = t227 * t532;
2274:   t842 = 0.2e1 * t33 * t11 * t18 * t15 + t123 * t41 * t66 - 0.4e1 * t493 * t819 - 0.2e1 * t27 * t822 - 0.16e2 * t368 * t170 - 0.4e1 * t169 * t463 - t139 * t830 - 0.4e1 * t649 * t179 * t127 + 0.12e2 * t27 * t835 - 0.16e2 * t368 * t434 - 0.2e1 * t40 * t790;
2275:   t845 = t87 * t202;
2276:   t854 = t338 * t15;
2277:   t859 = t12 * t207;
2278:   t868 = t139 * t348 - 0.2e1 * t27 * t845 + 0.8e1 * t169 * t755 - 0.2e1 * t58 * t380 + 0.6e1 * t206 * t331 + 0.8e1 * t310 * t854 - 0.2e1 * t169 * t822 + 0.2e1 * t98 * t859 + 0.8e1 * t159 * t671 + 0.8e1 * t74 * t634 - 0.2e1 * t169 * t253;
2279:   t880 = t60 * t443;
2280:   t891 = t101 * t128;
2281:   t894 = -t123 * t539 - 0.2e1 * t147 * t796 + 0.32e2 * t368 * t230 + t139 * t674 - 0.16e2 * t98 * t60 * t124 + 0.32e2 * t9 * t244 + 0.8e1 * t368 * t880 - 0.8e1 * t40 * t41 * xc * t36 - t123 * t82 * t128 - 0.6e1 * t58 * t233 + 0.2e1 * t58 * t891;
2282:   t903 = t179 * t19;
2283:   t920 = t56 * t1 * t160;
2284:   t925 = -0.2e1 * t174 * t175 * t66 - 0.4e1 * t493 * t714 + 0.4e1 * t649 * t903 - 0.4e1 * t81 * t43 + t123 * t82 * t207 + 0.4e1 * t206 * t891 - 0.16e2 * t273 * t759 - 0.8e1 * t27 * t203 + 0.32e2 * t221 * ZB * t51 - 0.16e2 * t920 * t759 - 0.8e1 * t9 * t453;
2285:   t932 = t87 * t29;
2286:   t945 = t82 * t21;
2287:   t953 = -0.16e2 * t920 * t276 - 0.8e1 * t169 * t30 - 0.8e1 * t633 * t77 - 0.2e1 * t27 * t932 - 0.4e1 * t174 * t49 * t162 + 0.8e1 * t206 * t87 * t124 - 0.2e1 * t147 * t768 + 0.4e1 * t169 * t522 - 0.12e2 * t81 * t945 + 0.4e1 * t33 * t28 * t115 + 0.4e1 * t525 * t819;
2288:   t971  = t282 * t127;
2289:   t978  = -0.6e1 * t98 * t102 + 0.2e1 * t169 * t515 - 0.2e1 * t310 * t377 + 0.2e1 * t147 * t830 + 0.8e1 * t368 * t22 - 0.2e1 * t169 * t617 + 0.16e2 * t662 * t276 - 0.8e1 * t355 * t854 + 0.4e1 * t493 * t971 - 0.16e2 * t9 * t533 - 0.2e1 * t169 * t279;
2290:   t997  = xc * t127;
2291:   t998  = t997 * t59;
2292:   t1003 = 0.4e1 * t40 * t579 + 0.2e1 * t169 * t845 + 0.16e2 * t9 * t515 + 0.8e1 * t206 * t551 + t123 * t41 * t128 + 0.16e2 * t98 * t60 * t162 + 0.2e1 * t169 * t364 - 0.2e1 * t169 * t932 + t139 * t778 + 0.4e1 * t648 * t998 + 0.2e1 * t147 * t412;
2293:   t1006 = t2 * t59;
2294:   t1017 = xc * t35;
2295:   t1033 = 0.4e1 * t1006 * t335 + 0.4e1 * t81 * t806 - 0.2e1 * t33 * t34 * t115 + 0.8e1 * t498 * t374 - 0.16e2 * t261 * t7 * t1017 * t15 + 0.8e1 * t206 * t101 * t124 - t123 * t448 + 0.2e1 * t147 * t735 + 0.6e1 * t98 * t208 + 0.6e1 * t98 * t88 - 0.4e1 * t33 * t755;
2296:   t1055 = -0.4e1 * t173 * t971 + 0.2e1 * t98 * t891 + 0.8e1 * t9 * t880 + 0.4e1 * t169 * t835 - t304 * t184 + t344 * t184 - t123 * t41 * t62 - 0.2e1 * t98 * t598 + 0.2e1 * t58 * t859 + 0.32e2 * t47 * t351 * t224 + 0.2e1 * t98 * t389;
2297:   t1070 = t15 * t19;
2298:   t1089 = -0.16e2 * t368 * t352 - 0.8e1 * t9 * t719 + 0.4e1 * t96 * t2 * xc * t134 - 0.2e1 * t91 * t236 * t115 + 0.4e1 * t27 * t573 + 0.4e1 * t493 * t282 * t1070 + 0.2e1 * t33 * t59 * t18 * t15 + 0.12e2 * t40 * t945 - 0.4e1 * t492 * xc * t82 * t1070 - 0.2e1 * t91 * t528 * t20 + 0.8e1 * t324 * t608;
2299:   t1113 = t123 * t82 * t124 + 0.8e1 * t421 * t428 - t139 * t417 + 0.4e1 * t40 * t645 + 0.16e2 * t393 * t759 - 0.2e1 * t33 * t179 * t115 - 0.4e1 * t525 * t335 + 0.4e1 * t33 * t28 * t36 - 0.4e1 * t1006 * t714 + 0.6e1 * t206 * t166 - 0.8e1 * t421 * t450;
2300:   t1119 = t321 * t46;
2301:   t1122 = t157 * t11;
2302:   t1123 = t1122 * t2;
2303:   t1124 = t184 * t46;
2304:   t1128 = t108 * nz;
2305:   t1132 = t7 * t7;
2306:   t1133 = t1132 * t11;
2307:   t1134 = t1133 * t108;
2308:   t1135 = t15 * t46;
2309:   t1139 = t7 * ZA;
2310:   t1140 = t1139 * ZB;
2311:   t1141 = t1 * t35;
2312:   t1145 = t629 * t2;
2313:   t1146 = t1135 * t730;
2314:   t1149 = t157 * t1128;
2315:   t1150 = t1149 * xc;
2316:   t1153 = t46 * xc;
2317:   t1154 = t1153 * t127;
2318:   t1158 = t184 * t1 * t46;
2319:   t1161 = t46 * t46;
2320:   t1162 = t35 * t1161;
2321:   t1166 = t7 * t1;
2322:   t1170 = -0.4e1 * t133 * t1119 + 0.16e2 * t1123 * t1124 * t730 - 0.8e1 * t1122 * t1128 * t196 - 0.64e2 * t1134 * t1135 * t1017 - 0.32e2 * t1140 * t1141 * t1135 + 0.16e2 * t1145 * t1146 - 0.8e1 * t1150 * t650 - 0.16e2 * t1123 * t1154 - 0.4e1 * t133 * t1158 - 0.16e2 * t1140 * t1162 * t15 + 0.8e1 * t1166 * t35 * t312;
2323:   t1171 = t1161 * t184;
2324:   t1175 = t1122 * nz;
2325:   t1176 = t15 * t1161;
2326:   t1180 = t1132 * ZA;
2327:   t1181 = t1180 * t355;
2328:   t1182 = t1176 * t1017;
2329:   t1185 = t1161 * xc;
2330:   t1189 = t1133 * t1;
2331:   t1192 = t108 * t1;
2332:   t1193 = t1132 * t1192;
2333:   t1195 = t10 * t35;
2334:   t1199 = t157 * t15;
2335:   t1203 = t1141 * t46;
2336:   t1211 = t184 * t108;
2337:   t1218 = 0.2e1 * t133 * t1171 * t35 + 0.8e1 * t1175 * t1176 * t997 + 0.64e2 * t1181 * t1182 - 0.8e1 * t1175 * t1185 * t127 - 0.32e2 * t1189 * t1182 - 0.64e2 * t1193 * ZA * t1195 * t228 + 0.8e1 * t1199 * t416 * t1128 + 0.8e1 * t1140 * t1203 - 0.4e1 * t75 * t1158 - 0.8e1 * t1199 * t560 * t1128 - 0.2e1 * t133 * t1211 - 0.8e1 * t1199 * t127 * t11 * t1128;
2338:   t1221 = t256 * t1161;
2339:   t1224 = t35 * t108;
2340:   t1233 = t7 * t256;
2341:   t1236 = -t75 * t1211 - t75 * t1221 - t133 * t1221 + t75 * t1224 - t75 * t1171 - t133 * t1171 + t133 * t1224 + t75 * t1162 - t75 * t108 * t256 + t133 * t1162 - t1233 * t59 * t108;
2342:   t1240 = t1135 * t1195;
2343:   t1252 = t629 * t127;
2344:   t1263 = t1171 * ZA;
2345:   t1280 = -0.128e3 * t1180 * ZB * t108 * t1240 + 0.32e2 * t1193 * t10 * t112 + 0.4e1 * t133 * t1203 + 0.4e1 * t109 * t256 * ZA * ZB - 0.8e1 * t1252 * nz * t15 * t1185 + 0.8e1 * t1175 * t1171 * t730 - 0.8e1 * t1175 * t1176 * t127 + 0.4e1 * t223 * t1263 - 0.8e1 * t1175 * t1176 * t730 + 0.8e1 * t1166 * ZA * t341 * ZB + 0.64e2 * t1134 * t1240 + 0.8e1 * t1122 * xc * t1128 * t127 * t15;
2346:   t1283 = t1199 * t19;
2347:   t1287 = t1199 * t127;
2348:   t1289 = t59 * nz * t1161;
2349:   t1293 = t157 * nz * xc;
2350:   t1304 = t1132 * t108;
2351:   t1310 = t263 * ZB;
2352:   t1316 = t2 * t15;
2353:   t1323 = -0.16e2 * t1283 * t1006 * t46 + 0.8e1 * t1287 * t1289 + 0.8e1 * t1293 * t127 * t1161 * t59 + 0.16e2 * t1123 * t1135 * t19 + 0.8e1 * t1293 * t560 * t1176 + 0.64e2 * t1304 * t59 * t1240 + 0.4e1 * t75 * t1203 + 0.4e1 * t1310 * t1263 + 0.4e1 * t223 * t338 * t108 - 0.16e2 * t1252 * t1316 * t1153 - 0.16e2 * t1310 * t221 * t15;
2354:   t1330 = t1132 * t15;
2355:   t1336 = t1132 * t1;
2356:   t1338 = t1162 * t179;
2357:   t1370 = 0.8e1 * t1175 * t1176 * t19 + 0.4e1 * t1139 * t318 * t1161 + 0.128e3 * t1330 * t318 * t108 * t46 * t227 - 0.32e2 * t1336 * xc * t1338 + 0.4e1 * t1233 * ZA * t1161 * ZB - 0.8e1 * t1287 * t59 * t1128 * xc + 0.2e1 * t75 * t305 * t108 + 0.8e1 * t1199 * t127 * t59 * t1128 - 0.8e1 * t1283 * t1289 - 0.8e1 * t1293 * t560 * t1171 + 0.4e1 * t133 * t35 * t1158 + 0.8e1 * t157 * t184 * t19 * t11 * t1128 * xc;
2358:   t1376 = t7 * t184;
2359:   t1380 = t1176 * t1195;
2360:   t1393 = t1330 * t35;
2361:   t1411 = 0.16e2 * t1145 * t1154 + 0.8e1 * t1149 * t998 + 0.4e1 * t1376 * t35 * t48 + 0.32e2 * t1189 * t1380 + 0.32e2 * t1193 * t11 * t1195 * t15 - 0.64e2 * t1304 * xc * t111 * t1135 - 0.16e2 * t1123 * t1146 + 0.64e2 * t1393 * t28 * t1192 * xc - 0.16e2 * t1123 * t1135 * t127 - 0.8e1 * t1122 * xc * t1128 * t127 - 0.32e2 * t1193 * xc * t112 + 0.16e2 * t1252 * t1316 * t46;
2362:   t1450 = 0.2e1 * t1376 * t767 * t1161 + 0.2e1 * t1376 * t111 * t108 + 0.4e1 * t223 * t311 * t108 + 0.4e1 * t109 * t35 * t520 * ZA + 0.16e2 * t1123 * t1135 * t997 - 0.64e2 * t1181 * t1380 + 0.8e1 * t1150 * t903 - 0.32e2 * t1393 * t11 * t1192 * xc - 0.16e2 * t157 * t2 * xc * t560 * t1124 + 0.8e1 * t223 * t184 * t317 * t46 + 0.32e2 * t1336 * t10 * t1338 - 0.4e1 * t75 * t1119;
2363:   _PC3B = (t606 + t722 + t1089 + t781 + 0.16e2 * t48 * t51 + t978 + t868 + t507 - t304 * t256 + 0.8e1 * t9 * t22 + t752 + 0.4e1 * t174 * t144 - 0.2e1 * t81 * t469 + 0.6e1 * t139 * t166 + t362 + 0.2e1 * t98 * t211 + t925 + t137 - t290 * t184 + 0.12e2 * t81 * t83 + t842 + 0.8e1 * t74 * t77 + 0.16e2 * t98 * t12 * t162 - 0.4e1 * t33 * t28 * t443 - 0.8e1 * t27 * t70 - 0.2e1 * t33 * t34 * t36 - 0.8e1 * t27 * t30 + 0.2e1 * t58 * t67 - 0.4e1 * t40 * t43 + 0.2e1 * t58 * t63 + t1033 - t290 * t256 + t290 * t35 + t193 + t1113 + t578 + t442 + t474 + t544 + t329 + t679 + t401 + t953 + t811 + t644 + t894 + t289 + t240 + t1055 + t1003) / (t1170 + t1218 + 0.2e1 * t1236 + t1280 + t1323 + t1370 + t1411 + t1450);
2364:   /****************************************************************************************/
2365:   t1   = nz * nz;
2366:   t2   = t1 * xc;
2367:   t3   = ZB * ZB;
2368:   t5   = t2 * 0.3141592654e1 * t3;
2369:   t6   = nx * 0.3141592654e1;
2370:   t7   = t6 * xc;
2371:   t8   = PetscCosReal(t7);
2372:   t9   = nx * nx;
2373:   t10  = t8 * t9;
2374:   t11  = nz * 0.3141592654e1;
2375:   t12  = PetscExpReal(t11);
2376:   t13  = t12 * t12;
2377:   t16  = PetscExpReal(xc * nz * 0.3141592654e1);
2378:   t17  = t16 * t16;
2379:   t18  = t17 * t16;
2380:   t19  = t17 * t17;
2381:   t20  = t19 * t18;
2382:   t21  = t13 * t20;
2383:   t22  = t10 * t21;
2384:   t25  = ZA * ZA;
2385:   t26  = t1 * t25;
2386:   t27  = xc * 0.3141592654e1;
2387:   t28  = t26 * t27;
2388:   t29  = t19 * t16;
2389:   t30  = t13 * t13;
2390:   t31  = t29 * t30;
2391:   t35  = t9 * nx;
2392:   t36  = t3 * t35;
2393:   t37  = PetscSinReal(t6);
2394:   t38  = t13 * t12;
2395:   t39  = t37 * t38;
2396:   t40  = t39 * t19;
2397:   t42  = t1 * t1;
2398:   t43  = nx * t42;
2399:   t44  = xc * xc;
2400:   t45  = t25 * t44;
2401:   t46  = t43 * t45;
2402:   t47  = 0.3141592654e1 * 0.3141592654e1;
2403:   t48  = t47 * t37;
2404:   t49  = t17 * t38;
2405:   t54  = 0.3141592654e1 * t35;
2406:   t55  = ZA * nz * t54;
2407:   t56  = t37 * ZB;
2408:   t57  = t19 * t12;
2409:   t61  = t25 * t8;
2410:   t62  = t61 * t9;
2411:   t63  = nz * t30;
2412:   t64  = t63 * t16;
2413:   t67  = t1 * nz;
2414:   t69  = t47 * ZB;
2415:   t70  = t67 * t44 * t69;
2416:   t75  = nx * t3;
2417:   t76  = t75 * t37;
2418:   t77  = t67 * 0.3141592654e1;
2419:   t78  = t19 * t19;
2420:   t79  = t78 * t12;
2421:   t80  = t77 * t79;
2422:   t82  = t3 * t38;
2423:   t84  = t54 * t37;
2424:   t87  = PetscSinReal(t7);
2425:   t88  = t29 * t87;
2426:   t89  = t47 * t44;
2427:   t93  = nx * t25;
2428:   t94  = t87 * t42;
2429:   t95  = t93 * t94;
2430:   t96  = t47 * xc;
2431:   t97  = t13 * t29;
2432:   t98  = t96 * t97;
2433:   t101 = t87 * t67;
2434:   t102 = t93 * t101;
2435:   t103 = t13 * t18;
2436:   t107 = t47 * t35;
2437:   t108 = t26 * t107;
2438:   t109 = t37 * t44;
2439:   t110 = t19 * t17;
2440:   t111 = t12 * t110;
2441:   t116 = t37 * t19 * t12;
2442:   t118 = t37 * xc;
2443:   t119 = ZB * t19;
2444:   t120 = t119 * t12;
2445:   t121 = t118 * t120;
2446:   t125 = xc * t3;
2447:   t126 = t1 * t47 * t125;
2448:   t127 = t35 * t37;
2449:   t128 = t38 * t19;
2450:   t129 = t127 * t128;
2451:   t132 = t26 * 0.3141592654e1;
2452:   t133 = t16 * t13;
2453:   t134 = t10 * t133;
2454:   t137 = 0.3141592654e1 * ZB;
2455:   t138 = t2 * t137;
2456:   t139 = ZA * t8;
2457:   t140 = t9 * t13;
2458:   t145 = t30 * t18;
2459:   t146 = t10 * t145;
2460:   t149 = t3 * t8;
2461:   t150 = t149 * t9;
2462:   t153 = 0.2e1 * t5 * t22 + 0.2e1 * t28 * t10 * t31 + t36 * t40 - 0.2e1 * t46 * t48 * t49 - 0.2e1 * t55 * t56 * t57 - 0.2e1 * t62 * t64 + 0.16e2 * t70 * t29 * ZA * t10 - t76 * t80 + t82 * nz * t84 + 0.8e1 * t43 * t3 * t88 * t89 + 0.16e2 * t95 * t98 + 0.2e1 * t102 * t27 * t103 - 0.2e1 * t108 * t109 * t111 + t36 * t116 + 0.8e1 * t55 * t121 - 0.4e1 * t126 * t129 - 0.4e1 * t132 * t134 - 0.4e1 * t138 * t139 * t140 * t20 + 0.8e1 * t28 * t146 - 0.2e1 * t150 * t64;
2463:   t154 = t42 * nz;
2464:   t155 = nx * t154;
2465:   t156 = t44 * xc;
2466:   t157 = t47 * 0.3141592654e1;
2467:   t158 = t156 * t157;
2468:   t159 = t155 * t158;
2469:   t162 = t56 * ZA * t19 * t12;
2470:   t165 = t77 * t49;
2471:   t167 = t1 * t3;
2472:   t168 = t167 * t89;
2473:   t169 = t127 * t49;
2474:   t172 = t37 * t67;
2475:   t173 = t75 * t172;
2476:   t174 = t38 * t110;
2477:   t175 = t27 * t174;
2478:   t179 = t47 * t25;
2479:   t181 = t10 * t97;
2480:   t184 = t27 * t31;
2481:   t187 = t67 * t47;
2482:   t188 = t44 * t3;
2483:   t189 = t187 * t188;
2484:   t192 = t25 * t35;
2485:   t193 = t37 * t17;
2486:   t194 = t193 * t12;
2487:   t196 = nx * ZA;
2488:   t197 = t196 * t172;
2489:   t198 = ZB * t38;
2490:   t199 = t198 * t19;
2491:   t204 = t1 * t12 * t110;
2492:   t207 = nx * ZB;
2493:   t209 = t1 * ZA;
2494:   t215 = t67 * t3;
2495:   t216 = t47 * t8;
2496:   t217 = t215 * t216;
2497:   t218 = t9 * xc;
2498:   t222 = nx * t67;
2499:   t223 = t222 * t27;
2500:   t224 = t3 * t87;
2501:   t228 = t167 * t107;
2502:   t232 = t26 * t96;
2503:   t235 = t207 * t94;
2504:   t236 = t47 * ZA;
2505:   t243 = xc * t13;
2506:   t244 = t243 * t29;
2507:   t248 = t25 * nz;
2508:   t249 = t248 * 0.3141592654e1;
2509:   t253 = ZB * ZA;
2510:   t254 = t253 * t8;
2511:   t255 = t9 * nz;
2512:   t256 = t30 * t16;
2513:   t260 = 0.2e1 * t207 * t37 * t209 * t128 + 0.2e1 * t5 * t134 - 0.16e2 * t217 * t218 * t97 - 0.2e1 * t223 * t224 * t31 - 0.2e1 * t228 * t109 * t174 - 0.2e1 * t232 * t169 - 0.16e2 * t235 * t236 * t44 * t30 * t18 - 0.4e1 * t196 * t101 * t137 * t244 + t249 * t169 + 0.8e1 * t168 * t129 + 0.4e1 * t254 * t255 * t256;
2514:   t263 = t43 * t179;
2515:   t267 = t3 * nz;
2516:   t268 = t267 * t54;
2517:   t269 = t118 * t57;
2518:   t272 = t39 * t1;
2519:   t274 = t67 * t25;
2520:   t275 = t274 * t158;
2521:   t278 = t75 * t87;
2522:   t279 = t77 * t103;
2523:   t282 = t25 * t38;
2524:   t285 = ZA * t38;
2525:   t290 = t267 * 0.3141592654e1;
2526:   t296 = t77 * t111;
2527:   t298 = t196 * t37;
2528:   t299 = t1 * ZB;
2529:   t303 = t37 * t42;
2530:   t304 = t196 * t303;
2531:   t308 = t77 * t57;
2532:   t310 = t26 * t89;
2533:   t313 = t77 * t128;
2534:   t316 = t101 * t27;
2535:   t319 = t93 * t87;
2536:   t320 = t77 * t97;
2537:   t323 = t127 * t57;
2538:   t326 = t10 * nz;
2539:   t329 = t118 * t174;
2540:   t332 = -0.8e1 * t263 * t109 * t57 - 0.4e1 * t268 * t269 + t93 * t272 + 0.8e1 * t275 * t129 - 0.4e1 * t278 * t279 + t282 * nz * t84 - 0.2e1 * t285 * nz * t54 * t56 - t290 * t169 - 0.2e1 * t196 * t38 * t172 * t137 + t76 * t296 - 0.2e1 * t298 * t299 * t79 + 0.8e1 * t304 * t96 * t120 + t76 * t308 - 0.2e1 * t310 * t169 - t76 * t313 + 0.2e1 * t75 * t18 * t316 + 0.4e1 * t319 * t320 + t249 * t323 - 0.2e1 * t25 * t18 * t326 + 0.2e1 * t228 * t329;
2541:   t335 = t75 * t101;
2542:   t336 = t27 * t21;
2543:   t342 = t77 * t133;
2544:   t347 = t209 * t137;
2545:   t350 = t9 * t1;
2546:   t351 = t149 * t350;
2547:   t355 = t37 * t78 * t12;
2548:   t359 = t93 * t303;
2549:   t367 = t172 * 0.3141592654e1;
2550:   t369 = t96 * t103;
2551:   t376 = t209 * t107;
2552:   t379 = t10 * t103;
2553:   t383 = t207 * t101;
2554:   t389 = 0.3141592654e1 * ZA;
2555:   t390 = t222 * t389;
2556:   t391 = t87 * ZB;
2557:   t398 = -0.2e1 * t102 * t336 + t93 * t38 * t367 + 0.16e2 * t95 * t369 - t82 * t127 - 0.8e1 * t197 * t27 * t120 + 0.8e1 * t376 * t121 - 0.8e1 * t189 * t379 - t249 * t129 - 0.4e1 * t383 * t27 * ZA * t16 * t13 - 0.8e1 * t390 * t391 * t21 - 0.2e1 * t197 * t137 * t57;
2558:   t402 = t39 * t110;
2559:   t404 = t193 * t38;
2560:   t406 = t127 * t174;
2561:   t408 = t167 * 0.3141592654e1;
2562:   t411 = t44 * t157;
2563:   t412 = t155 * t411;
2564:   t413 = t285 * t19;
2565:   t414 = t56 * t413;
2566:   t417 = ZA * t30;
2567:   t424 = t93 * t37;
2568:   t426 = t248 * t54;
2569:   t427 = t17 * t12;
2570:   t428 = t118 * t427;
2571:   t431 = t77 * t21;
2572:   t438 = ZA * t13;
2573:   t443 = t93 * t172;
2574:   t444 = t27 * t427;
2575:   t448 = t1 * t78 * t12;
2576:   t455 = t274 * t89;
2577:   t461 = t118 * t111;
2578:   t464 = -t36 * t402 + t36 * t404 - t249 * t406 - 0.4e1 * t408 * t134 + 0.16e2 * t412 * t414 - 0.4e1 * t383 * t27 * t417 * t18 + 0.2e1 * t28 * t22 - t424 * t80 - 0.2e1 * t426 * t428 + 0.4e1 * t278 * t431 + 0.4e1 * t254 * t255 * t103 + t290 * t323 + 0.4e1 * t383 * t27 * t438 * t20 + 0.2e1 * t443 * t444 + t424 * t448 - t36 * t194 - 0.32e2 * t235 * t236 * t243 * t18 + 0.8e1 * t455 * t181 - 0.4e1 * t359 * t96 * t128 - 0.2e1 * t426 * t461;
2579:   t469 = nz * t16 * t13;
2580:   t474 = t1 * t38;
2581:   t475 = t474 * t19;
2582:   t480 = t89 * t103;
2583:   t483 = t67 * ZA;
2584:   t484 = t483 * t411;
2585:   t485 = t127 * t120;
2586:   t488 = t127 * t111;
2587:   t497 = t77 * t427;
2588:   t502 = t27 * t97;
2589:   t508 = t1 * t19 * t12;
2590:   t511 = t155 * t25 * t156;
2591:   t512 = t157 * t37;
2592:   t513 = t512 * t128;
2593:   t527 = t1 * t17;
2594:   t528 = t527 * t38;
2595:   t530 = -t76 * t497 - 0.4e1 * t254 * t255 * t97 - 0.2e1 * t102 * t502 - 0.4e1 * t108 * t269 - t76 * t508 + 0.8e1 * t511 * t513 + 0.4e1 * t150 * t63 * t18 + 0.4e1 * t383 * t27 * t438 * t18 + 0.4e1 * t132 * t379 + 0.2e1 * t168 * t488 - t76 * t528;
2596:   t535 = t44 * t13;
2597:   t542 = t527 * t12;
2598:   t544 = nz * t13;
2599:   t545 = t544 * t20;
2600:   t548 = t75 * t303;
2601:   t549 = t96 * t111;
2602:   t552 = ZA * t35;
2603:   t553 = t552 * t37;
2604:   t562 = t43 * t96;
2605:   t563 = t3 * t37;
2606:   t564 = t563 * t128;
2607:   t579 = t474 * t110;
2608:   t590 = t9 * t30;
2609:   t591 = t590 * t18;
2610:   t595 = t127 * t427;
2611:   t598 = t77 * t174;
2612:   t600 = 0.4e1 * t5 * t146 + 0.16e2 * t235 * t236 * t535 * t18 + 0.8e1 * t455 * t146 + t76 * t542 - 0.2e1 * t150 * t545 + 0.2e1 * t548 * t549 - 0.2e1 * t553 * t120 + t290 * t488 - 0.8e1 * t274 * t47 * t44 * t29 * t10 - 0.4e1 * t562 * t564 - 0.2e1 * t132 * xc * t20 * t10 - 0.32e2 * t562 * ZA * t87 * ZB * t13 * t29 - 0.8e1 * t347 * t379 + t76 * t579 - 0.4e1 * t359 * t96 * t57 + 0.4e1 * t408 * t181 - 0.4e1 * t223 * t564 - 0.12e2 * t209 * t27 * ZB * t8 * t591 + 0.2e1 * t310 * t595 + t76 * t598;
2613:   t601 = t27 * t49;
2614:   t604 = t127 * t79;
2615:   t606 = ZB * t29;
2616:   t616 = t139 * t140 * t18;
2617:   t638 = t10 * t256;
2618:   t643 = t118 * t199;
2619:   t653 = t544 * t29;
2620:   t658 = t3 * t29;
2621:   t660 = t350 * t27;
2622:   t663 = -0.4e1 * t254 * t255 * t145 + 0.2e1 * t267 * t20 * t8 * t9 - 0.4e1 * t138 * t139 * t9 * t16 * t13 - 0.2e1 * t5 * t638 + 0.2e1 * t126 * t169 + 0.8e1 * t376 * t643 + 0.4e1 * t335 * t27 * t145 + 0.16e2 * t235 * t236 * t535 * t29 + 0.6e1 * t150 * t653 - 0.4e1 * t426 * t269 + 0.4e1 * t658 * t8 * t660;
2623:   t670 = t274 * t411;
2624:   t673 = t118 * t49;
2625:   t694 = t155 * t45;
2626:   t713 = nz * t29 * t30;
2627:   t717 = t20 * t87;
2628:   t723 = t512 * t57;
2629:   t728 = -0.2e1 * t443 * t175 - 0.8e1 * t670 * t129 + 0.2e1 * t426 * t673 - 0.16e2 * t207 * t88 * t42 * t47 * ZA * t44 + 0.4e1 * t254 * t255 * t21 + t249 * t595 + 0.8e1 * t25 * t29 * t8 * t660 + 0.2e1 * t268 * t461 + 0.8e1 * t189 * t181 - 0.8e1 * t694 * t513 + 0.2e1 * t198 * t553 - 0.12e2 * t606 * t139 * t660 - 0.2e1 * t359 * t549 + 0.4e1 * t138 * t139 * t590 * t16 + 0.8e1 * t93 * t29 * t94 * t89 - 0.2e1 * t150 * t713 + 0.2e1 * t222 * t3 * t717 * t27 + 0.8e1 * t670 * t323 + 0.8e1 * t694 * t723 - 0.2e1 * t62 * t653;
2630:   t734 = t43 * t89;
2631:   t735 = t563 * t427;
2632:   t740 = t75 * t94;
2633:   t744 = ZB * xc;
2634:   t750 = t563 * t57;
2635:   t754 = t218 * t103;
2636:   t771 = t127 * t199;
2637:   t776 = t89 * t174;
2638:   t791 = -0.4e1 * t207 * t717 * t77 * xc * ZA + 0.4e1 * t443 * t27 * t57 + t192 * t40 - 0.8e1 * t55 * t643 - 0.16e2 * t209 * t89 * t771 - 0.8e1 * t275 * t323 + 0.2e1 * t359 * t776 + 0.16e2 * t304 * t89 * t199 + 0.4e1 * t278 * t320 + 0.2e1 * t207 * t172 * t389 * t79 - 0.8e1 * t390 * t391 * t97;
2639:   t794 = t483 * t158;
2640:   t801 = t2 * 0.3141592654e1;
2641:   t818 = t215 * t411;
2642:   t827 = t96 * t174;
2643:   t837 = t37 * t12 * t110;
2644:   t845 = 0.16e2 * t794 * t485 + 0.8e1 * t159 * t564 - 0.8e1 * t455 * t379 - 0.2e1 * t801 * t3 * t20 * t10 - 0.4e1 * t132 * t22 - 0.8e1 * t734 * t564 - 0.8e1 * t187 * t44 * t658 * t10 - 0.8e1 * t412 * t564 + 0.4e1 * t132 * t181 - 0.8e1 * t818 * t129 + 0.2e1 * t46 * t48 * t427 - 0.4e1 * t75 * t29 * t316 - 0.2e1 * t359 * t827 - t290 * t595 + 0.16e2 * t217 * t754 - t424 * t542 - 0.8e1 * t734 * t750 - t192 * t837 - 0.4e1 * t254 * t255 * t133 + 0.8e1 * t304 * t96 * t199;
2645:   t864 = t544 * t18;
2646:   t867 = t3 * t18;
2647:   t884 = t27 * t256;
2648:   t891 = t187 * t744;
2649:   t894 = t563 * t49;
2650:   t900 = -0.2e1 * t263 * t428 + 0.2e1 * t228 * t428 - 0.6e1 * t223 * t224 * t103 - t192 * t404 + 0.2e1 * t268 * t428 - 0.2e1 * t335 * t884 - t424 * t296 + 0.2e1 * t93 * t20 * t316 - 0.32e2 * t891 * t616 + 0.2e1 * t562 * t894 - 0.2e1 * t801 * t867 * t10;
2651:   t904 = t27 * t111;
2652:   t907 = t118 * t128;
2653:   t915 = t89 * t145;
2654:   t947 = t139 * t140 * t29;
2655:   t952 = -0.2e1 * t173 * t904 + 0.4e1 * t426 * t907 + 0.12e2 * t253 * t10 * t1 * 0.3141592654e1 * t244 + 0.8e1 * t95 * t915 - t36 * t355 - 0.16e2 * t794 * t771 - 0.8e1 * t511 * t723 + 0.16e2 * t734 * t162 + t36 * t837 + 0.2e1 * t298 * t299 * t57 - 0.2e1 * t28 * t638 - 0.2e1 * t62 * t545 + 0.2e1 * t310 * t406 + 0.12e2 * t138 * t616 + 0.4e1 * t223 * t750 + t424 * t497 + 0.2e1 * t734 * t894 + 0.2e1 * t132 * xc * t18 * t10 - 0.16e2 * t70 * t947 + 0.32e2 * t891 * t947;
2656:   t969  = t67 * t157 * t156 * t3;
2657:   t974  = t27 * t133;
2658:   t1001 = -0.8e1 * t159 * t750 - 0.16e2 * t412 * t162 - t290 * t129 + 0.8e1 * t310 * t323 - 0.4e1 * t319 * t342 + t75 * t272 + t192 * t402 - 0.8e1 * t359 * t89 * t128 - 0.10e2 * t61 * t350 * t502 + 0.8e1 * t818 * t323 - 0.4e1 * t108 * t907;
2659:   t1042 = t89 * t97;
2660:   t1055 = -0.2e1 * t168 * t595 + 0.16e2 * t484 * t771 + 0.4e1 * t11 * t125 * t129 - 0.2e1 * t173 * t444 + 0.2e1 * ZB * nz * t54 * t37 * ZA * t79 - t424 * t475 + 0.2e1 * t562 * t735 - 0.2e1 * t548 * t776 + t424 * t204 + 0.2e1 * t25 * t20 * t326 + 0.8e1 * t383 * t389 * t133 + t75 * t38 * t367 + 0.2e1 * t62 * t469 + 0.2e1 * t197 * t137 * t128 - 0.2e1 * t102 * t884 - 0.2e1 * t5 * t379 - 0.8e1 * t740 * t1042 - 0.16e2 * t159 * t414 - 0.2e1 * ZB * t35 * t37 * t413 + 0.2e1 * t553 * ZB * t78 * t12;
2661:   t1096 = 0.2e1 * t443 * t904 - 0.2e1 * t268 * t329 - 0.2e1 * t443 * t601 + 0.2e1 * t102 * t974 - 0.2e1 * t263 * t673 + t424 * t165 + 0.2e1 * t62 * t713 + t424 * t308 - t424 * t313 + 0.8e1 * t347 * t22 - t424 * t598;
2662:   t1103 = t42 * t1 * t157;
2663:   t1104 = t1103 * t25;
2664:   t1108 = t3 * t19;
2665:   t1112 = nz * t47;
2666:   t1113 = t9 * t9;
2667:   t1118 = t42 * t157;
2668:   t1119 = t1118 * t9;
2669:   t1120 = t25 * xc;
2670:   t1121 = t13 * t110;
2671:   t1122 = t1120 * t1121;
2672:   t1125 = t47 * t47;
2673:   t1126 = t67 * t1125;
2674:   t1127 = t1113 * ZA;
2675:   t1128 = t1126 * t1127;
2676:   t1129 = t19 * t13;
2677:   t1130 = t744 * t1129;
2678:   t1133 = t154 * t1125;
2679:   t1134 = t1133 * t9;
2680:   t1135 = t45 * t1129;
2681:   t1138 = t154 * t47;
2682:   t1139 = t25 * t30;
2683:   t1142 = t1126 * t1113;
2684:   t1145 = t125 * t1129;
2685:   t1148 = t1103 * xc;
2686:   t1149 = t3 * t13;
2687:   t1150 = t1149 * t17;
2688:   t1153 = t25 * t78;
2689:   t1156 = -0.8e1 * t1104 * t243 * t17 + 0.4e1 * t187 * t1108 * t9 - 0.2e1 * t1112 * t3 * t1113 * t30 + 0.16e2 * t1119 * t1122 + 0.64e2 * t1128 * t1130 + 0.64e2 * t1134 * t1135 - 0.2e1 * t1138 * t1139 + 0.32e2 * t1142 * t1135 - 0.32e2 * t1142 * t1145 + 0.8e1 * t1148 * t1150 - 0.2e1 * t1138 * t1153;
2690:   t1157 = t25 * t13;
2691:   t1158 = t1157 * t17;
2692:   t1161 = t13 * t17;
2693:   t1162 = t1120 * t1161;
2694:   t1165 = t3 * t78;
2695:   t1170 = t42 * t67 * t1125;
2696:   t1172 = t1108 * t13;
2697:   t1175 = t1 * t157;
2698:   t1176 = t1175 * t1113;
2699:   t1182 = t1120 * t1129;
2700:   t1189 = t110 * t9 * xc;
2701:   t1192 = t1149 * t110;
2702:   t1201 = 0.8e1 * t1103 * t1158 - 0.16e2 * t1119 * t1162 - 0.2e1 * t1112 * t1165 * t1113 + 0.32e2 * t1170 * t44 * t1172 - 0.8e1 * t1176 * t1162 + 0.8e1 * t1104 * t243 * t110 - 0.64e2 * t1134 * t1182 - 0.64e2 * t1134 * t1145 + 0.16e2 * t1118 * t3 * t1189 + 0.16e2 * t1119 * t1192 - 0.4e1 * t187 * t1165 * t9 - 0.4e1 * t187 * t1139 * t9;
2703:   t1209 = t17 * t30;
2704:   t1210 = t125 * t1209;
2705:   t1213 = t1138 * ZA;
2706:   t1214 = ZB * t30;
2707:   t1218 = t1157 * t110;
2708:   t1226 = t3 * t30;
2709:   t1237 = t1170 * t25;
2710:   t1242 = 0.4e1 * t1112 * ZA * t119 * t1113 - 0.16e2 * t1119 * t1150 - 0.8e1 * t1176 * t1210 + 0.4e1 * t1213 * t1214 * t19 - 0.16e2 * t1119 * t1218 - 0.32e2 * t1142 * t1182 - 0.8e1 * t1103 * t1120 * t110 - 0.4e1 * t187 * t1226 * t9 + 0.8e1 * t1103 * t1192 + 0.4e1 * t1112 * ZB * t1113 * t30 * ZA - 0.32e2 * t1237 * xc * t19 * t13;
2711:   t1251 = t125 * t1121;
2712:   t1260 = t1120 * t1209;
2713:   t1263 = t1139 * t19;
2714:   t1282 = 0.8e1 * t1103 * t110 * t3 * xc + 0.8e1 * t1104 * xc * t17 * t30 - 0.8e1 * t1176 * t1251 + 0.16e2 * t1119 * t1158 + 0.4e1 * t1112 * t78 * t1127 * ZB + 0.16e2 * t1119 * t1260 + 0.2e1 * t1138 * t1263 - 0.32e2 * t1170 * xc * t1172 - 0.16e2 * t1213 * t119 * t13 + 0.4e1 * t1138 * t1214 * ZA + 0.32e2 * t1237 * t44 * t19 * t13 - 0.16e2 * t1118 * t25 * t1189;
2715:   t1287 = t188 * t1129;
2716:   t1292 = t25 * t19;
2717:   t1296 = t187 * t9;
2718:   t1297 = t1226 * t19;
2719:   t1311 = t1112 * t1113;
2720:   t1317 = -0.8e1 * t1176 * t1150 + 0.32e2 * t1142 * t1287 - 0.8e1 * t1103 * t1150 + 0.2e1 * t1112 * t1292 * t1113 + 0.4e1 * t1296 * t1297 + 0.8e1 * t1176 * t1192 + 0.4e1 * t1296 * t1263 + 0.8e1 * t1176 * t1158 - 0.8e1 * t1175 * t25 * t1113 * xc * t110 + 0.2e1 * t1311 * t1297 + 0.2e1 * t1112 * t1108 * t1113;
2721:   t1320 = t253 * t1129;
2722:   t1328 = t253 * t30 * t19;
2723:   t1333 = t125 * t1161;
2724:   t1343 = ZB * t44 * t1129;
2725:   t1350 = -0.8e1 * t1176 * t1218 - 0.16e2 * t1311 * t1320 + 0.8e1 * t1176 * t1260 - 0.16e2 * t1119 * t1210 + 0.4e1 * t1311 * t1328 + 0.2e1 * t1311 * t1263 + 0.8e1 * t1176 * t1333 + 0.8e1 * t187 * ZB * t417 * t9 - 0.2e1 * t1138 * t1165 - 0.64e2 * t1128 * t1343 + 0.64e2 * t1134 * t1287 + 0.2e1 * t1138 * t1108;
2726:   t1369 = t1133 * t9 * ZA;
2727:   t1378 = t187 * ZA;
2728:   t1383 = t1170 * ZA;
2729:   t1388 = 0.2e1 * t1138 * t1297 - 0.8e1 * t1148 * t1192 + 0.2e1 * t1138 * t1292 - 0.16e2 * t1119 * t1251 + 0.8e1 * t1175 * xc * t110 * t1113 * t3 - 0.2e1 * t1112 * t1153 * t1113 + 0.128e3 * t1369 * t1130 + 0.16e2 * t1119 * t1333 + 0.4e1 * t1138 * t78 * ZA * ZB + 0.8e1 * t1378 * t78 * t9 * ZB - 0.64e2 * t1383 * t1343 + 0.64e2 * t1383 * t1130;
2730:   t1420 = 0.4e1 * t1138 * t119 * ZA - 0.128e3 * t1369 * t1343 - 0.4e1 * t187 * t1153 * t9 - 0.2e1 * t1138 * t1226 + 0.8e1 * t1296 * t1328 - 0.2e1 * t1112 * t1139 * t1113 - 0.8e1 * t1148 * t3 * t17 * t30 - 0.32e2 * t1296 * t1320 + 0.8e1 * t1176 * t1122 + 0.4e1 * t187 * t1292 * t9 + 0.8e1 * t1378 * t119 * t9 - 0.8e1 * t1103 * t1218;

