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: SOLZERO,
26: NUM_SOL_TYPES
27: } SolutionType;
29: const char *solTypes[NUM_SOL_TYPES + 1] = {"solkx", "solcx", "zero", "unknown"};
31: typedef struct {
32: PetscInt n, m; /* x- and y-wavelengths for variation across the domain */
33: /* SolKx */
34: PetscReal B; /* Exponential scale for viscosity variation */
35: /* SolCx */
36: PetscReal etaA, etaB; /* Two viscosities for discontinuous change */
37: PetscReal xc; /* The location of viscosity jump */
38: } Parameter;
40: typedef struct {
41: SolutionType solType; /* The type of exact solution */
42: PetscBag bag; /* Holds problem parameters */
43: } AppCtx;
45: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
46: {
47: PetscInt c;
48: for (c = 0; c < Nc; ++c) u[c] = 0.0;
49: return PETSC_SUCCESS;
50: }
52: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
53: {
54: PetscInt c;
55: for (c = 0; c < Nc; ++c) u[c] = 1.0;
56: return PETSC_SUCCESS;
57: }
59: 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[])
60: {
61: f0[0] = 0.0;
62: f0[1] = -PetscSinScalar(constants[1] * PETSC_PI * x[1]) * PetscCosScalar(constants[0] * PETSC_PI * x[0]);
63: }
65: static void f0_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 f0[])
66: {
67: f0[0] = 0.0;
68: f0[1] = 0.0;
69: }
71: 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[])
72: {
73: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
75: for (PetscInt c = 0; c < dim; ++c) {
76: for (PetscInt d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
77: f1[c * dim + c] -= u[dim];
78: }
79: }
81: 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[])
82: {
83: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
85: for (PetscInt c = 0; c < dim; ++c) {
86: for (PetscInt d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
87: f1[c * dim + c] -= u[dim];
88: }
89: }
91: 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[])
92: {
93: f0[0] = 0.0;
94: for (PetscInt d = 0; d < dim; ++d) f0[0] -= u_x[d * dim + d];
95: }
97: 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[])
98: {
99: for (PetscInt d = 0; d < dim * dim; ++d) f1[d] = 0.0;
100: }
102: /* < q, \nabla\cdot u >, J_{pu} */
103: 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[])
104: {
105: for (PetscInt d = 0; d < dim; ++d) g1[d * dim + d] = -1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
106: }
108: /* -< \nabla\cdot v, p >, J_{up} */
109: 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[])
110: {
111: for (PetscInt d = 0; d < dim; ++d) g2[d * dim + d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
112: }
114: /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu}
115: This just gives \nabla u, give the perdiagonal for the transpose */
116: 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[])
117: {
118: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
120: for (PetscInt cI = 0; cI < dim; ++cI) {
121: for (PetscInt d = 0; d < dim; ++d) {
122: g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
123: g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
124: }
125: }
126: }
127: 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[])
128: {
129: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
131: for (PetscInt cI = 0; cI < dim; ++cI) {
132: for (PetscInt d = 0; d < dim; ++d) {
133: g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
134: g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
135: }
136: }
137: }
139: /* 1/mu < q, I q >, Jp_{pp} */
140: 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[])
141: {
142: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
143: g0[0] = 1.0 / mu;
144: }
146: 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[])
147: {
148: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
149: g0[0] = 1.0 / mu;
150: }
152: /*
153: SolKxSolution - Exact Stokes solutions for exponentially varying viscosity
155: Input Parameters:
156: + pos - The (x,z) coordinate at which to evaluate the solution
157: . n - The constant defining the x-dependence of the forcing function
158: . m - The constant defining the z-dependence of the forcing function
159: - B - The viscosity coefficient
161: Output Parameters:
162: + vel - The (x,z)-velocity at (x,z), or NULL
163: . p - The pressure at (x,z), or NULL
164: . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
165: . gamma - The strain rate, or NULL
166: - mu - The viscosity at (x,z), or NULL
168: Note:
169: .vb
170: The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
171: conditions everywhere. The forcing term f is given by
173: fx = 0
174: fz = sigma*sin(km*z)*cos(kn*x)
176: where
178: km = m*Pi (m may be non-integral)
179: kn = n*Pi
181: meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
182: The viscosity eta is exp(2*B*x).
183: .ve
185: */
186: static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
187: {
188: PetscReal sigma = 1.0;
189: PetscReal Z;
190: PetscReal u1, u2, u3, u4, u5, u6;
191: PetscReal sum1, sum2, sum3, sum4, sum5, sum6;
192: PetscReal kn, km, x, z;
193: PetscReal _PC1, _PC2, _PC3, _PC4;
194: PetscReal Rp, UU, VV;
195: PetscReal a, b, r, _aa, _bb, AA, BB, Rm;
196: PetscReal num1, num2, num3, num4, den1;
198: PetscReal t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
199: PetscReal t11, t12, t13, t14, t15, t16, t17, t18, t19, t20;
200: PetscReal t21, t22, t23, t24, t25, t26, t27, t28, t29, t30;
201: PetscReal t31, t32, t33, t34, t35, t36, t37, t38, t39, t40;
202: PetscReal t41, t42, t43, t44, t45, t46, t47, t49, t51, t53;
203: PetscReal t56, t58, t61, t62, t63, t64, t65, t66, t67, t68;
204: PetscReal t69, t70, t71, t72, t73, t74, t75, t76, t77, t78;
205: PetscReal t79, t80, t81, t82, t83, t84, t85, t86, t87, t88;
206: PetscReal t89, t90, t91, t92, t93, t94, t95, t96, t97, t99;
207: PetscReal t100, t101, t103, t104, t105, t106, t107, t108, t109, t110;
208: PetscReal t111, t112, t113, t114, t115, t116, t117, t118, t119, t120;
209: PetscReal t121, t124, t125, t126, t127, t129, t130, t132, t133, t135;
210: PetscReal t136, t138, t140, t141, t142, t143, t152, t160, t162;
212: PetscFunctionBegin;
213: /*************************************************************************/
214: /*************************************************************************/
215: /* rho = -sin(km*z)*cos(kn*x) */
216: x = pos[0];
217: z = pos[1];
218: Z = PetscExpReal(2.0 * B * x);
219: km = m * PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */
220: kn = (PetscReal)n * PETSC_PI;
221: /*************************************************************************/
222: /*************************************************************************/
223: a = B * B + km * km;
224: b = 2.0 * km * B;
225: r = PetscSqrtReal(a * a + b * b);
226: Rp = PetscSqrtReal((r + a) / 2.0);
227: Rm = PetscSqrtReal((r - a) / 2.0);
228: UU = Rp - B;
229: VV = Rp + B;
231: sum1 = 0.0;
232: sum2 = 0.0;
233: sum3 = 0.0;
234: sum4 = 0.0;
235: sum5 = 0.0;
236: sum6 = 0.0;
237: /*sum7=0.0;*/
239: /*******************************************/
240: /* calculate the constants */
241: /*******************************************/
243: t1 = kn * kn;
244: t4 = km * km;
245: t5 = t4 + t1;
246: t6 = t5 * t5;
247: t8 = pow(km + kn, 0.2e1);
248: t9 = B * B;
249: t16 = pow(km - kn, 0.2e1);
250: _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9);
252: t2 = km * km;
253: t3 = kn * kn;
254: t5 = pow(t2 + t3, 0.2e1);
255: t6 = km - kn;
256: t7 = km + kn;
257: t9 = B * B;
258: t13 = t7 * t7;
259: t19 = t6 * t6;
260: _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9);
262: AA = _aa;
263: BB = _bb;
265: /*******************************************/
266: /* calculate the velocities etc */
267: /*******************************************/
268: t1 = Rm * Rm;
269: t2 = B - Rp;
270: t4 = Rp + B;
271: t6 = UU * x;
272: t9 = PetscExpReal(t6 - 0.4e1 * Rp);
273: t13 = B * B;
274: t16 = Rp * t1;
275: t18 = Rp * Rp;
276: t19 = B * t18;
277: t20 = t13 * Rp;
278: t22 = kn * kn;
279: t24 = B * t1;
280: t32 = 0.8e1 * t13 * BB * kn * Rp;
281: t34 = 0.2e1 * Rm;
282: t35 = PetscCosReal(t34);
283: t37 = Rp * Rm;
284: t49 = PetscSinReal(t34);
285: t63 = PetscExpReal(t6 - 0.2e1 * Rp);
286: t65 = Rm * t2;
287: t67 = 0.2e1 * B * kn;
288: t68 = B * Rm;
289: t69 = t67 + t68 + t37;
290: t73 = 0.3e1 * t13;
291: t75 = 0.2e1 * B * Rp;
292: t76 = t73 - t75 + t1 - t22 - t18;
293: t78 = t65 * t76 * BB;
294: t80 = Rm - kn;
295: t81 = PetscCosReal(t80);
296: t83 = -t67 + t68 + t37;
297: t88 = Rm + kn;
298: t89 = PetscCosReal(t88);
299: t92 = t65 * t76 * AA;
300: t97 = PetscSinReal(t80);
301: t103 = PetscSinReal(t88);
302: t108 = PetscExpReal(t6 - 0.3e1 * Rp - B);
303: t110 = Rm * t4;
304: t111 = t67 + t68 - t37;
305: t115 = t73 + t75 + t1 - t22 - t18;
306: t117 = t110 * t115 * BB;
307: t120 = -t67 + t68 - t37;
308: t127 = t110 * t115 * AA;
309: t140 = PetscExpReal(t6 - Rp - B);
310: 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;
312: t1 = Rp + B;
313: t2 = Rm * t1;
314: t3 = B * B;
315: t4 = 0.3e1 * t3;
316: t5 = B * Rp;
317: t7 = Rm * Rm;
318: t8 = kn * kn;
319: t9 = Rp * Rp;
320: t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9;
321: t12 = t2 * t10 * AA;
322: t14 = B * Rm;
323: t20 = UU * x;
324: t23 = PetscExpReal(t20 - 0.4e1 * Rp);
325: t25 = Rp * Rm;
326: t32 = Rm * kn;
327: t37 = 0.2e1 * Rm;
328: t38 = PetscCosReal(t37);
329: t40 = t3 * B;
330: t44 = B * t9;
331: t45 = t3 * Rp;
332: t53 = t3 * BB;
333: t58 = PetscSinReal(t37);
334: t69 = PetscExpReal(t20 - 0.2e1 * Rp);
335: t72 = 0.3e1 * t40 * Rm;
336: t73 = t9 * Rp;
337: t74 = t73 * Rm;
338: t75 = t7 * Rm;
339: t76 = B * t75;
340: t77 = t14 * t8;
341: t78 = Rp * t75;
342: t80 = 0.8e1 * t45 * kn;
343: t81 = t25 * t8;
344: t83 = 0.5e1 * t45 * Rm;
345: t84 = t44 * Rm;
346: t85 = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84;
347: t88 = 0.2e1 * t9 * t3;
348: t90 = 0.3e1 * t40 * Rp;
349: t91 = t7 * t3;
350: t93 = 0.2e1 * t5 * t32;
351: t94 = t5 * t7;
352: t95 = t5 * t8;
353: t96 = B * t73;
354: t97 = t7 * t9;
355: t100 = 0.2e1 * t3 * Rm * kn;
356: t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100;
357: t105 = Rm - kn;
358: t106 = PetscCosReal(t105);