2732:   _PC4B = (-t424 * t508 + 0.8e1 * t412 * t750 - 0.2e1 * t232 * t595 - 0.4e1 * t126 * t323 + t1096 - t76 * t204 + t728 + 0.2e1 * t548 * t827 + 0.2e1 * t150 * t469 + t398 + 0.8e1 * t189 * t146 + t260 - 0.2e1 * t351 * t184 - 0.2e1 * t268 * t673 - 0.4e1 * t319 * t279 + t464 - 0.2e1 * t108 * t461 + 0.16e2 * t740 * t369 + 0.16e2 * t274 * t216 * t754 - 0.16e2 * t70 * t139 * t591 + 0.2e1 * t55 * t56 * t128 - 0.2e1 * t359 * t89 * t111 + 0.2e1 * t734 * t563 * t111 + 0.6e1 * t223 * t224 * t97 + 0.8e1 * t383 * t389 * t103 + 0.4e1 * t606 * ZA * t326 - 0.2e1 * t93 * t18 * t316 - 0.4e1 * t443 * t27 * t128 + 0.8e1 * t197 * t27 * t199 + 0.8e1 * t108 * t109 * t128 - t249 * t604 + 0.16e2 * t70 * t616 - 0.8e1 * t969 * t323 + t845 - t424 * t579 + 0.16e2 * t159 * t162 + t290 * t406 - 0.6e1 * t150 * t864 + t192 * t116 + 0.2e1 * t867 * t326 - 0.4e1 * t658 * t326 - 0.2e1 * t351 * t502 - t76 * t165 + t900 + 0.8e1 * t168 * t323 + t791 + 0.8e1 * t740 * t915 - 0.4e1 * t562 * t750 - 0.4e1 * t278 * t342 + 0.4e1 * t319 * t431 + 0.2e1 * t173 * t175 + t424 * t528 + 0.8e1 * t969 * t129 - 0.8e1 * t347 * t181 + t332 + t530 - 0.2e1 * t108 * t329 - 0.2e1 * t207 * t38 * t37 * t1 * ZA + t1001 + 0.4e1 * t408 * t379 + t76 * t448 + 0.2e1 * t102 * t184 + 0.2e1 * t426 * t329 + 0.16e2 * t740 * t98 - t282 * t127 - 0.16e2 * t1 * t44 * t69 * t552 * t116 + 0.2e1 * t168 * t169 + 0.2e1 * t28 * t134 - t290 * t604 - 0.16e2 * t484 * t485 - 0.8e1 * t740 * t480 + 0.2e1 * t173 * t601 - 0.2e1 * t335 * t336 + t600 + 0.2e1 * t62 * t864 + t952 + 0.8e1 * t347 * t134 - t192 * t355 + t192 * t194 + 0.2e1 * t228 * t461 + t663 + 0.4e1 * t383 * t27 * t417 * t16 + 0.4e1 * t138 * t20 * ZA * t10 - 0.4e1 * t20 * ZB * ZA * t326 + 0.4e1 * t196 * t88 * t77 * t744 - 0.16e2 * t67 * xc * t179 * t181 - 0.8e1 * t95 * t480 - t249 * t488 - t76 * t475 + t1055 - 0.4e1 * t408 * t22 - 0.10e2 * t28 * t379 + 0.2e1 * t335 * t974 + t153 - 0.8e1 * t95 * t1042 - 0.2e1 * t734 * t735) / (t1156 + t1201 + t1242 + t1282 + t1317 + t1350 + t1388 + t1420);
2733:   /****************************************************************************************/
2734:   /****************************************************************************************/

2736:   if (x > xc) {
2737:     _PC1 = _PC1B;
2738:     _PC2 = _PC2B;
2739:     _PC3 = _PC3B;
2740:     _PC4 = _PC4B;
2741:     Z    = ZB;
2742:   } else {
2743:     _PC1 = _PC1A;
2744:     _PC2 = _PC2A;
2745:     _PC3 = _PC3A;
2746:     _PC4 = _PC4A;
2747:     Z    = ZA;
2748:   }
2749:   /****************************************************************************************/
2750:   /****************************************************************************************/
2751:   t1  = nz * nz;
2752:   t2  = t1 * t1;
2753:   t3  = t2 * nz;
2754:   t4  = x * t3;
2755:   t5  = 0.3141592654e1 * 0.3141592654e1;
2756:   t6  = t5 * 0.3141592654e1;
2757:   t11 = _PC3 * t6;
2758:   t12 = x * nz;
2759:   t13 = nx * nx;
2760:   t14 = t13 * t13;
2761:   t15 = t12 * t14;
2762:   t19 = PetscExpReal(t12 * 0.3141592654e1);
2763:   t20 = t19 * t19;
2764:   t21 = t4 * t20;
2765:   t24 = _PC1 * t5;
2766:   t25 = Z * t20;
2767:   t29 = _PC1 * t6;
2768:   t30 = t29 * Z;
2769:   t31 = t1 * nz;
2770:   t32 = x * t31;
2771:   t33 = t32 * t13;
2772:   t36 = t11 * x;
2773:   t41 = nz * t20;
2774:   t45 = t6 * _PC4;
2775:   t49 = t20 * t1;
2776:   t51 = _PC2 * Z;
2777:   t55 = -0.2e1 * t4 * t6 * _PC2 * Z - 0.2e1 * t11 * t15 - 0.2e1 * t11 * t21 + 0.2e1 * t24 * t25 * t14 - t13 + 0.4e1 * t30 * t33 - 0.4e1 * t36 * t31 * t20 * t13 - 0.2e1 * t36 * t41 * t14 - 0.2e1 * t4 * t45 * t20 - t49 - 0.2e1 * t4 * t6 * t51 * t20;
2778:   t58 = t32 * t6;
2779:   t59 = _PC4 * t20;
2780:   t63 = t20 * t13;
2781:   t67 = t12 * t6;
2782:   t68 = t20 * t14;
2783:   t87 = t49 * t13;
2784:   t90 = -0.4e1 * t11 * t33 - 0.4e1 * t58 * t59 * t13 - 0.4e1 * t58 * t51 * t63 - 0.2e1 * t67 * t51 * t68 + 0.4e1 * t32 * t45 * t13 - 0.2e1 * t67 * t59 * t14 - 0.2e1 * t30 * t21 + t1 + 0.2e1 * t24 * t25 * t2 + 0.2e1 * t12 * t45 * t14 + 0.4e1 * t24 * Z * t87;
2785:   t106 = _PC3 * t5;
2786:   t120 = -0.4e1 * t30 * t32 * t63 + t63 + 0.4e1 * t24 * Z * t1 * t13 + 0.2e1 * t29 * Z * x * t3 - 0.4e1 * t58 * t51 * t13 - 0.2e1 * t106 * t2 + t32 * 0.3141592654e1 - 0.2e1 * t106 * t14 - 0.2e1 * t30 * t12 * t68 - 0.2e1 * t67 * t51 * t14 + 0.4e1 * t106 * t87;
2787:   t129 = PetscSinReal(nx * 0.3141592654e1 * x);
2788:   t155 = 0.2e1 * t30 * t15 + x * 0.3141592654e1 * t41 * t13 - 0.4e1 * t19 * nx * t129 * nz + t32 * 0.3141592654e1 * t20 + 0.2e1 * t106 * t68 + 0.2e1 * t106 * t20 * t2 - 0.4e1 * t106 * t1 * t13 - 0.2e1 * t11 * t4 + 0.2e1 * t4 * t45 + 0.2e1 * t24 * Z * t2 + 0.2e1 * t24 * Z * t14 + t12 * 0.3141592654e1 * t13;
2789:   t158 = t5 * Z;