359: t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77;
360: t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94;
361: t114 = Rm + kn;
362: t115 = PetscCosReal(t114);
363: t121 = PetscSinReal(t105);
364: t127 = PetscSinReal(t114);
365: t132 = PetscExpReal(t20 - 0.3e1 * Rp - B);
366: t135 = 0.2e1 * B * kn;
367: t136 = t135 + t14 - t25;
368: t142 = -t135 + t14 - t25;
369: t152 = t2 * t10 * BB;
370: t162 = PetscExpReal(t20 - Rp - B);
371: 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;
373: t1 = Rm * Rm;
374: t2 = B - Rp;
375: t4 = Rp + B;
376: t6 = VV * x;
377: t7 = PetscExpReal(-t6);
378: t11 = kn * kn;
379: t13 = B * t1;
380: t14 = Rp * Rp;
381: t15 = B * t14;
382: t16 = B * B;
383: t17 = t16 * Rp;
384: t21 = Rp * t1;
385: t30 = 0.8e1 * t16 * BB * kn * Rp;
386: t32 = 0.2e1 * Rm;
387: t33 = PetscCosReal(t32);
388: t35 = Rp * Rm;
389: t47 = PetscSinReal(t32);
390: t61 = PetscExpReal(-t6 - 0.2e1 * Rp);
391: t63 = Rm * t2;
392: t65 = 0.2e1 * B * kn;
393: t66 = B * Rm;
394: t67 = t65 + t66 + t35;
395: t71 = 0.3e1 * t16;
396: t73 = 0.2e1 * B * Rp;
397: t74 = t71 - t73 + t1 - t11 - t14;
398: t76 = t63 * t74 * BB;
399: t78 = Rm - kn;
400: t79 = PetscCosReal(t78);
401: t81 = -t65 + t66 + t35;
402: t86 = Rm + kn;
403: t87 = PetscCosReal(t86);
404: t90 = t63 * t74 * AA;
405: t95 = PetscSinReal(t78);
406: t101 = PetscSinReal(t86);
407: t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B);
408: t108 = Rm * t4;
409: t109 = t65 + t66 - t35;
410: t113 = t71 + t73 + t1 - t11 - t14;
411: t115 = t108 * t113 * BB;
412: t118 = -t65 + t66 - t35;
413: t125 = t108 * t113 * AA;
414: t138 = PetscExpReal(-t6 - Rp - B);
415: 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;
417: t1 = B - Rp;
418: t2 = Rm * t1;
419: t3 = B * B;
420: t4 = 0.3e1 * t3;
421: t5 = B * Rp;
422: t7 = Rm * Rm;
423: t8 = kn * kn;
424: t9 = Rp * Rp;
425: t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9;
426: t12 = t2 * t10 * AA;
427: t14 = B * Rm;
428: t20 = VV * x;
429: t21 = PetscExpReal(-t20);
430: t23 = Rp * Rm;
431: t30 = Rm * kn;
432: t35 = 0.2e1 * Rm;
433: t36 = PetscCosReal(t35);
434: t40 = B * t9;
435: t41 = t3 * Rp;
436: t43 = t3 * B;
437: t51 = t3 * BB;
438: t56 = PetscSinReal(t35);
439: t67 = PetscExpReal(-t20 - 0.2e1 * Rp);
440: t70 = 0.2e1 * B * kn;
441: t71 = t70 + t14 + t23;
442: t76 = Rm - kn;
443: t77 = PetscCosReal(t76);
444: t79 = -t70 + t14 + t23;
445: t84 = Rm + kn;
446: t85 = PetscCosReal(t84);
447: t91 = t2 * t10 * BB;
448: t93 = PetscSinReal(t76);
449: t99 = PetscSinReal(t84);
450: t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B);
451: t107 = 0.3e1 * t43 * Rm;
452: t108 = t9 * Rp;
453: t109 = t108 * Rm;
454: t110 = t7 * Rm;
455: t111 = B * t110;
456: t112 = t14 * t8;
457: t113 = Rp * t110;
458: t115 = 0.8e1 * t41 * kn;
459: t116 = t23 * t8;
460: t118 = 0.5e1 * t41 * Rm;
461: t119 = t40 * Rm;
462: t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119;
463: t124 = 0.2e1 * t3 * Rm * kn;
464: t125 = t5 * t8;
465: t126 = B * t108;
466: t127 = t7 * t9;
467: t129 = 0.2e1 * t9 * t3;
468: t130 = t5 * t7;
469: t132 = 0.3e1 * t43 * Rp;
470: t133 = t7 * t3;
471: t135 = 0.2e1 * t5 * t30;
472: t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135;
473: t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112;
474: t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135;
475: t160 = PetscExpReal(-t20 - Rp - B);
476: 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;
478: t1 = Rm * Rm;
479: t2 = Rp * Rp;
480: t3 = t1 * t2;
481: t4 = B * B;
482: t5 = t1 * t4;
483: t9 = PetscExpReal(-0.4e1 * Rp);
484: t15 = PetscCosReal(0.2e1 * Rm);
485: t22 = PetscExpReal(-0.2e1 * Rp);
486: 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;
488: _PC1 = num1 / den1;
489: _PC2 = num2 / den1;
490: _PC3 = num3 / den1;
491: _PC4 = num4 / den1;
493: t1 = Rm * x;
494: t2 = PetscCosReal(t1);
495: t4 = PetscSinReal(t1);
496: t10 = PetscExpReal(-0.2e1 * x * B);
497: t12 = kn * x;
498: t13 = PetscCosReal(t12);
499: t16 = PetscSinReal(t12);
500: u1 = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16);
502: t2 = Rm * x;
503: t3 = PetscCosReal(t2);
504: t6 = PetscSinReal(t2);
505: t22 = PetscExpReal(-0.2e1 * x * B);
506: t23 = B * t22;
507: t24 = kn * x;
508: t25 = PetscCosReal(t24);
509: t29 = PetscSinReal(t24);
510: 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;
512: t3 = PetscExpReal(0.2e1 * x * B);
513: t4 = t3 * B;
514: t8 = km * km;
515: t9 = t3 * t8;
516: t11 = 0.3e1 * t9 * Rm;
517: t12 = Rm * Rm;
518: t14 = t3 * t12 * Rm;
519: t15 = UU * UU;
520: t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm;
521: t20 = Rm * x;
522: t21 = PetscSinReal(t20);
523: t27 = 0.2e1 * B * t9;
524: t33 = 0.2e1 * t4 * t12;
525: t36 = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU;
526: t37 = PetscCosReal(t20);
527: t49 = VV * VV;
528: t53 = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14;
529: t64 = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12;
530: t76 = B * t8;
531: t80 = kn * kn;
532: t83 = B * B;
533: t87 = t80 * kn;
534: t90 = kn * x;
535: t91 = PetscSinReal(t90);
536: t106 = PetscCosReal(t90);
537: 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;
539: t3 = PetscExpReal(0.2e1 * x * B);
540: t4 = km * km;
541: t5 = t3 * t4;
542: t6 = Rm * x;
543: t7 = PetscCosReal(t6);
544: t8 = _PC1 * t7;
545: t10 = PetscSinReal(t6);
546: t11 = _PC2 * t10;
547: t13 = _PC3 * t7;
548: t15 = _PC4 * t10;
549: t18 = kn * x;
550: t19 = PetscCosReal(t18);
551: t22 = PetscSinReal(t18);
552: t24 = UU * UU;
553: t25 = t3 * t24;
554: t28 = t3 * UU;
555: t38 = Rm * Rm;
556: t39 = t7 * t38;
557: t42 = t10 * t38;
558: 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;
559: t45 = VV * VV;
560: t46 = t3 * t45;
561: t49 = t3 * VV;
562: t62 = B * B;
563: t78 = kn * kn;
564: 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;
565: u4 = t44 + t82;
567: t3 = PetscExpReal(0.2e1 * x * B);
568: t4 = t3 * B;
569: t8 = km * km;
570: t9 = t3 * t8;
571: t10 = t9 * Rm;
572: t11 = Rm * Rm;
573: t13 = t3 * t11 * Rm;
574: t14 = UU * UU;
575: t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm;
576: t19 = Rm * x;
577: t20 = PetscSinReal(t19);
578: t26 = 0.2e1 * B * t9;
579: t31 = 0.2e1 * t4 * t11;
580: t34 = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU;
581: t35 = PetscCosReal(t19);
582: t47 = VV * VV;
583: t51 = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13;
584: t61 = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11;
585: t72 = B * t8;
586: t76 = kn * kn;
587: t79 = B * B;
588: t83 = t76 * kn;
589: t86 = kn * x;
590: t87 = PetscSinReal(t86);
591: t101 = PetscCosReal(t86);
592: 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;
594: t3 = PetscExpReal(0.2e1 * x * B);
595: t4 = UU * UU;
596: t8 = km * km;
597: t9 = t3 * t8;
598: t10 = t9 * Rm;
599: t11 = Rm * Rm;
600: t13 = t3 * t11 * Rm;
601: t14 = t3 * B;
602: t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm;
603: t19 = Rm * x;
604: t20 = PetscSinReal(t19);
605: t28 = 0.2e1 * B * t9;
606: t33 = 0.2e1 * t14 * t11;
607: t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33;
608: t35 = PetscCosReal(t19);
609: t47 = VV * VV;
610: t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm;
611: t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28;
612: t71 = kn * kn;
613: t74 = B * B;
614: t80 = t71 * kn;
615: t83 = kn * x;
616: t84 = PetscSinReal(t83);
617: t96 = PetscCosReal(t83);
618: 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;
620: /* 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))); */
622: /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */
624: sum5 += u5 * PetscCosReal(km * z); /* pressure */
625: sum6 += u6 * PetscCosReal(km * z); /* zz total stress */
627: u1 *= PetscCosReal(km * z); /* x velocity */
628: sum1 += u1;
629: u2 *= PetscSinReal(km * z); /* z velocity */
630: sum2 += u2;
632: u3 *= PetscCosReal(km * z); /* xx total stress */
633: sum3 += u3;
634: u4 *= PetscSinReal(km * z); /* zx stress */
635: sum4 += u4;
637: /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */
638: /* sum7 += rho; */
640: /* Output */
641: if (mu) *mu = Z;
642: if (vel) {
643: vel[0] = sum1;
644: vel[1] = sum2;
645: }
646: if (p) (*p) = sum5;
647: if (s) {
648: s[0] = sum3;
649: s[1] = sum4;
650: s[2] = sum6;
651: }
652: if (gamma) {
653: /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
654: gamma[0] = (sum3 + sum5) / (2.0 * Z);
655: gamma[1] = (sum4) / (2.0 * Z);
656: gamma[2] = (sum6 + sum5) / (2.0 * Z);
657: }
658: PetscFunctionReturn(PETSC_SUCCESS);
659: }
661: static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], PetscCtx ctx)
662: {
663: Parameter *s = (Parameter *)ctx;
665: PetscFunctionBegin;
666: PetscCall(SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL));
667: PetscFunctionReturn(PETSC_SUCCESS);
668: }
670: static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], PetscCtx ctx)
671: {
672: Parameter *s = (Parameter *)ctx;
674: PetscFunctionBegin;
675: PetscCall(SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL));
676: PetscFunctionReturn(PETSC_SUCCESS);
677: }
679: /*
680: SolCxSolution - Exact Stokes solutions for discontinuous viscosity
682: Input Parameters:
683: + pos - The (x,z) coordinate at which to evaluate the solution
684: . n - The constant defining the x-dependence of the forcing function
685: . m - The constant defining the z-dependence of the forcing function
686: . xc - The x coordinate at which the viscosity is discontinuous
687: . etaA - The viscosity coefficient for x < xc
688: - etaB - The viscosity coefficient for x > xc
690: Output Parameters:
691: + vel - The (x,z)-velocity at (x,z), or NULL
692: . p - The pressure at (x,z), or NULL
693: . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
694: . gamma - The strain rate, or NULL
695: - mu - The viscosity at (x,z), or NULL
697: Note:
698: .vb
699: The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
700: conditions everywhere. The forcing term f is given by
702: fx = 0
703: fz = sigma*sin(km*z)*cos(kn*x)
705: where
707: km = m*Pi (m may be non-integral)
708: kn = n*Pi
710: meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
711: The viscosity eta jumps from etaA to etaB at x = xc.