2791:   u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14);
2792:   /****************************************************************************************/
2793:   /****************************************************************************************/
2794:   t1  = nz * nz;
2795:   t2  = t1 * nz;
2796:   t3  = x * t2;
2797:   t4  = 0.3141592654e1 * 0.3141592654e1;
2798:   t5  = t4 * 0.3141592654e1;
2799:   t6  = t3 * t5;
2800:   t7  = _PC2 * Z;
2801:   t8  = nx * nx;
2802:   t12 = t1 * t1;
2803:   t13 = t12 * nz;
2804:   t14 = x * t13;
2805:   t15 = t5 * _PC4;
2806:   t16 = x * nz;
2807:   t18 = PetscExpReal(t16 * 0.3141592654e1);
2808:   t19 = t18 * t18;
2809:   t23 = t16 * t5;
2810:   t24 = t8 * t8;
2811:   t28 = _PC3 * t5;
2812:   t29 = t14 * t19;
2813:   t32 = _PC1 * t5;
2814:   t33 = t32 * Z;
2815:   t34 = t16 * t24;
2816:   t37 = _PC4 * t19;
2817:   t45 = _PC2 * t4;
2818:   t53 = t19 * t8;
2819:   t58 = _PC4 * t4;
2820:   t60 = t1 * t19 * t8;
2821:   t63 = t19 * t24;
2822:   t67 = t3 * t8;
2823:   t73 = nz * t19;
2824:   t86 = t28 * x;
2825:   t91 = 0.4e1 * t58 * t60 + 0.2e1 * t33 * t16 * t63 + 0.4e1 * t33 * t67 + 0.2e1 * t33 * t29 - x * 0.3141592654e1 * t73 * t8 - 0.2e1 * t53 + 0.2e1 * t32 * Z * x * t13 - 0.2e1 * t58 * t12 - 0.2e1 * t58 * t24 + t3 * 0.3141592654e1 + 0.4e1 * t86 * t2 * t19 * t8;
2826:   t94 = Z * t12;
2827:   t121 = -0.2e1 * t8 + 0.2e1 * t45 * t94 * t19 + 0.2e1 * t14 * t5 * t7 * t19 + 0.4e1 * t6 * t7 * t53 + 0.2e1 * t23 * t7 * t63 - 0.4e1 * t28 * t67 + 0.2e1 * t45 * t94 + 0.2e1 * t58 * t12 * t19 + t16 * 0.3141592654e1 * t8 + 0.2e1 * t14 * t15 - 0.2e1 * t28 * t14;
2828:   t146 = PetscCosReal(nx * 0.3141592654e1 * x);
2829:   t156 = -t3 * 0.3141592654e1 * t19 + 0.2e1 * t58 * t63 - 0.4e1 * t58 * t1 * t8 + 0.4e1 * t45 * Z * t1 * t8 - 0.2e1 * t28 * t34 + 0.2e1 * t86 * t73 * t24 + 0.4e1 * t3 * t15 * t8 + 0.4e1 * t45 * Z * t60 + 0.4e1 * t18 * t146 * t8 + 0.2e1 * t45 * Z * t24 + 0.2e1 * t16 * t15 * t24;
2830:   t159 = t4 * Z;

2832:   u2 = (-0.4e1 * t6 * t7 * t8 + 0.2e1 * t14 * t15 * t19 - 0.2e1 * t23 * t7 * t24 + 0.2e1 * t28 * t29 + 0.2e1 * t33 * t34 + 0.4e1 * t6 * t37 * t8 - 0.2e1 * t14 * t5 * _PC2 * Z + 0.2e1 * t45 * Z * t19 * t24 + 0.2e1 * t23 * t37 * t24 + 0.4e1 * t33 * t3 * t53 + t91 + t121 + t156) / (0.4e1 * t159 * t18 * t12 + 0.8e1 * t159 * t18 * t1 * t8 + 0.4e1 * t159 * t18 * t24);
2833:   /****************************************************************************************/
2834:   /****************************************************************************************/
2835:   t1  = 0.3141592654e1 * 0.3141592654e1;
2836:   t2  = t1 * 0.3141592654e1;
2837:   t3  = _PC1 * t2;
2838:   t4  = t3 * Z;
2839:   t5  = nz * nz;
2840:   t6  = t5 * t5;
2841:   t7  = t6 * nz;
2842:   t8  = x * t7;
2843:   t9  = x * nz;
2844:   t11 = PetscExpReal(t9 * 0.3141592654e1);
2845:   t12 = t11 * t11;
2846:   t13 = t8 * t12;
2847:   t16 = t5 * nz;
2848:   t17 = x * t16;
2849:   t18 = t17 * t2;
2850:   t19 = _PC4 * t12;
2851:   t20 = nx * nx;
2852:   t24 = t2 * _PC4;
2853:   t28 = _PC3 * t2;
2854:   t29 = t28 * x;
2855:   t30 = t12 * nz;
2856:   t31 = t20 * t20;
2857:   t40 = _PC2 * Z;
2858:   t44 = t9 * t2;
2859:   t48 = t12 * t20;
2860:   t52 = t17 * t20;
2861:   t57 = -0.2e1 * t4 * t13 - 0.4e1 * t18 * t19 * t20 - 0.2e1 * t8 * t24 * t12 - 0.2e1 * t29 * t30 * t31 + 0.2e1 * t8 * t2 * _PC2 * Z - 0.2e1 * t8 * t2 * t40 * t12 - 0.2e1 * t44 * t19 * t31 - 0.4e1 * t18 * t40 * t48 + t20 + 0.4e1 * t28 * t52 + t17 * 0.3141592654e1 * t12;
2862:   t58 = t9 * t31;
2863:   t61 = _PC3 * t1;
2864:   t62 = t12 * t31;
2865:   t73 = t5 * t20;
2866:   t78 = _PC1 * t1;
2867:   t90 = Z * t12;
2868:   t94 = 0.2e1 * t28 * t58 + 0.2e1 * t61 * t62 + 0.2e1 * t61 * t12 * t6 - 0.4e1 * t4 * t17 * t48 + 0.2e1 * t28 * t8 + 0.4e1 * t61 * t73 - 0.2e1 * t8 * t24 - 0.2e1 * t78 * Z * t6 - 0.2e1 * t44 * t40 * t62 - 0.2e1 * t78 * Z * t31 - t9 * 0.3141592654e1 * t20 + 0.2e1 * t78 * t90 * t6;
2869:   t101 = PetscCosReal(nx * 0.3141592654e1 * x);
2870:   t102 = t11 * t101;
2871:   t109 = t12 * t5;
2872:   t110 = t109 * t20;
2873:   t128 = 0.2e1 * t61 * t6 - t17 * 0.3141592654e1 + 0.2e1 * t102 * t5 - 0.4e1 * t17 * t24 * t20 + 0.4e1 * t78 * Z * t110 - 0.2e1 * t9 * t24 * t31 - 0.4e1 * t4 * t52 - 0.2e1 * t4 * t9 * t62 + x * 0.3141592654e1 * t30 * t20 - t5 - 0.4e1 * t78 * Z * t5 * t20;
2874:   t156 = 0.2e1 * t78 * t90 * t31 - 0.2e1 * t3 * Z * x * t7 + t48 + 0.4e1 * t61 * t110 + 0.4e1 * t18 * t40 * t20 - 0.2e1 * t102 * t20 + 0.2e1 * t61 * t31 + 0.2e1 * t44 * t40 * t31 - t109 - 0.2e1 * t4 * t58 - 0.2e1 * t28 * t13 - 0.4e1 * t29 * t16 * t12 * t20;
2875:   t159 = t1 * t11;