712: .ve
713: */
714: 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)
715: {
716: PetscReal _PC1A, _PC2A, _PC3A, _PC4A, _PC1B, _PC2B, _PC3B, _PC4B, _PC1, _PC2, _PC3, _PC4;
717: 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;
718: 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;
719: 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;
720: 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;
721: 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;
722: 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;
723: 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;
724: 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;
725: 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;
726: 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;
727: 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;
728: 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;
729: 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;
730: 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;
731: PetscReal t561, t562, t563, t564, t567, t568, t571, t573, t575, t576, t578, t579, t583, t590, t591, t594, t595, t596, t597, t598, t600;
732: 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;
733: 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;
734: 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;
735: 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;
736: 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;
737: PetscReal t801, t806, t807, t808, t809, t811, t812, t817, t818, t819, t821, t822, t824, t827, t828, t830, t834, t835, t837, t840;
738: 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;
739: PetscReal t884, t888, t891, t894, t900, t901, t903, t904, t907, t908, t909, t911, t914, t915, t916, t919, t920;
740: 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;
741: PetscReal t961, t964, t965, t966, t967, t968, t969, t971, t972, t974, t977, t978, t981, t983, t987, t988, t992, t993, t994, t997, t998;
742: PetscReal t1001, t1003, t1005, t1006, t1009, t1010, t1012, t1013, t1015, t1016, t1017, t1018, t1020, t1021, t1029, t1031, t1032, t1033, t1040;
743: PetscReal t1041, t1042, t1044, t1047, t1050, t1054, t1055, t1057, t1058, t1063, t1068, t1069, t1070, t1079, t1080;
744: PetscReal t1088, t1089, t1091, t1092, t1094, t1096, t1101, t1102, t1103, t1104, t1105, t1108, t1112, t1113, t1118, t1119, t1120;
745: 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;
746: PetscReal t1161, t1162, t1165, t1166, t1170, t1171, t1172, t1173, t1175, t1176, t1178, t1180, t1181, t1182, t1185, t1189, t1192, t1193, t1195, t1196, t1199;
747: PetscReal t1201, t1203, t1209, t1210, t1211, t1213, t1214, t1218, t1221, t1224, t1225, t1226, t1228, t1233, t1234, t1235, t1236, t1237, t1240;
748: PetscReal t1241, t1242, t1243, t1244, t1245, t1248, t1251, t1252, t1257, t1258, t1259, t1260, t1263, t1268, t1269, t1272, t1280;
749: PetscReal t1282, t1283, t1284, t1285, t1287, t1288, t1289, t1292, t1293, t1296, t1297, t1300, t1304, t1307, t1310, t1311, t1312, t1316, t1317, t1320;
750: PetscReal t1321, t1323, t1328, t1330, t1331, t1332, t1333, t1336, t1338, t1343, t1344, t1346, t1349, t1350, t1354;
751: PetscReal t1366, t1369, t1370, t1371, t1376, t1378, t1380, t1383, t1386, t1387, t1388, t1391, t1393, t1399;
752: PetscReal t1411, t1412, t1420, t1427;
753: PetscReal t1450, t1456, t1468, t1472, t1474, t1478;
754: PetscReal t1504, t1511;
755: PetscReal t1545;
756: PetscReal t1564, t1583;
758: PetscReal sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, sum6 = 0.0;
759: PetscReal ZA = etaA, ZB = etaB;
760: PetscInt nz = m, nx = n;
761: PetscReal u1, u2, u3, u4, u5, u6, Z, x = pos[0], z = pos[1];
763: PetscFunctionBegin;
764: /* Note that there is no Fourier sum here. */
765: /****************************************************************************************/
766: _PC1A = 0;
767: /****************************************************************************************/
768: t1 = nx * 0.3141592654e1;
769: t2 = PetscSinReal(t1);
770: t3 = nx * t2;
771: t4 = nz * nz;
772: t5 = t4 * t4;
773: t6 = 0.3141592654e1 * 0.3141592654e1;
774: t8 = t3 * t5 * t6;
775: t9 = ZA * xc;
776: t12 = PetscExpReal(xc * nz * 0.3141592654e1);
777: t13 = t12 * t12;
778: t15 = nz * 0.3141592654e1;
779: t16 = PetscExpReal(t15);
780: t17 = t16 * t16;
781: t18 = t17 * t16;
782: t19 = ZB * t13 * t18;
783: t20 = t9 * t19;
784: t23 = ZA * ZA;
785: t24 = nx * nx;
786: t25 = t24 * nx;
787: t26 = t23 * t25;
788: t28 = t13 * t13;
789: t29 = t28 * t13;
790: t33 = nx * ZB;
791: t34 = t1 * xc;
792: t35 = PetscSinReal(t34);
793: t36 = t4 * nz;
794: t37 = t35 * t36;
795: t38 = t33 * t37;
796: t39 = 0.3141592654e1 * ZA;
797: t40 = t13 * t12;
798: t41 = t17 * t40;
799: t45 = ZB * ZB;
800: t46 = t45 * t24;
801: t47 = t46 * t4;
802: t48 = 0.3141592654e1 * xc;
803: t49 = t13 * t17;
804: t53 = xc * xc;
805: t54 = t36 * t53;
806: t56 = t54 * t6 * t45;
807: t57 = PetscCosReal(t34);
808: t58 = t57 * t24;
809: t59 = t28 * t12;
810: t60 = t17 * t59;
811: t61 = t58 * t60;
812: t64 = t25 * t2;
813: t65 = t64 * t15;
814: t72 = nx * t23;
815: t74 = t72 * t2 * t5;
816: t75 = t6 * t53;
817: t76 = t16 * t29;
818: t80 = t23 * nz;
819: t81 = t80 * 0.3141592654e1;
820: t82 = t18 * t28;
821: t86 = nx * t5;
822: t87 = t23 * t6;
823: t89 = xc * t2;
824: t90 = t13 * t18;
825: t91 = t89 * t90;
826: t94 = t28 * t28;
827: t96 = t24 * nz;
828: t98 = t4 * t45;
829: t99 = t98 * 0.3141592654e1;
830: t100 = t58 * t41;
831: t104 = 0.3141592654e1 * t25;
832: t105 = ZA * nz * t104;
833: t106 = t2 * ZB;
834: t110 = t17 * t17;
835: t111 = ZA * t110;
836: t116 = nz * t28;
837: t122 = t64 * t4 * t6;
838: t126 = t23 * t29 * t4;
839: t128 = t24 * xc;
840: t132 = t36 * t23;
841: t133 = t6 * t57;
842: t135 = t128 * t41;
843: t138 = t6 * xc;
844: t142 = t72 * t2;
845: 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;
846: t149 = ZA * t25 * t2;
847: t150 = ZB * t28;
848: t154 = t35 * t5;
849: t155 = t72 * t154;
850: t156 = t75 * t41;
851: t159 = nx * ZA;
852: t160 = t2 * t36;
853: t161 = t159 * t160;
854: t162 = 0.3141592654e1 * ZB;
855: t163 = t28 * t16;
856: t167 = t23 * t57;
857: t168 = t167 * t24;
858: t169 = nz * t110;
859: t170 = t169 * t40;
860: t173 = ZA * ZB;
861: t174 = t173 * t90;
862: t177 = t36 * 0.3141592654e1;
863: t181 = t80 * t104;
864: t184 = nz * t17;
865: t188 = t17 * t29;
866: t190 = t4 * 0.3141592654e1;
867: t191 = t190 * t24;
868: t206 = t138 * t60;
869: t209 = t23 * t4;
870: t211 = t209 * t6 * t25;
871: t212 = t89 * t76;
872: t216 = ZB * t16 * t29;
873: t217 = t9 * t216;
874: t220 = ZB * t110;
875: t221 = ZA * t24;
876: t222 = t221 * nz;
877: t225 = t132 * t75;
878: t232 = t45 * t28;
879: t233 = t110 * t24;
880: t234 = t233 * nz;
881: t236 = t209 * 0.3141592654e1;
882: t237 = t17 * xc;
883: t239 = t237 * t13 * t24;
884: 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;
885: t244 = nx * t45;
886: t245 = t244 * t37;
887: t246 = t110 * t40;
888: t251 = t237 * t59;
889: t256 = t64 * t90;
890: t260 = t36 * t45 * t133;
891: t263 = t45 * t57;
892: t264 = t263 * t24;
893: t265 = t169 * t12;
894: t269 = t6 * t36;
895: t270 = t17 * t24;
896: t274 = t110 * t13;
897: t276 = t190 * t128;
898: t279 = nx * t36;
899: t281 = t28 * t40;
900: t282 = t281 * t35;
901: t286 = t138 * t41;
902: t289 = t75 * t60;
903: t296 = t190 * t173;
904: t305 = t86 * t45 * t35;
905: t312 = t33 * t154;
906: t313 = t6 * ZA;
907: t324 = t232 * t270;
908: 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;
909: t328 = t3 * t4;
910: t331 = t72 * t37;
911: t332 = t48 * t60;
912: t335 = nz * t94;
913: t345 = t72 * t35;
914: t349 = t173 * t57;
915: t355 = t53 * t17;
916: t364 = t54 * t6 * ZB;
917: t365 = t28 * t17;
918: t369 = xc * ZB;
919: t370 = t269 * t369;
920: t371 = ZA * t57;
921: t373 = t371 * t270 * t40;
922: t385 = nx * t35;
923: t396 = t4 * xc;
924: t397 = t396 * t162;
925: t415 = t37 * t48;
926: 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;
927: t427 = t371 * t270 * t59;
928: t439 = t209 * t48;
929: t440 = t110 * t12;
930: t441 = t58 * t440;
931: t447 = t36 * xc;
932: t455 = t48 * t440;
933: t471 = ZB * t17;
934: 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;
935: t499 = ZA * t53 * t19;
936: t505 = t396 * 0.3141592654e1;
937: t518 = t173 * t53 * t16 * t29;
938: t533 = t23 * t28;
939: t535 = t188 * t45;
940: t538 = t24 * t4;
941: t545 = t3 * t177;
942: t546 = t173 * t76;
943: t555 = t45 * t110;
944: t557 = t72 * t160;
945: 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;
946: t567 = t396 * 0.3141592654e1 * t45;
947: t568 = t58 * t246;
948: t597 = t58 * nz;
949: t615 = t13 * t45;
950: t616 = t615 * t233;
951: t619 = t94 * t45;
952: t621 = t45 * t59;
953: 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;
954: t626 = t49 * t45;
955: t660 = t29 * t45;
956: 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;
957: t690 = t6 * 0.3141592654e1;
958: t691 = ZA * t690;
959: t693 = t24 * t24;
960: t694 = t693 * xc;
961: t695 = t188 * t694;
962: t698 = t23 * ZA;
963: t699 = t698 * t690;
964: t700 = t699 * t5;
965: t704 = t5 * t4;
966: t705 = t691 * t704;
967: t709 = t691 * t5;
968: t713 = t5 * nz;
969: t714 = t713 * ZB;
970: t718 = t698 * t6;
971: t719 = t713 * t28;
972: t722 = t699 * t704;
973: t726 = t713 * t94;
974: t733 = t713 * t45;
975: t736 = t87 * t36;
976: 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;
977: t746 = t313 * t36;
978: t752 = t6 * t6;
979: t753 = t23 * t752;
980: t759 = t698 * t752;
981: t760 = t759 * t36;
982: t761 = t17 * t693;
983: t762 = xc * t28;
984: t763 = t761 * t762;
985: t766 = t87 * t713;
986: t773 = t699 * t4;
987: t774 = t110 * t693;
988: t775 = xc * t13;
989: t785 = t704 * t17;
990: 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;
991: t791 = t691 * t4;
992: t792 = t45 * t693;
993: t793 = t49 * t792;
994: t796 = t759 * t713;
995: t797 = t53 * t28;
996: t798 = t270 * t797;
997: t801 = t87 * nz;
998: t818 = t5 * t36;
999: t819 = t753 * t818;
1000: t827 = t753 * t36 * ZB;
1001: t830 = xc * t45;
1002: 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;
1003: t842 = xc * t29;
1004: t843 = t270 * t842;
1005: t849 = t759 * t818;
1006: t853 = t691 * t396;
1007: t857 = t691 * t5 * t45;
1008: t869 = t313 * nz;
1009: 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;
1010: t877 = ZA * t752;
1011: t878 = t877 * t818;
1012: 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;
1013: t916 = t110 * t28;
1014: t945 = t28 * t693 * t45 * t17;
1015: 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;
1016: t974 = t761 * t797;
1017: 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;