2877:   u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31);
2878:   /****************************************************************************************/
2879:   /****************************************************************************************/
2880:   t1  = _PC2 * Z;
2881:   t2  = 0.3141592654e1 * 0.3141592654e1;
2882:   t3  = t2 * 0.3141592654e1;
2883:   t4  = nz * nz;
2884:   t5  = t4 * t4;
2885:   t6  = t5 * t4;
2886:   t8  = t3 * t6 * x;
2887:   t11 = x * t4;
2888:   t12 = t11 * t3;
2889:   t15 = PetscExpReal(x * nz * 0.3141592654e1);
2890:   t16 = t15 * t15;
2891:   t17 = _PC3 * t16;
2892:   t18 = nx * nx;
2893:   t19 = t18 * t18;
2894:   t23 = t5 * nz;
2895:   t24 = t2 * t23;
2896:   t28 = t1 * t3;
2897:   t29 = t6 * x;
2898:   t30 = t29 * t16;
2899:   t33 = _PC4 * t3;
2900:   t34 = t5 * x;
2901:   t35 = t34 * t18;
2902:   t41 = PetscSinReal(nx * 0.3141592654e1 * x);
2903:   t47 = t11 * t19;
2904:   t54 = t3 * _PC3;
2905:   t57 = 0.2e1 * t1 * t8 + 0.2e1 * t12 * t17 * t19 + 0.2e1 * t1 * t24 * t16 + 0.2e1 * t28 * t30 - 0.4e1 * t33 * t35 + 0.2e1 * t15 * nx * t41 * t4 + 0.4e1 * t28 * t35 - 0.2e1 * t33 * t47 - 0.2e1 * t1 * t24 - 0.2e1 * t33 * t29 + 0.2e1 * t29 * t54;
2906:   t58 = 0.3141592654e1 * t16;
2907:   t60 = t2 * _PC4;
2908:   t69 = t4 * nz;
2909:   t73 = t1 * t2;
2910:   t75 = t69 * t16 * t18;
2911:   t79 = x * t16;
2912:   t83 = nz * t16;
2913:   t84 = t83 * t19;
2914:   t95 = -t34 * t58 + 0.2e1 * t60 * t23 * t16 + 0.2e1 * t60 * nz * t19 - t11 * 0.3141592654e1 * t18 + 0.4e1 * t60 * t69 * t18 + 0.4e1 * t73 * t75 + 0.4e1 * t33 * t5 * t79 * t18 + 0.2e1 * t73 * t84 + 0.2e1 * t60 * t84 + 0.2e1 * t33 * t4 * t79 * t19 + 0.4e1 * t60 * t75;
2915:   t97  = t34 * t3;
2916:   t101 = Z * _PC1;
2917:   t102 = t16 * t19;
2918:   t106 = t16 * t18;
2919:   t127 = t2 * t69;
2920:   t131 = t2 * nz;
2921:   t135 = 0.4e1 * t97 * t17 * t18 + 0.2e1 * t12 * t101 * t102 + 0.4e1 * t28 * t34 * t106 + 0.2e1 * t28 * t11 * t102 - 0.2e1 * t29 * t3 * Z * _PC1 - 0.4e1 * t97 * t101 * t18 - 0.2e1 * t12 * t101 * t19 + 0.2e1 * t60 * t23 - 0.2e1 * t83 * t18 - 0.4e1 * t1 * t127 * t18 - 0.2e1 * t1 * t131 * t19;
2922:   t164 = 0.2e1 * t28 * t47 + 0.2e1 * t11 * t54 * t19 + 0.2e1 * t8 * t101 * t16 + 0.2e1 * t33 * t30 - t11 * t58 * t18 + 0.2e1 * t29 * t54 * t16 + 0.4e1 * t34 * t54 * t18 + 0.4e1 * t97 * t101 * t106 - 0.2e1 * t15 * t18 * nx * t41 - t34 * 0.3141592654e1 + 0.2e1 * nz * t18;

2924:   u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19);

2926:   /****************************************************************************************/
2927:   /****************************************************************************************/

2929:   u5 = (PetscReal)(-2 * Z * nz * PETSC_PI * u2 - u3 * 2 * nz * PETSC_PI) * PetscCosReal(nz * PETSC_PI * z); /* pressure */

2931:   u6 = (PetscReal)(u3 * 2 * nz * PETSC_PI + 4 * Z * nz * PETSC_PI * u2) * PetscCosReal(nz * PETSC_PI * z); /* zz stress */
2932:   sum5 += u5;
2933:   sum6 += u6;

2935:   u1 *= PetscCosReal(nz * PETSC_PI * z); /* x velocity */
2936:   sum1 += u1;
2937:   u2 *= PetscSinReal(nz * PETSC_PI * z); /* z velocity */
2938:   sum2 += u2;
2939:   u3 *= 2 * nz * PETSC_PI * PetscCosReal(nz * PETSC_PI * z); /* xx stress */
2940:   sum3 += u3;
2941:   u4 *= 2 * nz * PETSC_PI * PetscSinReal(nz * PETSC_PI * z); /* zx stress */
2942:   sum4 += u4;

2944:   /* Output */
2945:   if (mu) *mu = Z;
2946:   if (vel) {
2947:     vel[0] = sum1;
2948:     vel[1] = sum2;
2949:   }
2950:   if (p) (*p) = sum5;
2951:   if (s) {
2952:     s[0] = sum3;
2953:     s[1] = sum4;
2954:     s[2] = sum6;
2955:   }
2956:   if (gamma) {
2957:     /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
2958:     gamma[0] = (sum3 + sum5) / (2.0 * Z);
2959:     gamma[1] = (sum4) / (2.0 * Z);
2960:     gamma[2] = (sum6 + sum5) / (2.0 * Z);
2961:   }
2962:   PetscFunctionReturn(PETSC_SUCCESS);
2963: }

2965: static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
2966: {
2967:   Parameter *s = (Parameter *)ctx;

2969:   PetscFunctionBegin;
2970:   PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL));
2971:   PetscFunctionReturn(PETSC_SUCCESS);
2972: }

2974: static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
2975: {
2976:   Parameter *s = (Parameter *)ctx;

2978:   PetscFunctionBegin;
2979:   PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL));
2980:   PetscFunctionReturn(PETSC_SUCCESS);
2981: }

2983: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
2984: {
2985:   PetscInt sol;

2987:   PetscFunctionBeginUser;
2988:   options->solType = SOLKX;
2989:   PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");
2990:   sol = options->solType;
2991:   PetscCall(PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL));
2992:   options->solType = (SolutionType)sol;
2993:   PetscOptionsEnd();
2994:   PetscFunctionReturn(PETSC_SUCCESS);
2995: }

2997: static PetscErrorCode SetUpParameters(AppCtx *user)
2998: {
2999:   PetscBag   bag;
3000:   Parameter *p;