1018: 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;
1020: _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);
1021: /****************************************************************************************/
1022: t1 = nz * nz;
1023: t2 = t1 * nz;
1024: t3 = t2 * 0.3141592654e1;
1025: t4 = t3 * xc;
1026: t5 = ZB * ZB;
1027: t7 = PetscExpReal(nz * 0.3141592654e1);
1028: t8 = t7 * t7;
1029: t9 = t5 * t8;
1030: t12 = PetscExpReal(xc * nz * 0.3141592654e1);
1031: t13 = t12 * t12;
1032: t14 = t13 * t13;
1033: t15 = t14 * t13;
1034: t19 = nx * nx;
1035: t21 = nx * 0.3141592654e1;
1036: t22 = PetscSinReal(t21);
1037: t23 = t19 * nx * t22;
1038: t24 = t23 * 0.3141592654e1;
1039: t25 = ZA * ZB;
1040: t26 = t7 * t15;
1041: t27 = t25 * t26;
1042: t30 = t21 * xc;
1043: t31 = PetscSinReal(t30);
1044: t32 = t31 * nx;
1045: t33 = t32 * nz;
1046: t34 = ZA * ZA;
1047: t35 = t8 * t8;
1048: t36 = t34 * t35;
1049: t40 = t2 * t34;
1050: t41 = 0.3141592654e1 * t8;
1051: t42 = t41 * t15;
1052: t45 = t1 * t5;
1053: t46 = t14 * t14;
1054: t49 = t19 * t5;
1055: t51 = t19 * t46;
1056: t53 = t19 * t34;
1057: t55 = t8 * t7;
1058: t56 = t13 * t55;
1059: t57 = t25 * t56;
1060: t60 = t2 * nx;
1061: t61 = 0.3141592654e1 * 0.3141592654e1;
1062: t63 = t60 * t31 * t61;
1063: t64 = xc * xc;
1064: t65 = ZA * t64;
1065: t66 = ZB * t8;
1066: t67 = t14 * t12;
1067: t68 = t66 * t67;
1068: t69 = t65 * t68;
1069: 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;
1070: t73 = t1 * nx;
1071: t75 = t73 * t31 * 0.3141592654e1;
1072: t76 = t8 * t67;
1073: t77 = t25 * t76;
1074: t80 = t1 * t1;
1075: t81 = t80 * t34;
1076: t83 = t61 * t14;
1077: t87 = t1 * t19;
1078: t88 = PetscCosReal(t30);
1079: t90 = t87 * t88 * t61;
1080: t91 = t5 * t64;
1081: t92 = t13 * t12;
1082: t93 = t8 * t92;
1083: t94 = t91 * t93;
1084: t100 = ZB * t64 * ZA * t8 * t92;
1085: t103 = nz * t19;
1086: t105 = t103 * t88 * 0.3141592654e1;
1087: t106 = ZA * xc;
1088: t107 = ZB * t35;
1089: t109 = t106 * t107 * t12;
1090: t112 = t34 * xc;
1091: t113 = t112 * t93;
1092: t116 = t35 * t14;
1093: t118 = t1 * ZA;
1094: t119 = ZB * t14;
1095: t122 = t1 * t46;
1096: t125 = t19 * ZB;
1097: t126 = t35 * ZA;
1098: t127 = t125 * t126;
1099: t129 = t1 * ZB;
1100: 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;
1101: t134 = t1 * t34;
1102: t136 = t34 * t64;
1103: t137 = t136 * t76;
1104: t141 = t91 * t76;
1105: t145 = t103 * t34;
1106: t146 = 0.3141592654e1 * xc;
1107: t147 = t8 * t13;
1108: t153 = t14 * ZA;
1109: t156 = xc * t5;
1110: t157 = t156 * t93;
1111: t160 = t103 * t5;
1112: t162 = t146 * t8 * t15;
1113: t166 = t34 * t7 * t15;
1114: 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;
1115: t170 = t106 * t68;
1116: t177 = t35 * t92;
1117: t178 = t112 * t177;
1118: t181 = t156 * t76;
1119: t186 = t35 * t12;
1120: t187 = t112 * t186;
1121: t193 = t5 * 0.3141592654e1;
1122: t206 = t34 * t14;
1123: t207 = t206 * t7;
1124: 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;
1125: t217 = t106 * t66 * t92;
1126: t226 = t88 * t19 * nz;
1127: t227 = 0.3141592654e1 * t34;
1128: t229 = t227 * xc * t67;
1129: t232 = t73 * t31;
1130: t234 = t146 * t5 * t67;
1131: t238 = t61 * ZB;
1132: t239 = t14 * t8;
1133: t240 = t238 * t239;
1134: t243 = t136 * t93;
1135: 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;
1136: t247 = t14 * t92;
1137: t249 = t227 * t247 * xc;
1138: t254 = t73 * t22;
1139: t259 = t60 * t22 * t61;
1140: t260 = t112 * t26;
1141: t264 = t146 * t247 * t5;
1142: t268 = xc * t14;
1143: t274 = t5 * t14;
1144: t275 = t274 * t8;
1145: t280 = nz * nx;
1146: t281 = t280 * t22;
1147: t282 = t55 * t14;
1148: t283 = t25 * t282;
1149: t290 = ZA * t247 * xc * ZB;
1150: t295 = t22 * nx * t1 * 0.3141592654e1;
1151: 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;
1152: t301 = t61 * t5;
1153: t307 = t87 * t34;
1154: t312 = t61 * xc;
1155: t313 = t312 * t239;
1156: t317 = t34 * t55 * t14;
1157: t329 = ZB * t13 * t55;
1158: t330 = t65 * t329;
1159: 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;
1160: t340 = t5 * t35;
1161: t344 = t25 * t93;
1162: t356 = t41 * t13;
1163: t360 = t23 * nz * t61;
1164: t363 = t25 * t64 * t7 * t15;
1165: t366 = t156 * t177;
1166: t369 = t14 * t7;
1167: t370 = t25 * t369;
1168: t373 = t156 * t186;
1169: 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;
1170: t382 = t112 * t76;
1171: t387 = t80 * t61;
1172: t391 = t136 * t26;
1173: 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;
1174: t423 = t153 * t8;
1175: t426 = t34 * t13;
1176: t427 = t426 * t55;
1177: t430 = t34 * t8;
1178: t437 = t80 * ZA;
1179: 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;
1180: t453 = t106 * ZB * t7 * t15;
1181: t456 = t2 * t5;
1182: t459 = t112 * t56;
1183: t462 = t126 * t14;
1184: t474 = t40 * 0.3141592654e1;
1185: t475 = xc * t8;
1186: t480 = t146 * t13 * t35;
1187: 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;
1188: t497 = t136 * t56;
1189: t504 = t9 * t13;
1190: t509 = t475 * t13;
1191: 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;
1192: t528 = t5 * t13;
1193: t529 = t528 * t35;
1194: t532 = t106 * t329;
1195: 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;
1196: t557 = t146 * t15;
1197: t562 = xc * t15;
1198: t563 = t562 * t5;
1199: 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;
1200: 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;
1201: t623 = xc * t13;
1202: 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;
1203: t632 = t61 * 0.3141592654e1;
1204: t633 = t632 * t8;
1205: t634 = t80 * nz;
1206: t638 = t632 * t634;
1207: t639 = t638 * xc;
1208: t642 = t61 * t34;
1209: t643 = t122 * t19;
1210: t649 = t61 * t61;
1211: t650 = t649 * t1;
1212: t652 = t19 * t19;
1213: t653 = t14 * t652;
1214: t654 = t653 * t9;
1215: t657 = t14 * t1;
1216: t658 = t657 * t19;
1217: t665 = t632 * t34;
1218: t666 = t665 * t2;
1219: t667 = t8 * t19;
1220: t668 = t667 * t623;
1221: t674 = t665 * nz;
1222: t675 = t652 * xc;
1223: 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;
1224: t683 = t46 * t652;
1225: t686 = t633 * t15;
1226: t691 = t35 * t80;
1227: t698 = t35 * t652;
1228: t705 = t14 * t80;
1229: t708 = t61 * t35;
1230: 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;
1231: t727 = t61 * t46;
1232: t737 = t649 * t34;
1233: t738 = t737 * t1;
1234: t739 = t8 * t652;
1235: t740 = t739 * t268;
1236: t746 = t61 * ZA;
1237: t754 = t632 * nz * xc;
1238: 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;
1239: t762 = t633 * t13;
1240: t764 = t5 * nz * t652;
1241: t767 = t80 * t1;
1242: t768 = t649 * t767;
1243: t772 = t649 * ZA;
1244: t773 = t772 * t129;
1245: t777 = t35 * t1 * t19;
1246: t780 = t632 * t5;
1247: t781 = t780 * t15;
1248: t786 = t698 * ZA;
1249: t790 = t64 * t14;
1250: t800 = t649 * t8;
1251: 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;
1252: t812 = t649 * t80;
1253: t817 = t83 * ZB;
1254: t824 = t746 * ZB;
1255: t828 = t800 * t14;
1256: 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;
1257: t858 = t35 * t19;
1258: t873 = t2 * t8;
1259: t878 = t61 * t1;
1260: 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;
1261: t903 = t739 * t790;
1262: t923 = t737 * t80;
1263: t924 = t667 * t790;
1264: t927 = t780 * t2;
1265: t937 = t15 * t19 * xc;
1266: 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;
1267: 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;
1269: _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);
1270: /****************************************************************************************/
1271: _PC4A = 0;
1272: /****************************************************************************************/
1273: t1 = nx * 0.3141592654e1;
1274: t2 = t1 * xc;
1275: t3 = PetscCosReal(t2);
1276: t4 = nx * nx;
1277: t6 = nz * 0.3141592654e1;
1278: t7 = t3 * t4 * t6;
1279: t8 = ZA * ZB;
1280: t9 = PetscExpReal(t6);
1281: t10 = t9 * t9;
1282: t11 = xc * nz;
1283: t13 = PetscExpReal(t11 * 0.3141592654e1);
1284: t14 = t13 * t13;
1285: t15 = t14 * t13;
1286: t16 = t14 * t14;
1287: t17 = t16 * t15;
1288: t18 = t10 * t17;
1289: t19 = t8 * t18;
1290: t22 = PetscSinReal(t2);
1291: t23 = nx * t22;
1292: t24 = t23 * nz;
1293: t25 = ZB * ZB;
1294: t30 = nz * nz;
1295: t31 = t30 * nz;
1296: t32 = t31 * nx;
1297: t33 = 0.3141592654e1 * 0.3141592654e1;
1298: t35 = t32 * t22 * t33;
1299: t36 = ZA * ZA;
1300: t37 = t36 * xc;
1301: t38 = t16 * t13;
1302: t39 = t10 * t38;
1303: t40 = t37 * t39;
1304: t43 = PetscSinReal(t1);
1305: t44 = nx * t43;
1306: t45 = t30 * 0.3141592654e1;
1307: t46 = t44 * t45;
1308: t47 = ZA * xc;
1309: t49 = ZB * t16 * t9;
1310: t54 = t4 * nx * t43;
1311: t55 = xc * xc;
1312: t57 = t54 * t30 * t55;
1313: t58 = t33 * 0.3141592654e1;
1314: t59 = t58 * t25;
1315: t60 = t16 * t9;
1316: t61 = t59 * t60;
1317: t64 = xc * t25;
1318: t65 = t14 * t9;
1319: t66 = t64 * t65;
1320: t70 = t44 * t31 * t33;
1321: t71 = t37 * t65;
1322: t74 = t10 * t15;
1323: t75 = t64 * t74;
1324: t78 = t25 * t10;
1325: t83 = t54 * nz * t33;
1326: t84 = t55 * t25;
1327: t85 = t10 * t9;
1328: t86 = t14 * t85;
1329: t87 = t84 * t86;
1330: t90 = t30 * t30;
1331: t92 = t44 * t90 * t58;
1332: t93 = t55 * xc;
1333: t94 = t93 * t25;
1334: t95 = t85 * t16;
1335: t96 = t94 * t95;
1336: t102 = t23 * t45;
1337: t103 = t10 * t10;
1338: t104 = ZB * t103;
1339: t106 = t47 * t104 * t15;
1340: t111 = t54 * 0.3141592654e1;
1341: t112 = t25 * t85;
1342: t113 = t112 * t16;
1343: t115 = t8 * t39;
1344: t118 = t16 * t14;
1345: t119 = t85 * t118;
1346: t120 = t37 * t119;
1347: t123 = t16 * t16;
1348: t124 = t36 * t123;
1349: t125 = t124 * t9;
1350: 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;
1351: t128 = t37 * t74;
1352: t131 = t44 * nz;
1353: t133 = t25 * t9 * t118;
1354: t136 = t36 * t14;
1355: t137 = t136 * t9;
1356: t140 = t30 * t4;
1357: t142 = t140 * t3 * t33;
1358: t143 = t64 * t39;
1359: t147 = t30 * nx * t43;
1360: t148 = 0.3141592654e1 * t36;
1361: t149 = t9 * t118;
1362: t153 = t44 * t31 * ZA;
1363: t154 = t33 * xc;
1364: t155 = t154 * t49;
1365: t160 = ZA * t17 * xc * ZB;
1366: t163 = t103 * t13;
1367: t164 = t64 * t163;
1368: t170 = t44 * t90 * t55;
1369: t171 = t58 * ZB;
1370: t172 = ZA * t16;
1371: t174 = t171 * t172 * t9;
1372: t177 = t36 * t55;
1373: t178 = t177 * t149;
1374: t181 = t54 * t11;
1375: t182 = t33 * t25;
1376: t186 = t25 * t14;
1377: t187 = t186 * t9;
1378: t193 = t186 * t85;
1379: t198 = ZB * t55;
1380: t199 = ZA * t103;
1381: t201 = t198 * t199 * t15;
1382: 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;
1383: t210 = t32 * t22;
1384: t211 = t33 * t55;
1385: t212 = t25 * t38;
1386: t213 = t211 * t212;
1387: t216 = nz * nx;
1388: t217 = t22 * t25;
1389: t222 = ZB * t85 * t16;
1390: t226 = t23 * t30;
1391: t227 = t13 * t10;
1392: t228 = t148 * t227;
1393: t233 = t37 * t163;
1394: t237 = nz * t4 * t3;
1395: t238 = t148 * t74;
1396: t241 = t64 * t86;
1397: t245 = t148 * xc * t15;
1398: t248 = t112 * t118;
1399: t250 = t22 * t36;
1400: t256 = 0.3141592654e1 * t25;
1401: t257 = t256 * t39;
1402: t262 = t38 * t103;
1403: t263 = t37 * t262;
1404: t267 = t148 * t17 * xc;
1405: 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;
1406: t273 = t37 * t149;
1407: t277 = t47 * t104 * t13;
1408: t285 = t31 * t36;
1409: t286 = t44 * t285;
1410: t291 = t25 * t123 * t9;
1411: t304 = 0.3141592654e1 * xc;
1412: t305 = t304 * t212;
1413: t312 = t256 * t18;
1414: t315 = t8 * t60;
1415: t319 = t54 * t30 * t58;
1416: t323 = t90 * t36;
1417: t324 = t44 * t323;
1418: t325 = t55 * t58;
1419: t326 = t325 * t60;
1420: 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;
1421: t332 = t8 * t95;
1422: t335 = t136 * t85;
1423: t337 = t256 * t227;
1424: t340 = t177 * t119;
1425: t346 = t37 * t86;
1426: t351 = t103 * t15;
1427: t352 = t177 * t351;
1428: t355 = t64 * t119;
1429: t358 = t8 * t227;
1430: t361 = t85 * 0.3141592654e1;
1431: t365 = t84 * t39;
1432: t372 = ZB * t10;
1433: t373 = t372 * t38;
1434: t374 = t47 * t373;
1435: t379 = t177 * t39;
1436: 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;
1437: t386 = t54 * t30 * t93;
1438: t387 = ZA * t85;
1439: t389 = t171 * t387 * t16;
1440: t394 = t64 * t60;
1441: t398 = t304 * t25 * t15;
1442: t401 = t361 * t25;
1443: t405 = t84 * t65;
1444: t410 = t148 * t18;
1445: t414 = t25 * t16 * t9;
1446: t417 = t84 * t74;
1447: t422 = t177 * t86;
1448: t428 = ZB * t38;
1449: t429 = t47 * t428;
1450: t432 = t148 * t39;
1451: 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;
1452: t442 = t36 * t9 * t118;
1453: t444 = t123 * t9;
1454: t445 = t8 * t444;
1455: t448 = t361 * t36;
1456: t451 = t47 * t372 * t17;
1457: t454 = t94 * t60;
1458: t457 = t25 * t103;
1459: t465 = t47 * t372 * t15;
1460: t468 = t36 * t85;
1461: t469 = t468 * t16;
1462: t474 = t43 * t85;
1463: t478 = t8 * t74;
1464: t484 = t256 * t74;
1465: t489 = t198 * ZA * t10 * t15;
1466: 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;
1467: t504 = t33 * t36 * t55 * t38;
1468: t507 = t37 * t18;
1469: t512 = t47 * ZB * t13 * t10;
1470: t518 = t59 * t95;
1471: t530 = t84 * t351;
1472: t534 = t37 * t227;
1473: 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;
1474: t557 = t468 * t118;
1475: t562 = t93 * t58;
1476: t563 = t562 * t60;
1477: t567 = t44 * t90 * t93;
1478: t575 = ZA * t55;
1479: t576 = t575 * t428;
1480: t583 = t37 * t60;
1481: t590 = t140 * t3;
1482: 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;
1483: t604 = nz * t36;
1484: t606 = t154 * t95;
1485: t625 = t36 * t103;
1486: t640 = t30 * t36;
1487: t641 = t54 * t640;
1488: t642 = t325 * t95;
1489: 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;
1490: t652 = t36 * t16;
1491: t653 = t652 * t9;
1492: t655 = t64 * t227;
1493: t658 = t182 * t95;
1494: t663 = t562 * t95;
1495: t684 = t64 * t351;
1496: t689 = t36 * t10;
1497: t695 = t154 * t222;
1498: 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;
1499: t711 = t575 * t373;
1500: t717 = t304 * t17 * t25;
1501: t736 = t177 * t74;
1502: 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;
1503: t750 = t64 * t262;
1504: t763 = t44 * t640;
1505: t770 = t84 * t119;
1506: 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;
1507: t797 = t64 * t149;
1508: 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;
1509: t827 = t84 * t149;
1510: t846 = t54 * nz * ZA;
1511: t854 = t64 * t18;
1512: 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;
1513: 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;
1514: t914 = t25 * ZB;
1515: t915 = t33 * t914;
1516: t919 = t4 * t4;
1517: t920 = t16 * t919;
1518: t929 = t123 * t90;
1519: t932 = t919 * t103;
1520: t935 = t33 * ZB;
1521: t939 = t652 * t919;
1522: t942 = t16 * t30;
1523: t943 = t942 * t4;
1524: t949 = t103 * t16;
1525: t950 = t949 * t90;
1526: 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;
1527: t954 = t171 * t36;
1528: t955 = t90 * nz;
1529: t956 = xc * t955;
1530: t957 = t118 * t10;
1531: t964 = t33 * t33;
1532: t965 = t964 * ZB;
1533: t966 = t965 * t640;
1534: t967 = t10 * t919;
1535: t968 = t55 * t16;
1536: t969 = t967 * t968;
1537: t972 = t935 * t36;
1538: t974 = t103 * t30 * t4;
1539: t977 = xc * t16;
1540: t978 = t967 * t977;
1541: t981 = t90 * t30;
1542: t983 = t16 * t10;
1543: t987 = t182 * ZA;
1544: t988 = t4 * t10;
1545: t992 = t171 * t604;
1546: t993 = xc * t14;
1547: t994 = t932 * t993;
1548: t997 = t182 * t30;
1549: t1005 = t171 * t285;
1550: t1006 = t988 * t993;
1551: t1009 = t58 * t914;
1552: t1010 = t1009 * t31;
1553: 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;
1554: t1015 = t964 * t25;
1555: t1016 = ZA * t30;
1556: t1017 = t1015 * t1016;
1557: t1020 = t967 * t993;
1558: t1031 = t1009 * t118;
1559: t1032 = t31 * t10;
1560: t1040 = t964 * t914;
1561: t1041 = t1040 * t90;
1562: t1044 = t55 * t10 * t4 * t16;
1563: t1047 = t1040 * t30;
1564: t1050 = t123 * ZA;
1565: t1054 = t977 * t988;
1566: 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;
1567: t1058 = t1009 * nz;
1568: t1063 = t932 * ZA;
1569: t1069 = t123 * t30 * t4;
1570: t1080 = t993 * t103 * t4;
1571: t1088 = t935 * t103;
1572: 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;
1573: t1113 = t955 * t118 * xc;
1574: t1120 = t4 * t118;
1575: t1125 = t981 * xc;
1576: t1133 = nz * t10;
1577: 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;
1578: t1153 = xc * t118;
1579: t1165 = t182 * t16;
1580: t1170 = t171 * t10;
1581: t1178 = ZA * t90;
1582: 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;
1583: t1195 = t1040 * t981;
1584: t1199 = t1009 * t955;
1585: t1203 = t1009 * t10;
1586: t1211 = t965 * t323;
1587: 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;
1588: 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;
1590: _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);
1591: /****************************************************************************************/
1592: t1 = nz * nz;
1593: t2 = t1 * nz;
1594: t3 = nx * t2;
1595: t4 = 0.3141592654e1 * ZA;
1596: t5 = t3 * t4;
1597: t6 = nx * 0.3141592654e1;
1598: t7 = t6 * xc;
1599: t8 = PetscSinReal(t7);
1600: t9 = t8 * ZB;
1601: t10 = nz * 0.3141592654e1;
1602: t11 = PetscExpReal(t10);
1603: t12 = t11 * t11;
1604: t15 = PetscExpReal(xc * nz * 0.3141592654e1);
1605: t16 = t15 * t15;
1606: t17 = t16 * t16;
1607: t18 = t17 * t15;
1608: t19 = t12 * t18;
1609: t23 = t1 * t1;
1610: t24 = nx * t23;
1611: t25 = ZB * ZB;
1612: t27 = t18 * t8;
1613: t28 = 0.3141592654e1 * 0.3141592654e1;
1614: t29 = xc * xc;
1615: t30 = t28 * t29;
1616: t34 = t1 * xc;
1617: t35 = 0.3141592654e1 * ZB;
1618: t36 = t34 * t35;
1619: t37 = PetscCosReal(t7);
1620: t38 = ZA * t37;
1621: t39 = nx * nx;
1622: t40 = t39 * t12;
1623: t41 = t16 * t15;
1624: t43 = t38 * t40 * t41;
1625: t46 = t25 * nz;
1626: t47 = t46 * 0.3141592654e1;
1627: t48 = t39 * nx;
1628: t49 = PetscSinReal(t6);
1629: t50 = t48 * t49;
1630: t51 = t12 * t11;
1631: t52 = t51 * t17;
1632: t53 = t50 * t52;
1633: t56 = t34 * 0.3141592654e1 * t25;
1634: t57 = t37 * t39;
1635: t58 = t17 * t41;
1636: t59 = t12 * t58;
1637: t60 = t57 * t59;
1638: t63 = t25 * t18;
1639: t64 = t57 * nz;
1640: t67 = ZA * ZA;
1641: t68 = t67 * nz;
1642: t69 = 0.3141592654e1 * t48;
1643: t70 = t68 * t69;
1644: t71 = t49 * xc;
1645: t72 = t17 * t16;
1646: t73 = t11 * t72;
1647: t74 = t71 * t73;
1648: t77 = t1 * t67;
1649: t78 = t77 * 0.3141592654e1;
1650: t81 = nx * t25;
1651: t82 = t81 * t49;
1652: t83 = t17 * t17;
1653: t85 = t1 * t83 * t11;
1654: t87 = nx * ZB;
1655: t88 = t8 * t2;
1656: t89 = t87 * t88;
1657: t90 = 0.3141592654e1 * xc;
1658: t91 = t12 * t12;
1659: t92 = ZA * t91;
1660: t97 = ZB * ZA;
1661: t98 = t97 * t37;
1662: t99 = t39 * nz;
1663: t100 = t12 * t41;
1664: 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;
1665: t105 = t67 * t48;
1666: t106 = t49 * t51;
1667: t107 = t106 * t72;
1668: t109 = t1 * 0.3141592654e1;
1669: t110 = t109 * xc;
1670: t115 = nx * t67;
1671: t116 = t115 * t49;
1672: t117 = t1 * t16;
1673: t118 = t117 * t11;
1674: t120 = t2 * t25;
1675: t121 = t28 * 0.3141592654e1;
1676: t122 = t121 * t29;
1677: t123 = t120 * t122;
1678: t129 = t1 * ZB;
1679: t130 = t129 * t4;
1680: t131 = t57 * t100;
1681: t134 = t12 * t16;
1682: t136 = t109 * t39;
1683: t139 = ZB * t18;
1684: t141 = t39 * t1;
1685: t142 = t141 * t90;
1686: t145 = t77 * t90;
1687: t146 = t91 * t41;
1688: t147 = t57 * t146;
1689: t151 = t25 * t39 * t1;
1690: t152 = t72 * t12;
1691: t156 = t49 * t2;
1692: t158 = t83 * t11;
1693: 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;
1694: t164 = t115 * t88;
1695: t165 = t90 * t19;
1696: t168 = t25 * t48;
1697: t169 = t49 * t16;
1698: t170 = t169 * t11;
1699: t174 = ZA * nz * t69;
1700: t175 = ZB * t51;
1701: t176 = t175 * t17;
1702: t177 = t71 * t176;
1703: t180 = t1 * t29;
1704: t181 = t28 * t25;
1705: t182 = t180 * t181;
1706: t183 = t50 * t73;
1707: t186 = ZA * t1;
1708: t187 = t28 * t48;
1709: t188 = t186 * t187;
1710: t189 = ZB * t17;
1711: t190 = t189 * t11;
1712: t191 = t71 * t190;
1713: t194 = t50 * t158;
1714: t196 = t115 * t156;
1715: t197 = t90 * t73;
1716: t201 = t49 * t17 * t11;
1717: t204 = t88 * t90;
1718: t207 = t68 * 0.3141592654e1;
1719: t208 = t17 * t11;
1720: t209 = t50 * t208;
1721: 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;
1722: t212 = t2 * 0.3141592654e1;
1723: t213 = t212 * t52;
1724: t215 = t81 * t8;
1725: t216 = t212 * t59;
1726: t219 = t3 * t90;
1727: t220 = t25 * t8;
1728: t221 = t18 * t91;
1729: t225 = t71 * t52;
1730: t231 = t16 * t51;
1731: t232 = t50 * t231;
1732: t237 = ZA * t12;
1733: t243 = t67 * t28;
1734: t244 = t24 * t243;
1735: t245 = t71 * t231;
1736: 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;
1737: t252 = t25 * t37;
1738: t253 = t252 * t39;
1739: t255 = nz * t15 * t12;
1740: t258 = t2 * t29;
1741: t259 = ZB * t28;
1742: t260 = t258 * t259;
1743: t263 = t106 * t17;
1744: t265 = xc * t25;
1745: t269 = t25 * t49;
1746: t270 = t269 * t52;
1747: t273 = t1 * t25;
1748: t274 = t273 * 0.3141592654e1;
1749: t275 = t57 * t19;
1750: t278 = t24 * t30;
1751: t288 = t1 * t11 * t72;
1752: t290 = t212 * t208;
1753: t292 = t2 * xc;
1754: 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;
1755: t301 = t50 * t176;
1756: t304 = t51 * t72;
1757: t305 = t71 * t304;
1758: t308 = t25 * t41;
1759: t311 = ZA * t48;