3002:   PetscFunctionBeginUser;
3003:   /* setup PETSc parameter bag */
3004:   PetscCall(PetscBagGetData(user->bag, (void **)&p));
3005:   PetscCall(PetscBagSetName(user->bag, "par", "Problem parameters"));
3006:   bag = user->bag;
3007:   switch (user->solType) {
3008:   case SOLKX:
3009:     PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3010:     PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3011:     PetscCall(PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation"));
3012:     break;
3013:   case SOLCX:
3014:     PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3015:     PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3016:     PetscCall(PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc"));
3017:     PetscCall(PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc"));
3018:     PetscCall(PetscBagRegisterReal(bag, &p->xc, 0.5, "xc", "x-coordinate of the viscosity jump"));
3019:     break;
3020:   default:
3021:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3022:   }
3023:   PetscCall(PetscBagSetFromOptions(bag));
3024:   PetscCall(PetscBagViewFromOptions(bag, NULL, "-param_view"));
3025:   PetscFunctionReturn(PETSC_SUCCESS);
3026: }

3028: /* Make split labels so that we can have corners in multiple labels */
3029: static PetscErrorCode CreateSplitLabels(DM dm)
3030: {
3031:   const char *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"};
3032:   PetscInt    ids[4]   = {1, 2, 3, 4};
3033:   DMLabel     label;
3034:   IS          is;
3035:   PetscInt    f;

3037:   PetscFunctionBeginUser;
3038:   for (f = 0; f < 4; ++f) {
3039:     PetscCall(DMCreateLabel(dm, names[f]));
3040:     PetscCall(DMGetStratumIS(dm, "marker", ids[f], &is));
3041:     if (!is) continue;
3042:     PetscCall(DMGetLabel(dm, names[f], &label));
3043:     PetscCall(DMLabelInsertIS(label, is, 1));
3044:     PetscCall(ISDestroy(&is));
3045:   }
3046:   PetscFunctionReturn(PETSC_SUCCESS);
3047: }

3049: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
3050: {
3051:   DM cdm;

3053:   PetscFunctionBeginUser;
3054:   PetscCall(DMCreate(comm, dm));
3055:   PetscCall(DMSetType(*dm, DMPLEX));
3056:   PetscCall(DMSetFromOptions(*dm));
3057:   cdm = *dm;
3058:   while (cdm) {
3059:     PetscCall(CreateSplitLabels(cdm));
3060:     PetscCall(DMGetCoarseDM(cdm, &cdm));
3061:   }
3062:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
3063:   PetscFunctionReturn(PETSC_SUCCESS);
3064: }

3066: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
3067: {
3068:   PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3069:   PetscDS        prob;
3070:   DMLabel        label;
3071:   const PetscInt id = 1;
3072:   PetscInt       dim, comp;
3073:   Parameter     *ctx;
3074:   void          *data;

3076:   PetscFunctionBeginUser;
3077:   PetscCall(DMGetDimension(dm, &dim));
3078:   PetscCall(DMGetDS(dm, &prob));
3079:   switch (user->solType) {
3080:   case SOLKX:
3081:     PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx));
3082:     PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3083:     PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3084:     PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3085:     PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3086:     PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3087:     PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL));
3088:     break;
3089:   case SOLCX:
3090:     PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx));
3091:     PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3092:     PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3093:     PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3094:     PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3095:     PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3096:     PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL));
3097:     break;
3098:   default:
3099:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3100:   }
3101:   PetscCall(PetscBagGetData(user->bag, &data));
3102:   switch (dim) {
3103:   case 2:
3104:     switch (user->solType) {
3105:     case SOLKX:
3106:       PetscCall(PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data));
3107:       PetscCall(PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data));
3108:       break;
3109:     case SOLCX:
3110:       PetscCall(PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data));
3111:       PetscCall(PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data));
3112:       break;
3113:     default:
3114:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3115:     }
3116:     break;
3117:   default:
3118:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %" PetscInt_FMT, dim);
3119:   }
3120:   /* Setup constants */
3121:   {
3122:     Parameter *param;

3124:     PetscCall(PetscBagGetData(user->bag, (void **)&param));
3125:     switch (user->solType) {
3126:     case SOLKX: {
3127:       PetscScalar constants[3];

3129:       constants[0] = param->m;
3130:       constants[1] = param->n;
3131:       constants[2] = param->B;
3132:       PetscCall(PetscDSSetConstants(prob, 3, constants));
3133:     } break;
3134:     case SOLCX: {
3135:       PetscScalar constants[5];

3137:       constants[0] = param->m;
3138:       constants[1] = param->n;
3139:       constants[2] = param->etaA;
3140:       constants[3] = param->etaB;
3141:       constants[4] = param->xc;
3142:       PetscCall(PetscDSSetConstants(prob, 5, constants));
3143:     } break;
3144:     default:
3145:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType);
3146:     }
3147:   }
3148:   /* Setup Boundary Conditions */
3149:   PetscCall(PetscDSGetExactSolution(prob, 0, &exactFunc, (void **)&ctx));
3150:   comp = 1;
3151:   PetscCall(DMGetLabel(dm, "markerBottom", &label));
3152:   PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3153:   comp = 0;
3154:   PetscCall(DMGetLabel(dm, "markerRight", &label));
3155:   PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3156:   comp = 1;
3157:   PetscCall(DMGetLabel(dm, "markerTop", &label));
3158:   PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3159:   comp = 0;
3160:   PetscCall(DMGetLabel(dm, "markerLeft", &label));
3161:   PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3162:   PetscFunctionReturn(PETSC_SUCCESS);
3163: }

3165: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
3166: {
3167:   Vec vec;
3168:   PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) = {zero, one};

3170:   PetscFunctionBeginUser;
3171:   PetscCheck(origField == 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Field %" PetscInt_FMT " should be 1 for pressure", origField);
3172:   funcs[field] = one;
3173:   {
3174:     PetscDS ds;
3175:     PetscCall(DMGetDS(dm, &ds));
3176:     PetscCall(PetscObjectViewFromOptions((PetscObject)ds, NULL, "-ds_view"));
3177:   }
3178:   PetscCall(DMCreateGlobalVector(dm, &vec));
3179:   PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec));
3180:   PetscCall(VecNormalize(vec, NULL));
3181:   PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace));
3182:   PetscCall(VecDestroy(&vec));
3183:   /* New style for field null spaces */
3184:   {
3185:     PetscObject  pressure;
3186:     MatNullSpace nullspacePres;

3188:     PetscCall(DMGetField(dm, field, NULL, &pressure));
3189:     PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres));
3190:     PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullspacePres));
3191:     PetscCall(MatNullSpaceDestroy(&nullspacePres));
3192:   }
3193:   PetscFunctionReturn(PETSC_SUCCESS);
3194: }

3196: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
3197: {
3198:   DM             cdm = dm;
3199:   PetscFE        fe[2];
3200:   DMPolytopeType ct;
3201:   PetscInt       dim, cStart;
3202:   PetscBool      simplex;

3204:   PetscFunctionBeginUser;
3205:   PetscCall(DMGetDimension(dm, &dim));
3206:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
3207:   PetscCall(DMPlexGetCellType(dm, cStart, &ct));
3208:   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
3209:   /* Create discretization of solution fields */
3210:   PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]));
3211:   PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity"));
3212:   PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]));
3214:   PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure"));
3215:   /* Set discretization and boundary conditions for each mesh */
3216:   PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0]));
3217:   PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1]));
3218:   PetscCall(DMCreateDS(dm));
3219:   PetscCall(SetupProblem(dm, user));
3220:   while (cdm) {
3221:     PetscCall(DMCopyDisc(dm, cdm));
3222:     PetscCall(DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace));
3223:     PetscCall(DMGetCoarseDM(cdm, &cdm));
3224:   }
3225:   PetscCall(PetscFEDestroy(&fe[0]));
3226:   PetscCall(PetscFEDestroy(&fe[1]));
3227:   {
3228:     PetscObject  pressure;
3229:     MatNullSpace nullSpacePres;

3231:     PetscCall(DMGetField(dm, 1, NULL, &pressure));
3232:     PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres));
3233:     PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullSpacePres));
3234:     PetscCall(MatNullSpaceDestroy(&nullSpacePres));
3235:   }
3236:   PetscFunctionReturn(PETSC_SUCCESS);
3237: }

3239: /* Add a vector in the nullspace to make the continuum integral 0.

3241:    If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0
3242: */
3243: static void pressure(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
3244: {
3245:   p[0] = u[uOff[1]];
3246: }
3247: static PetscErrorCode CorrectDiscretePressure(DM dm, MatNullSpace nullspace, Vec u, AppCtx *user)
3248: {
3249:   PetscDS     ds;
3250:   const Vec  *nullvecs;
3251:   PetscScalar pintd, intc[2], intn[2];
3252:   MPI_Comm    comm;

3254:   PetscFunctionBeginUser;
3255:   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
3256:   PetscCall(DMGetDS(dm, &ds));
3257:   PetscCall(PetscDSSetObjective(ds, 1, pressure));
3258:   PetscCall(MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs));
3259:   PetscCall(VecDot(nullvecs[0], u, &pintd));
3260:   PetscCheck(PetscAbsScalar(pintd) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g", (double)PetscRealPart(pintd));
3261:   PetscCall(DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, user));
3262:   PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3263:   PetscCall(VecAXPY(u, -intc[1] / intn[1], nullvecs[0]));
3264:   PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3265:   PetscCheck(PetscAbsScalar(intc[1]) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g", (double)PetscRealPart(intc[1]));
3266:   PetscFunctionReturn(PETSC_SUCCESS);
3267: }

3269: static PetscErrorCode SNESConvergenceCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *user)
3270: {
3271:   PetscFunctionBeginUser;
3272:   PetscCall(SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, user));
3273:   if (*reason > 0) {
3274:     DM           dm;
3275:     Mat          J;
3276:     Vec          u;
3277:     MatNullSpace nullspace;

3279:     PetscCall(SNESGetDM(snes, &dm));
3280:     PetscCall(SNESGetSolution(snes, &u));
3281:     PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
3282:     PetscCall(MatGetNullSpace(J, &nullspace));
3283:     PetscCheck(nullspace, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "SNES Jacobian has no attached null space");
3284:     PetscCall(CorrectDiscretePressure(dm, nullspace, u, (AppCtx *)user));
3285:   }
3286:   PetscFunctionReturn(PETSC_SUCCESS);
3287: }

3289: int main(int argc, char **argv)
3290: {
3291:   SNES         snes;      /* nonlinear solver */
3292:   DM           dm;        /* problem definition */
3293:   Vec          u, r;      /* solution, residual vectors */
3294:   Mat          J, M;      /* Jacobian and preconditiong matrix */
3295:   MatNullSpace nullSpace; /* May be necessary for pressure */
3296:   AppCtx       user;      /* user-defined work context */
3297:   PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) = {zero, zero};

3299:   PetscFunctionBeginUser;
3300:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
3301:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
3302:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
3303:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
3304:   PetscCall(SNESSetDM(snes, dm));
3305:   PetscCall(DMSetApplicationContext(dm, &user));
3306:   /* Setup problem parameters */
3307:   PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag));
3308:   PetscCall(SetUpParameters(&user));
3309:   /* Setup problem */
3310:   PetscCall(SetupDiscretization(dm, &user));
3311:   PetscCall(DMPlexCreateClosureIndex(dm, NULL));

3313:   PetscCall(DMCreateGlobalVector(dm, &u));
3314:   PetscCall(VecDuplicate(u, &r));