1760: t312 = t311 * t49;
1761: t317 = t91 * t15;
1762: t318 = t57 * t317;
1763: t321 = t81 * t88;
1764: t322 = t90 * t59;
1765: t325 = t212 * t231;
1766: t327 = t15 * t12;
1767: t328 = t57 * t327;
1768: t331 = t77 * t187;
1769: t334 = t2 * ZA;
1770: t335 = t334 * t122;
1771: t336 = t50 * t190;
1772: 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;
1773: t341 = t169 * t51;
1774: t344 = t49 * t11 * t72;
1775: t346 = t77 * t30;
1776: t347 = t50 * t304;
1777: t350 = t25 * t51;
1778: t352 = nx * ZA;
1779: t353 = t49 * t23;
1780: t354 = t352 * t353;
1781: t355 = t28 * xc;
1782: t362 = t25 * t91;
1783: t365 = t23 * nz;
1784: t366 = nx * t365;
1785: t367 = t366 * t122;
1786: t368 = ZB * t49;
1787: t369 = ZA * t51;
1788: t370 = t369 * t17;
1789: t371 = t368 * t370;
1790: t374 = t115 * t353;
1791: t375 = t355 * t73;
1792: 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;
1793: t382 = t71 * t208;
1794: t394 = t2 * t67;
1795: t395 = t394 * t122;
1796: t398 = t352 * t156;
1797: t402 = t17 * t12;
1798: t403 = t39 * ZA;
1799: t404 = t402 * t403;
1800: t407 = t269 * t208;
1801: t411 = t49 * t83 * t11;
1802: t413 = t46 * t69;
1803: 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;
1804: t424 = t16 * t11;
1805: t425 = t212 * t424;
1806: t427 = t258 * t181;
1807: t430 = t67 * t29;
1808: t431 = t366 * t430;
1809: t432 = t121 * t49;
1810: t433 = t432 * t52;
1811: t436 = nz * t12;
1812: t437 = t436 * t18;
1813: t440 = t29 * xc;
1814: t441 = t440 * t121;
1815: t442 = t394 * t441;
1816: t445 = t67 * t37;
1817: t446 = t445 * t39;
1818: t448 = nz * t18 * t91;
1819: t453 = t352 * t49;
1820: t458 = t8 * t23;
1821: t462 = t81 * t458;
1822: t463 = t30 * t19;
1823: 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;
1824: t470 = t436 * t58;
1825: t475 = t2 * t121 * t440 * t25;
1826: t485 = t212 * t73;
1827: t488 = t67 * t72 * t1;
1828: t490 = t39 * xc;
1829: 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;
1830: t503 = t115 * t8;
1831: t510 = t355 * t19;
1832: t513 = t432 * t208;
1833: t525 = t38 * t40 * t18;
1834: 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;
1835: t536 = t28 * t37;
1836: t538 = t490 * t100;
1837: t541 = t334 * t441;
1838: t547 = t394 * t30;
1839: t550 = t212 * t19;
1840: t553 = t366 * t441;
1841: t556 = nz * t17;
1842: 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;
1843: t583 = t90 * t317;
1844: t594 = t212 * t158;
1845: t596 = t152 * t67;
1846: t602 = t67 * t17;
1847: 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;
1848: t613 = t83 * t25;
1849: t616 = t81 * t156;
1850: t627 = t90 * t231;
1851: t630 = t91 * t16;
1852: 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;
1853: t643 = t77 * t355;
1854: t648 = t115 * t458;
1855: t651 = t134 * t67;
1856: t657 = t30 * t304;
1857: t660 = t30 * t146;
1858: t665 = t25 * t17;
1859: t668 = t50 * t424;
1860: 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;
1861: t672 = t90 * t424;
1862: t676 = t120 * t536;
1863: t680 = t436 * t41;
1864: t688 = t366 * t67 * t440;
1865: t696 = xc * t12;
1866: t697 = t696 * t18;
1867: t701 = t252 * t141;
1868: t702 = t90 * t221;
1869: 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;
1870: t712 = t24 * t430;
1871: t713 = t28 * t49;
1872: t721 = t1 * t17 * t11;
1873: t726 = ZB * xc;
1874: t737 = nz * t91;
1875: 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;
1876: t745 = t269 * t231;
1877: t749 = t1 * t28 * t265;
1878: t757 = t16 * t39;
1879: t758 = t696 * t757;
1880: t762 = t69 * t49;
1881: t772 = t355 * t100;
1882: t775 = t81 * t353;
1883: 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;
1884: t790 = t212 * t304;
1885: t793 = t156 * 0.3141592654e1;
1886: t795 = t355 * t304;
1887: t800 = t91 * t39;
1888: t801 = t800 * nz;
1889: t807 = t2 * t28;
1890: t808 = t807 * t726;
1891: 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;
1892: t812 = t117 * t51;
1893: t821 = t24 * t355;
1894: t827 = t90 * t304;
1895: t840 = t800 * t41;
1896: 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;
1897: t849 = t1 * t51;
1898: t850 = t849 * t17;
1899: t860 = t269 * t424;
1900: t863 = t273 * t187;
1901: 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;
1902: t879 = xc * ZA;
1903: t888 = t67 * t51;
1904: t901 = ZA * t17;
1905: t903 = t368 * t901 * t11;
1906: 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;
1907: t923 = t71 * t424;
1908: t926 = t87 * t458;
1909: t927 = t28 * ZA;
1910: 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;
1911: t948 = t90 * t327;
1912: t961 = t30 * t100;
1913: t964 = t29 * t49;
1914: t981 = t106 * t1;
1915: 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;
1916: 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;
1917: t1018 = t212 * t100;
1918: t1029 = t212 * t327;
1919: 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;
1920: 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;
1921: t1079 = t58 * t8;
1922: t1091 = t807 * t29;
1923: t1092 = t665 * t40;
1924: t1101 = ZB * t91;
1925: t1102 = t403 * nz;
1926: 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;
1927: t1108 = t849 * t72;
1928: t1121 = t737 * t15;
1929: t1124 = t29 * t12;
1930: 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;
1931: t1134 = t394 * t28;
1932: 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;
1933: t1161 = nz * t83;
1934: t1173 = ZB * t12;
1935: 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;
1936: 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;
1937: t1234 = t25 * ZB;
1938: t1235 = t1234 * t28;
1939: t1236 = t365 * t91;
1940: t1240 = ZB * t121;
1941: t1241 = t1240 * t77;
1942: t1242 = t39 * t39;
1943: t1243 = t12 * t1242;
1944: t1244 = xc * t72;
1945: t1245 = t1243 * t1244;
1946: t1248 = t365 * t25;
1947: t1252 = t243 * nz;
1948: t1257 = t23 * t1;
1949: t1258 = t1240 * t1257;
1950: t1259 = t67 * t12;
1951: t1260 = xc * t16;
1952: t1268 = t1234 * t121;
1953: t1269 = t1268 * t23;
1954: t1272 = t1242 * t91;
1955: t1280 = t67 * xc;
1956: t1284 = t28 * t28;
1957: t1285 = t67 * t1284;
1958: t1287 = t1285 * t2 * ZB;
1959: t1288 = t17 * xc;
1960: t1289 = t1243 * t1288;
1961: 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;
1962: t1293 = t365 * t83;
1963: t1300 = ZA * t1284;
1964: t1304 = t17 * t1242 * t25 * t12;
1965: t1307 = t927 * t2;
1966: t1311 = t23 * t2;
1967: t1312 = t1300 * t1311;
1968: t1316 = t1234 * t1284;
1969: t1317 = t1316 * t1311;
1970: t1321 = t1240 * t23;
1971: t1331 = t1240 * t23 * t67;
1972: t1332 = t40 * t1244;
1973: t1338 = t1243 * t1260;
1974: 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;
1975: t1346 = t1316 * t2;
1976: t1349 = t927 * nz;
1977: t1350 = t25 * t1242;
1978: t1354 = t1268 * t1257;
1979: t1366 = t1268 * t1;
1980: t1370 = t29 * t17;
1981: t1371 = t1243 * t1370;
1982: 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;
1983: t1387 = t1257 * t12;
1984: t1391 = t1240 * t1;
1985: t1399 = t1272 * t1260;
1986: t1412 = t1285 * t1311;
1987: 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;
1988: t1456 = t365 * ZB;
1989: 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;
1990: t1472 = t1316 * t365;
1991: t1474 = t1124 * t39 * t17;
1992: t1478 = t17 * t91;
1993: t1504 = t72 * t39;
1994: 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;
1995: 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;
1996: t1564 = t1260 * t800;
1997: 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;
1999: _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);
2000: /****************************************************************************************/
2001: t1 = nz * nz;
2002: t2 = t1 * nz;
2003: t3 = t2 * nx;
2004: t4 = nx * 0.3141592654e1;
2005: t5 = t4 * xc;
2006: t6 = PetscSinReal(t5);
2007: t7 = 0.3141592654e1 * 0.3141592654e1;
2008: t9 = t3 * t6 * t7;
2009: t10 = xc * xc;
2010: t11 = ZA * ZA;
2011: t12 = t10 * t11;
2012: t13 = nz * 0.3141592654e1;
2013: t14 = PetscExpReal(t13);
2014: t15 = t14 * t14;
2015: t16 = xc * nz;
2016: t18 = PetscExpReal(t16 * 0.3141592654e1);
2017: t19 = t18 * t18;
2018: t20 = t19 * t18;
2019: t21 = t15 * t20;
2020: t22 = t12 * t21;
2021: t25 = nx * t6;
2022: t26 = t1 * 0.3141592654e1;
2023: t27 = t25 * t26;
2024: t28 = ZA * ZB;
2025: t29 = t18 * t15;
2026: t30 = t28 * t29;
2027: t33 = t25 * nz;
2028: t34 = t11 * t15;
2029: t35 = t19 * t19;
2030: t36 = t35 * t18;
2031: t40 = t25 * t1;
2032: t41 = 0.3141592654e1 * t11;
2033: t42 = t15 * t36;
2034: t43 = t41 * t42;
2035: t46 = nx * nx;
2036: t47 = t1 * t46;
2037: t48 = t47 * t11;
2038: t49 = t7 * xc;
2039: t50 = t35 * t15;
2040: t51 = t49 * t50;
2041: t55 = PetscSinReal(t4);
2042: t56 = t46 * nx * t55;
2043: t58 = t56 * nz * t7;
2044: t59 = ZB * ZB;
2045: t60 = t10 * t59;
2046: t61 = t15 * t14;
2047: t62 = t19 * t61;
2048: t63 = t60 * t62;
2049: t66 = t19 * t14;
2050: t67 = t60 * t66;
2051: t70 = t28 * t42;
2052: t73 = PetscCosReal(t5);
2053: t74 = t47 * t73;
2054: t75 = t7 * t11;
2055: t77 = t75 * t10 * t36;
2056: t80 = t73 * t46;
2057: t81 = t80 * nz;
2058: t82 = 0.3141592654e1 * t59;
2059: t83 = t82 * t42;
2060: t87 = xc * t11;
2061: t88 = t87 * t62;
2062: t91 = nz * nx;
2063: t92 = t55 * t61;
2064: t96 = nx * t55;
2065: t98 = t96 * t2 * t7;
2066: t101 = xc * t59;
2067: t102 = t101 * t62;
2068: t108 = t1 * t1;
2069: t109 = t108 * t7;
2070: t111 = t59 * t35;
2071: t112 = t111 * t15;
2072: t115 = t35 * t20;
2073: t123 = t1 * nx * t55;
2074: t124 = t61 * t35;
2075: t127 = t35 * t19;
2076: t128 = t61 * t127;
2077: t129 = t60 * t128;
2078: t132 = t56 * t16;
2079: t133 = t7 * t59;
2080: t134 = t133 * t124;
2081: 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;
2082: t139 = t56 * 0.3141592654e1;
2083: t140 = t111 * t14;
2084: t144 = t49 * t124;
2085: t147 = t91 * t55;
2086: t148 = t61 * ZA;
2087: t154 = ZA * t115 * xc * ZB;
2088: t157 = t7 * 0.3141592654e1;
2089: t159 = t96 * t108 * t157;
2090: t160 = t10 * xc;
2091: t161 = t160 * t59;
2092: t162 = t35 * t14;
2093: t163 = t161 * t162;
2094: t166 = t28 * t162;
2095: t169 = t80 * t13;
2096: t170 = t101 * t42;
2097: t173 = t2 * t11;
2098: t174 = t96 * t173;
2099: t175 = t7 * t10;
2100: t179 = t59 * t15;
2101: t184 = t15 * t15;
2102: 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;
2103: t194 = t173 * 0.3141592654e1;
2104: t195 = xc * t15;
2105: t196 = t195 * t19;
2106: t202 = t15 * t115;
2107: t203 = t28 * t202;
2108: t206 = t96 * t26;
2109: t207 = t14 * t127;
2110: t208 = t101 * t207;
2111: t211 = t12 * t128;
2112: t218 = t11 * t61;
2113: t219 = t218 * t35;
2114: t221 = t108 * ZA;
2115: t223 = t7 * ZB;
2116: t224 = t223 * t50;
2117: t227 = ZA * xc;
2118: t228 = ZB * t15;
2119: t229 = t228 * t36;
2120: t230 = t227 * t229;
2121: t233 = t87 * t207;
2122: t236 = t6 * t11;
2123: 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;
2124: t244 = t227 * t228 * t20;
2125: t252 = t184 * t18;
2126: t253 = t101 * t252;
2127: t256 = t35 * t35;
2128: t257 = t256 * t14;
2129: t258 = t28 * t257;
2130: t261 = t108 * t11;
2131: t263 = t7 * t35;
2132: t268 = ZB * t61 * t35;
2133: t273 = t96 * t108 * t160;
2134: t274 = t157 * ZB;
2135: t276 = t274 * t148 * t35;
2136: t279 = t101 * t21;
2137: t282 = 0.3141592654e1 * xc;
2138: t283 = t59 * t36;
2139: t284 = t282 * t283;
2140: 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;
2141: t290 = t1 * t11;
2142: t291 = t96 * t290;
2143: t297 = t59 * t61;
2144: t298 = t297 * t127;
2145: t300 = ZB * t36;
2146: t301 = t227 * t300;
2147: t304 = t1 * t59;
2148: t305 = t184 * t35;
2149: t310 = t46 * ZB;
2150: t311 = t184 * ZA;
2151: t312 = t310 * t311;
2152: t314 = t60 * t21;
2153: t317 = t1 * ZA;
2154: t318 = ZB * t35;
2155: t321 = t1 * t256;
2156: t324 = t96 * t261;
2157: t325 = t10 * t157;
2158: t326 = t325 * t124;
2159: 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;
2160: t331 = t28 * t124;
2161: t334 = 0.3141592654e1 * t15;
2162: t335 = t334 * t127;
2163: t338 = t35 * ZA;
2164: t341 = t46 * t256;
2165: t344 = t46 * t11;
2166: t346 = t46 * t59;
2167: t348 = t297 * t35;
2168: t351 = ZA * t10;
2169: t352 = t351 * t300;
2170: t355 = t1 * ZB;
2171: 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;
2172: t363 = t36 * t184;
2173: t364 = t87 * t363;
2174: t368 = t47 * t73 * t7;
2175: t373 = t160 * t157;
2176: t374 = t373 * t124;
2177: t377 = t311 * t35;
2178: t380 = t12 * t62;
2179: t386 = ZB * t10 * ZA * t15 * t20;
2180: t389 = t87 * t66;
2181: t393 = t56 * t1 * t10;
2182: 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;
2183: t412 = t11 * t14 * t127;
2184: t416 = t11 * t19;
2185: t417 = t416 * t61;
2186: t421 = t96 * t2 * ZA;
2187: t426 = t56 * nz * ZA;
2188: t427 = t318 * t14;
2189: t428 = t49 * t427;
2190: t431 = t82 * t29;
2191: t434 = t87 * t21;
2192: 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;
2193: t443 = t184 * t20;
2194: t447 = t61 * 0.3141592654e1;
2195: t448 = t447 * t11;
2196: t450 = t49 * t268;
2197: t453 = t60 * t42;
2198: t456 = t41 * t202;
2199: t463 = t101 * t443;
2200: t469 = t41 * xc * t20;
2201: 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;
2202: t482 = t108 * t10;
2203: t492 = nz * t46;
2204: t493 = t492 * t11;
2205: t495 = t282 * t19 * t184;
2206: t498 = t56 * t290;
2207: t499 = t325 * t162;
2208: t502 = t416 * t14;
2209: t504 = t60 * t207;
2210: 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;
2211: t508 = t101 * t162;
2212: t512 = t41 * t115 * xc;
2213: t515 = t87 * t42;
2214: t520 = ZB * t184;
2215: t522 = t227 * t520 * t18;
2216: t525 = t492 * t59;
2217: t528 = t6 * t59;
2218: t532 = t520 * t20;
2219: t533 = t351 * t532;
2220: t539 = t447 * t59;
2221: 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;
2222: t551 = t87 * t162;
2223: t554 = t351 * t229;
2224: t560 = t59 * t19;
2225: t561 = t560 * t14;
2226: t564 = t101 * t202;
2227: t567 = t87 * t252;
2228: t573 = t227 * t228 * t115;
2229: 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;
2230: t579 = t82 * t202;
2231: t591 = t282 * t115 * t59;
2232: t598 = t101 * t66;
2233: 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;
2234: t608 = t373 * t162;
2235: t611 = t59 * t184;
2236: t617 = t101 * t29;
2237: t624 = t227 * ZB * t18 * t15;
2238: t629 = t157 * t59;
2239: t630 = t629 * t124;
2240: t633 = t3 * t6;
2241: t634 = t175 * t283;
2242: 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;
2243: t645 = t41 * t29;
2244: t648 = t2 * 0.3141592654e1;
2245: t649 = t648 * xc;
2246: t650 = t560 * t184;
2247: t656 = t56 * t1 * t157;
2248: t659 = t87 * t128;
2249: t662 = t96 * t482;
2250: t663 = t629 * t162;
2251: t671 = t161 * t124;
2252: t674 = t218 * t127;
2253: 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;
2254: t714 = t334 * t19;
2255: t719 = t12 * t42;
2256: 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;
2257: t730 = xc * t19;
2258: t735 = t59 * t256 * t14;
2259: 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;
2260: t755 = t28 * t21;
2261: t759 = t274 * t338 * t14;
2262: t767 = t11 * t35;
2263: t768 = t767 * t14;
2264: t778 = t560 * t61;
2265: 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;
2266: t786 = t12 * t443;
2267: t790 = t282 * t59 * t20;
2268: t796 = t59 * t14 * t127;
2269: t806 = t41 * t21;
2270: 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;
2271: t819 = t282 * t15 * t127;
2272: t822 = t101 * t363;
2273: t830 = t11 * t256 * t14;
2274: t835 = t227 * t532;
2275: 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;
2276: t845 = t87 * t202;
2277: t854 = t338 * t15;
2278: t859 = t12 * t207;
2279: 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;
2280: t880 = t60 * t443;
2281: t891 = t101 * t128;
2282: 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;
2283: t903 = t179 * t19;
2284: t920 = t56 * t1 * t160;
2285: 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;
2286: t932 = t87 * t29;
2287: t945 = t82 * t21;
2288: 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;
2289: t971 = t282 * t127;
2290: 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;
2291: t997 = xc * t127;
2292: t998 = t997 * t59;
2293: 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;
2294: t1006 = t2 * t59;
2295: t1017 = xc * t35;
2296: 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;
2297: 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;
2298: t1070 = t15 * t19;
2299: 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;
2300: 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;
2301: t1119 = t321 * t46;
2302: t1122 = t157 * t11;
2303: t1123 = t1122 * t2;
2304: t1124 = t184 * t46;
2305: t1128 = t108 * nz;
2306: t1132 = t7 * t7;
2307: t1133 = t1132 * t11;
2308: t1134 = t1133 * t108;
2309: t1135 = t15 * t46;
2310: t1139 = t7 * ZA;
2311: t1140 = t1139 * ZB;
2312: t1141 = t1 * t35;
2313: t1145 = t629 * t2;
2314: t1146 = t1135 * t730;
2315: t1149 = t157 * t1128;
2316: t1150 = t1149 * xc;
2317: t1153 = t46 * xc;
2318: t1154 = t1153 * t127;
2319: t1158 = t184 * t1 * t46;
2320: t1161 = t46 * t46;
2321: t1162 = t35 * t1161;
2322: t1166 = t7 * t1;
2323: 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;
2324: t1171 = t1161 * t184;
2325: t1175 = t1122 * nz;
2326: t1176 = t15 * t1161;
2327: t1180 = t1132 * ZA;
2328: t1181 = t1180 * t355;
2329: t1182 = t1176 * t1017;
2330: t1185 = t1161 * xc;
2331: t1189 = t1133 * t1;
2332: t1192 = t108 * t1;
2333: t1193 = t1132 * t1192;
2334: t1195 = t10 * t35;
2335: t1199 = t157 * t15;
2336: t1203 = t1141 * t46;
2337: t1211 = t184 * t108;
2338: 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;
2339: t1221 = t256 * t1161;
2340: t1224 = t35 * t108;
2341: t1233 = t7 * t256;
2342: 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;
2343: t1240 = t1135 * t1195;
2344: t1252 = t629 * t127;
2345: t1263 = t1171 * ZA;
2346: 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;
2347: t1283 = t1199 * t19;
2348: t1287 = t1199 * t127;
2349: t1289 = t59 * nz * t1161;
2350: t1293 = t157 * nz * xc;
2351: t1304 = t1132 * t108;
2352: t1310 = t263 * ZB;
2353: t1316 = t2 * t15;
2354: 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;
2355: t1330 = t1132 * t15;
2356: t1336 = t1132 * t1;
2357: t1338 = t1162 * t179;
2358: 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;
2359: t1376 = t7 * t184;
2360: t1380 = t1176 * t1195;
2361: t1393 = t1330 * t35;
2362: 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;
2363: 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;
2364: _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);
2365: /****************************************************************************************/
2366: t1 = nz * nz;
2367: t2 = t1 * xc;
2368: t3 = ZB * ZB;
2369: t5 = t2 * 0.3141592654e1 * t3;
2370: t6 = nx * 0.3141592654e1;
2371: t7 = t6 * xc;
2372: t8 = PetscCosReal(t7);
2373: t9 = nx * nx;
2374: t10 = t8 * t9;
2375: t11 = nz * 0.3141592654e1;
2376: t12 = PetscExpReal(t11);
2377: t13 = t12 * t12;
2378: t16 = PetscExpReal(xc * nz * 0.3141592654e1);
2379: t17 = t16 * t16;
2380: t18 = t17 * t16;
2381: t19 = t17 * t17;
2382: t20 = t19 * t18;
2383: t21 = t13 * t20;
2384: t22 = t10 * t21;
2385: t25 = ZA * ZA;
2386: t26 = t1 * t25;
2387: t27 = xc * 0.3141592654e1;
2388: t28 = t26 * t27;
2389: t29 = t19 * t16;
2390: t30 = t13 * t13;
2391: t31 = t29 * t30;
2392: t35 = t9 * nx;
2393: t36 = t3 * t35;
2394: t37 = PetscSinReal(t6);
2395: t38 = t13 * t12;
2396: t39 = t37 * t38;
2397: t40 = t39 * t19;
2398: t42 = t1 * t1;
2399: t43 = nx * t42;
2400: t44 = xc * xc;
2401: t45 = t25 * t44;
2402: t46 = t43 * t45;
2403: t47 = 0.3141592654e1 * 0.3141592654e1;
2404: t48 = t47 * t37;
2405: t49 = t17 * t38;
2406: t54 = 0.3141592654e1 * t35;
2407: t55 = ZA * nz * t54;
2408: t56 = t37 * ZB;
2409: t57 = t19 * t12;
2410: t61 = t25 * t8;
2411: t62 = t61 * t9;
2412: t63 = nz * t30;
2413: t64 = t63 * t16;
2414: t67 = t1 * nz;
2415: t69 = t47 * ZB;
2416: t70 = t67 * t44 * t69;
2417: t75 = nx * t3;
2418: t76 = t75 * t37;
2419: t77 = t67 * 0.3141592654e1;
2420: t78 = t19 * t19;
2421: t79 = t78 * t12;
2422: t80 = t77 * t79;
2423: t82 = t3 * t38;
2424: t84 = t54 * t37;
2425: t87 = PetscSinReal(t7);
2426: t88 = t29 * t87;
2427: t89 = t47 * t44;
2428: t93 = nx * t25;
2429: t94 = t87 * t42;
2430: t95 = t93 * t94;
2431: t96 = t47 * xc;
2432: t97 = t13 * t29;
2433: t98 = t96 * t97;
2434: t101 = t87 * t67;
2435: t102 = t93 * t101;
2436: t103 = t13 * t18;
2437: t107 = t47 * t35;
2438: t108 = t26 * t107;
2439: t109 = t37 * t44;
2440: t110 = t19 * t17;
2441: t111 = t12 * t110;
2442: t116 = t37 * t19 * t12;
2443: t118 = t37 * xc;
2444: t119 = ZB * t19;
2445: t120 = t119 * t12;
2446: t121 = t118 * t120;
2447: t125 = xc * t3;
2448: t126 = t1 * t47 * t125;
2449: t127 = t35 * t37;
2450: t128 = t38 * t19;
2451: t129 = t127 * t128;
2452: t132 = t26 * 0.3141592654e1;
2453: t133 = t16 * t13;
2454: t134 = t10 * t133;
2455: t137 = 0.3141592654e1 * ZB;
2456: t138 = t2 * t137;
2457: t139 = ZA * t8;
2458: t140 = t9 * t13;
2459: t145 = t30 * t18;
2460: t146 = t10 * t145;
2461: t149 = t3 * t8;
2462: t150 = t149 * t9;
2463: 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;
2464: t154 = t42 * nz;
2465: t155 = nx * t154;
2466: t156 = t44 * xc;
2467: t157 = t47 * 0.3141592654e1;
2468: t158 = t156 * t157;
2469: t159 = t155 * t158;
2470: t162 = t56 * ZA * t19 * t12;
2471: t165 = t77 * t49;
2472: t167 = t1 * t3;
2473: t168 = t167 * t89;
2474: t169 = t127 * t49;