3316:   PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
3317:   PetscCall(CreatePressureNullSpace(dm, 1, 1, &nullSpace));

3319:   { /* set tolerances */
3320:     KSP ksp;

3322:     PetscCall(SNESGetKSP(snes, &ksp));
3323:     PetscCall(KSPSetTolerances(ksp, 1.e-2 * PETSC_SMALL, PETSC_SMALL, PETSC_DEFAULT, PETSC_DEFAULT));
3324:   }

3326:   /* There should be a way to express this using the DM */
3327:   PetscCall(SNESSetFromOptions(snes));
3328:   PetscCall(SNESSetUp(snes));
3329:   PetscCall(SNESGetJacobian(snes, &J, &M, NULL, NULL));
3330:   PetscCall(MatSetNullSpace(J, nullSpace));
3331:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "prec_"));
3332:   PetscCall(MatSetFromOptions(M));
3333:   PetscCall(SNESSetConvergenceTest(snes, SNESConvergenceCorrectPressure, &user, NULL));

3335:   PetscCall(DMSNESCheckFromOptions(snes, u));
3336:   PetscCall(DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u));
3337:   PetscCall(PetscObjectSetName((PetscObject)u, "Solution"));
3338:   PetscCall(SNESSolve(snes, NULL, u));
3339:   {
3340:     PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3341:     void   *ectxs[2];
3342:     PetscDS ds;
3343:     Vec     e;

3345:     PetscCall(DMGetDS(dm, &ds));
3346:     PetscCall(PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]));
3347:     PetscCall(PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]));

3349:     PetscCall(DMGetGlobalVector(dm, &e));
3350:     PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", (PetscObject)dm));
3351:     PetscCall(DMPlexComputeL2DiffVec(dm, 0.0, exacts, ectxs, u, e));
3352:     PetscCall(PetscObjectSetName((PetscObject)e, "Solution Error"));
3353:     PetscCall(VecViewFromOptions(e, NULL, "-error_vec_view"));
3354:     PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", NULL));
3355:     PetscCall(DMRestoreGlobalVector(dm, &e));
3356:   }
3357:   PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view"));

3359:   PetscCall(MatNullSpaceDestroy(&nullSpace));
3360:   PetscCall(VecDestroy(&u));
3361:   PetscCall(VecDestroy(&r));
3362:   PetscCall(SNESDestroy(&snes));
3363:   PetscCall(DMDestroy(&dm));
3364:   PetscCall(PetscBagDestroy(&user.bag));
3365:   PetscCall(PetscFinalize());
3366:   return 0;
3367: }

3369: /*TEST

3371:   # 2D serial discretization tests
3372:   test:
3373:     suffix: p2p1
3374:     requires: triangle
3375:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3376:       -snes_error_if_not_converged -dmsnes_check .001 \
3377:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3378:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3379:         -fieldsplit_velocity_pc_type lu \
3380:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3381:   test:
3382:     suffix: p2p1_gmg
3383:     TODO: broken (requires subDMs hooks)
3384:     requires: triangle
3385:     args: -dm_plex_separate_marker -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3386:       -snes_error_if_not_converged -dmsnes_check .001 \
3387:       -ksp_type fgmres -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3388:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3389:         -fieldsplit_velocity_pc_type mg \
3390:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3391:   test:
3392:     suffix: p2p1_conv
3393:     requires: triangle
3394:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.2]
3395:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3396:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3397:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3398:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3399:         -fieldsplit_velocity_pc_type lu \
3400:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3401:   test:
3402:     suffix: q2q1_conv
3403:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.1]
3404:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3405:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3406:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3407:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3408:         -fieldsplit_velocity_pc_type lu \
3409:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3410:   test:
3411:     suffix: q1p0_conv
3412:     # -dm_refine 2 gives L_2 convergence rate: [2.0, 1.0]
3413:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
3414:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3415:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3416:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3417:         -fieldsplit_velocity_pc_type lu \
3418:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3419:   test:
3420:     suffix: q2p1_conv
3421:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.0]
3422:     args: -dm_plex_simplex 0 -dm_plex_separate_marker \
3423:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 \
3424:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3425:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3426:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3427:         -fieldsplit_velocity_pc_type lu \
3428:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu

3430:   # FETI-DP tests
3431:   testset:
3432:     output_file: output/ex69_q2p1fetidp.out
3433:     suffix: q2p1fetidp
3434:     requires: !single
3435:     nsize: 5
3436:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3437:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3438:       -snes_error_if_not_converged \
3439:       -ksp_error_if_not_converged \
3440:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3441:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd
3442:     test:
3443:       suffix: aij
3444:       args: -mat_is_localmat_type aij
3445:     test:
3446:       requires: viennacl !CUDA_VERSION_11PLUS broken
3447:       suffix: aijviennacl
3448:       args: -mat_is_localmat_type aijviennacl
3449:     test:
3450:       requires: cuda
3451:       suffix: aijcusparse
3452:       args: -mat_is_localmat_type aijcusparse

3454:   testset:
3455:     suffix: q2p1fetidp_deluxe
3456:     output_file: output/ex69_q2p1fetidp_deluxe.out
3457:     requires: mumps double
3458:     nsize: 5
3459:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3460:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3461:       -snes_error_if_not_converged \
3462:       -ksp_error_if_not_converged \
3463:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3464:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_pc_bddc_deluxe_zerorows \
3465:       -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
3466:     test:
3467:       suffix: aij
3468:       args: -mat_is_localmat_type aij
3469:     test:
3470:       suffix: aij_seqdense
3471:       args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3472:     test:
3473:       requires: viennacl !CUDA_VERSION_11PLUS
3474:       suffix: aijviennacl
3475:       args: -mat_is_localmat_type aijviennacl
3476:     test:
3477:       requires: cuda
3478:       suffix: aijcusparse
3479:       args: -mat_is_localmat_type aijcusparse

3481:   testset:
3484:     requires: mumps double
3485:     nsize: 5
3486:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3487:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3488:       -snes_error_if_not_converged \
3489:       -ksp_error_if_not_converged \
3490:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3491:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_pc_bddc_adaptive_userdefined -fetidp_bddc_pc_bddc_adaptive_threshold 1.3 \
3492:       -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
3493:     test:
3494:       suffix: aij
3495:       args: -mat_is_localmat_type aij
3496:     test:
3497:       suffix: aij_seqdense
3498:       args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3499:     test:
3500:       requires: viennacl !CUDA_VERSION_11PLUS
3501:       suffix: aijviennacl
3502:       args: -mat_is_localmat_type aijviennacl
3503:     test:
3504:       requires: cuda
3505:       suffix: aijcusparse
3506:       args: -mat_is_localmat_type aijcusparse

3508:   test:
3509:     suffix: p2p1fetidp
3510:     requires: triangle
3511:     nsize: 4
3512:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3513:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3514:       -snes_error_if_not_converged \
3515:       -ksp_error_if_not_converged \
3516:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3517:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3518:       -fetidp_fieldsplit_lag_ksp_type preonly \
3519:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd

3521:   test:
3522:     suffix: p2p1fetidp_allp
3523:     requires: triangle
3524:     nsize: 4
3525:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3526:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3527:       -snes_error_if_not_converged \
3528:       -ksp_error_if_not_converged \
3529:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -ksp_fetidp_pressure_all \
3530:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3531:       -fetidp_fieldsplit_lag_ksp_type preonly \
3532:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd

3534:   test:
3535:     suffix: p2p1fetidp_discharm
3536:     requires: triangle
3537:     nsize: 4
3538:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3539:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3540:       -snes_error_if_not_converged \
3541:       -ksp_error_if_not_converged \
3542:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_type cholesky \
3543:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3544:       -fetidp_fieldsplit_lag_ksp_type preonly \
3545:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd

3547:   test:
3548:     suffix: p2p1fetidp_lumped
3549:     requires: triangle
3550:     nsize: 4
3551:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3552:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3553:       -snes_error_if_not_converged \
3554:       -ksp_error_if_not_converged \
3555:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_pc_lumped \
3556:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3557:       -fetidp_fieldsplit_lag_ksp_type preonly \
3558:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd

3560:   test:
3561:     suffix: p2p1fetidp_deluxe
3562:     requires: triangle mumps
3563:     nsize: 4
3564:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3565:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3566:       -snes_error_if_not_converged \
3567:       -ksp_error_if_not_converged \
3568:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3569:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3570:       -fetidp_fieldsplit_lag_ksp_type preonly \
3571:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat \
3572:       -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0

3574:   test:
3575:     suffix: p2p1fetidp_deluxe_discharm
3576:     requires: triangle mumps
3577:     nsize: 4
3578:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3579:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3580:       -snes_error_if_not_converged \
3581:       -ksp_error_if_not_converged \
3582:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3583:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3584:       -fetidp_fieldsplit_lag_ksp_type preonly \
3585:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat \
3586:        -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0  -fetidp_bddc_sub_schurs_discrete_harmonic

3588:   testset:
3589:     nsize: 4
3590:     requires: triangle
3591:     output_file: output/ex69_p2p1fetidp_olof.out
3592:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3593:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3594:       -snes_error_if_not_converged \
3595:       -ksp_error_if_not_converged \
3596:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_discrete_harmonic 1 -fetidp_harmonic_pc_type cholesky -ksp_fetidp_pressure_schur \
3597:       -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none -fetidp_fieldsplit_p_ksp_type preonly \
3598:       -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 \
3599:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd
3600:     test:
3601:       suffix: p2p1fetidp_olof_full
3602:       args: -fetidp_pc_fieldsplit_schur_fact_type full
3603:     test:
3604:       suffix: p2p1fetidp_olof_diag
3605:       args: -fetidp_pc_fieldsplit_schur_fact_type diag
3606:     test:

3610:   #BDDC with benign trick
3611:   testset:
3612:     suffix: q2p1bddc
3613:     output_file: output/ex69_q2p1fetidp_deluxe.out
3614:     nsize: 5
3615:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 -petscds_jac_pre 0 -snes_error_if_not_converged -ksp_error_if_not_converged -ksp_type cg -ksp_norm_type natural -pc_type bddc -pc_bddc_benign_trick -pc_bddc_nonetflux -pc_bddc_detect_disconnected -pc_bddc_vertex_size 2 -pc_bddc_coarse_redundant_pc_type svd -pc_bddc_use_qr_single
3616:     test:
3617:       requires: double
3618:       suffix: benign_card
3619:       # no native support for saddle point factorizations from PETSc
3620:       args: -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd
3621:     test:
3622:       requires: mumps double
3623:       suffix: benign_deluxe_mumps
3624:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3625:     test:
3626:       requires: mumps double
3628:       args: -pc_bddc_adaptive_threshold 1.7 -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3629:     test:
3630:       TODO: broken (INDEFINITE PC)
3631:       requires: mkl_pardiso double !complex
3632:       suffix: benign_deluxe_mkl
3633:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3634:     test:
3635:       TODO: broken (INDEFINITE PC)
3636:       requires: mkl_pardiso double !complex