2475: t172 = t37 * t67;
2476: t173 = t75 * t172;
2477: t174 = t38 * t110;
2478: t175 = t27 * t174;
2479: t179 = t47 * t25;
2480: t181 = t10 * t97;
2481: t184 = t27 * t31;
2482: t187 = t67 * t47;
2483: t188 = t44 * t3;
2484: t189 = t187 * t188;
2485: t192 = t25 * t35;
2486: t193 = t37 * t17;
2487: t194 = t193 * t12;
2488: t196 = nx * ZA;
2489: t197 = t196 * t172;
2490: t198 = ZB * t38;
2491: t199 = t198 * t19;
2492: t204 = t1 * t12 * t110;
2493: t207 = nx * ZB;
2494: t209 = t1 * ZA;
2495: t215 = t67 * t3;
2496: t216 = t47 * t8;
2497: t217 = t215 * t216;
2498: t218 = t9 * xc;
2499: t222 = nx * t67;
2500: t223 = t222 * t27;
2501: t224 = t3 * t87;
2502: t228 = t167 * t107;
2503: t232 = t26 * t96;
2504: t235 = t207 * t94;
2505: t236 = t47 * ZA;
2506: t243 = xc * t13;
2507: t244 = t243 * t29;
2508: t248 = t25 * nz;
2509: t249 = t248 * 0.3141592654e1;
2510: t253 = ZB * ZA;
2511: t254 = t253 * t8;
2512: t255 = t9 * nz;
2513: t256 = t30 * t16;
2514: 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;
2515: t263 = t43 * t179;
2516: t267 = t3 * nz;
2517: t268 = t267 * t54;
2518: t269 = t118 * t57;
2519: t272 = t39 * t1;
2520: t274 = t67 * t25;
2521: t275 = t274 * t158;
2522: t278 = t75 * t87;
2523: t279 = t77 * t103;
2524: t282 = t25 * t38;
2525: t285 = ZA * t38;
2526: t290 = t267 * 0.3141592654e1;
2527: t296 = t77 * t111;
2528: t298 = t196 * t37;
2529: t299 = t1 * ZB;
2530: t303 = t37 * t42;
2531: t304 = t196 * t303;
2532: t308 = t77 * t57;
2533: t310 = t26 * t89;
2534: t313 = t77 * t128;
2535: t316 = t101 * t27;
2536: t319 = t93 * t87;
2537: t320 = t77 * t97;
2538: t323 = t127 * t57;
2539: t326 = t10 * nz;
2540: t329 = t118 * t174;
2541: 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;
2542: t335 = t75 * t101;
2543: t336 = t27 * t21;
2544: t342 = t77 * t133;
2545: t347 = t209 * t137;
2546: t350 = t9 * t1;
2547: t351 = t149 * t350;
2548: t355 = t37 * t78 * t12;
2549: t359 = t93 * t303;
2550: t367 = t172 * 0.3141592654e1;
2551: t369 = t96 * t103;
2552: t376 = t209 * t107;
2553: t379 = t10 * t103;
2554: t383 = t207 * t101;
2555: t389 = 0.3141592654e1 * ZA;
2556: t390 = t222 * t389;
2557: t391 = t87 * ZB;
2558: 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;
2559: t402 = t39 * t110;
2560: t404 = t193 * t38;
2561: t406 = t127 * t174;
2562: t408 = t167 * 0.3141592654e1;
2563: t411 = t44 * t157;
2564: t412 = t155 * t411;
2565: t413 = t285 * t19;
2566: t414 = t56 * t413;
2567: t417 = ZA * t30;
2568: t424 = t93 * t37;
2569: t426 = t248 * t54;
2570: t427 = t17 * t12;
2571: t428 = t118 * t427;
2572: t431 = t77 * t21;
2573: t438 = ZA * t13;
2574: t443 = t93 * t172;
2575: t444 = t27 * t427;
2576: t448 = t1 * t78 * t12;
2577: t455 = t274 * t89;
2578: t461 = t118 * t111;
2579: 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;
2580: t469 = nz * t16 * t13;
2581: t474 = t1 * t38;
2582: t475 = t474 * t19;
2583: t480 = t89 * t103;
2584: t483 = t67 * ZA;
2585: t484 = t483 * t411;
2586: t485 = t127 * t120;
2587: t488 = t127 * t111;
2588: t497 = t77 * t427;
2589: t502 = t27 * t97;
2590: t508 = t1 * t19 * t12;
2591: t511 = t155 * t25 * t156;
2592: t512 = t157 * t37;
2593: t513 = t512 * t128;
2594: t527 = t1 * t17;
2595: t528 = t527 * t38;
2596: 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;
2597: t535 = t44 * t13;
2598: t542 = t527 * t12;
2599: t544 = nz * t13;
2600: t545 = t544 * t20;
2601: t548 = t75 * t303;
2602: t549 = t96 * t111;
2603: t552 = ZA * t35;
2604: t553 = t552 * t37;
2605: t562 = t43 * t96;
2606: t563 = t3 * t37;
2607: t564 = t563 * t128;
2608: t579 = t474 * t110;
2609: t590 = t9 * t30;
2610: t591 = t590 * t18;
2611: t595 = t127 * t427;
2612: t598 = t77 * t174;
2613: 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;
2614: t601 = t27 * t49;
2615: t604 = t127 * t79;
2616: t606 = ZB * t29;
2617: t616 = t139 * t140 * t18;
2618: t638 = t10 * t256;
2619: t643 = t118 * t199;
2620: t653 = t544 * t29;
2621: t658 = t3 * t29;
2622: t660 = t350 * t27;
2623: 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;
2624: t670 = t274 * t411;
2625: t673 = t118 * t49;
2626: t694 = t155 * t45;
2627: t713 = nz * t29 * t30;
2628: t717 = t20 * t87;
2629: t723 = t512 * t57;
2630: 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;
2631: t734 = t43 * t89;
2632: t735 = t563 * t427;
2633: t740 = t75 * t94;
2634: t744 = ZB * xc;
2635: t750 = t563 * t57;
2636: t754 = t218 * t103;
2637: t771 = t127 * t199;
2638: t776 = t89 * t174;
2639: 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;
2640: t794 = t483 * t158;
2641: t801 = t2 * 0.3141592654e1;
2642: t818 = t215 * t411;
2643: t827 = t96 * t174;
2644: t837 = t37 * t12 * t110;
2645: 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;
2646: t864 = t544 * t18;
2647: t867 = t3 * t18;
2648: t884 = t27 * t256;
2649: t891 = t187 * t744;
2650: t894 = t563 * t49;
2651: 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;
2652: t904 = t27 * t111;
2653: t907 = t118 * t128;
2654: t915 = t89 * t145;
2655: t947 = t139 * t140 * t29;
2656: 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;
2657: t969 = t67 * t157 * t156 * t3;
2658: t974 = t27 * t133;
2659: 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;
2660: t1042 = t89 * t97;
2661: 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;
2662: 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;
2663: t1103 = t42 * t1 * t157;
2664: t1104 = t1103 * t25;
2665: t1108 = t3 * t19;
2666: t1112 = nz * t47;
2667: t1113 = t9 * t9;
2668: t1118 = t42 * t157;
2669: t1119 = t1118 * t9;
2670: t1120 = t25 * xc;
2671: t1121 = t13 * t110;
2672: t1122 = t1120 * t1121;
2673: t1125 = t47 * t47;
2674: t1126 = t67 * t1125;
2675: t1127 = t1113 * ZA;
2676: t1128 = t1126 * t1127;
2677: t1129 = t19 * t13;
2678: t1130 = t744 * t1129;
2679: t1133 = t154 * t1125;
2680: t1134 = t1133 * t9;
2681: t1135 = t45 * t1129;
2682: t1138 = t154 * t47;
2683: t1139 = t25 * t30;
2684: t1142 = t1126 * t1113;
2685: t1145 = t125 * t1129;
2686: t1148 = t1103 * xc;
2687: t1149 = t3 * t13;
2688: t1150 = t1149 * t17;
2689: t1153 = t25 * t78;
2690: 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;
2691: t1157 = t25 * t13;
2692: t1158 = t1157 * t17;
2693: t1161 = t13 * t17;
2694: t1162 = t1120 * t1161;
2695: t1165 = t3 * t78;
2696: t1170 = t42 * t67 * t1125;
2697: t1172 = t1108 * t13;
2698: t1175 = t1 * t157;
2699: t1176 = t1175 * t1113;
2700: t1182 = t1120 * t1129;
2701: t1189 = t110 * t9 * xc;
2702: t1192 = t1149 * t110;
2703: 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;
2704: t1209 = t17 * t30;
2705: t1210 = t125 * t1209;
2706: t1213 = t1138 * ZA;
2707: t1214 = ZB * t30;
2708: t1218 = t1157 * t110;
2709: t1226 = t3 * t30;
2710: t1237 = t1170 * t25;
2711: 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;
2712: t1251 = t125 * t1121;
2713: t1260 = t1120 * t1209;
2714: t1263 = t1139 * t19;
2715: 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;
2716: t1287 = t188 * t1129;
2717: t1292 = t25 * t19;
2718: t1296 = t187 * t9;
2719: t1297 = t1226 * t19;
2720: t1311 = t1112 * t1113;
2721: 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;
2722: t1320 = t253 * t1129;
2723: t1328 = t253 * t30 * t19;
2724: t1333 = t125 * t1161;
2725: t1343 = ZB * t44 * t1129;
2726: 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;
2727: t1369 = t1133 * t9 * ZA;
2728: t1378 = t187 * ZA;
2729: t1383 = t1170 * ZA;
2730: 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;
2731: 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;
2733: _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);
2734: /****************************************************************************************/
2735: /****************************************************************************************/
2737: if (x > xc) {
2738: _PC1 = _PC1B;
2739: _PC2 = _PC2B;
2740: _PC3 = _PC3B;
2741: _PC4 = _PC4B;
2742: Z = ZB;
2743: } else {
2744: _PC1 = _PC1A;
2745: _PC2 = _PC2A;
2746: _PC3 = _PC3A;
2747: _PC4 = _PC4A;
2748: Z = ZA;
2749: }
2750: /****************************************************************************************/
2751: /****************************************************************************************/
2752: t1 = nz * nz;
2753: t2 = t1 * t1;
2754: t3 = t2 * nz;
2755: t4 = x * t3;
2756: t5 = 0.3141592654e1 * 0.3141592654e1;
2757: t6 = t5 * 0.3141592654e1;
2758: t11 = _PC3 * t6;
2759: t12 = x * nz;
2760: t13 = nx * nx;
2761: t14 = t13 * t13;
2762: t15 = t12 * t14;
2763: t19 = PetscExpReal(t12 * 0.3141592654e1);
2764: t20 = t19 * t19;
2765: t21 = t4 * t20;
2766: t24 = _PC1 * t5;
2767: t25 = Z * t20;
2768: t29 = _PC1 * t6;
2769: t30 = t29 * Z;
2770: t31 = t1 * nz;
2771: t32 = x * t31;
2772: t33 = t32 * t13;
2773: t36 = t11 * x;
2774: t41 = nz * t20;
2775: t45 = t6 * _PC4;
2776: t49 = t20 * t1;
2777: t51 = _PC2 * Z;
2778: 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;
2779: t58 = t32 * t6;
2780: t59 = _PC4 * t20;
2781: t63 = t20 * t13;
2782: t67 = t12 * t6;
2783: t68 = t20 * t14;
2784: t87 = t49 * t13;
2785: 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;
2786: t106 = _PC3 * t5;
2787: 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;
2788: t129 = PetscSinReal(nx * 0.3141592654e1 * x);
2789: 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;
2790: t158 = t5 * Z;
2792: u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14);
2793: /****************************************************************************************/
2794: /****************************************************************************************/
2795: t1 = nz * nz;
2796: t2 = t1 * nz;
2797: t3 = x * t2;
2798: t4 = 0.3141592654e1 * 0.3141592654e1;
2799: t5 = t4 * 0.3141592654e1;
2800: t6 = t3 * t5;
2801: t7 = _PC2 * Z;
2802: t8 = nx * nx;
2803: t12 = t1 * t1;
2804: t13 = t12 * nz;
2805: t14 = x * t13;
2806: t15 = t5 * _PC4;
2807: t16 = x * nz;
2808: t18 = PetscExpReal(t16 * 0.3141592654e1);
2809: t19 = t18 * t18;
2810: t23 = t16 * t5;
2811: t24 = t8 * t8;
2812: t28 = _PC3 * t5;
2813: t29 = t14 * t19;
2814: t32 = _PC1 * t5;
2815: t33 = t32 * Z;
2816: t34 = t16 * t24;
2817: t37 = _PC4 * t19;
2818: t45 = _PC2 * t4;
2819: t53 = t19 * t8;
2820: t58 = _PC4 * t4;
2821: t60 = t1 * t19 * t8;
2822: t63 = t19 * t24;
2823: t67 = t3 * t8;
2824: t73 = nz * t19;
2825: t86 = t28 * x;
2826: 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;
2827: t94 = Z * t12;
2828: 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;
2829: t146 = PetscCosReal(nx * 0.3141592654e1 * x);
2830: 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;
2831: t159 = t4 * Z;
2833: 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);
2834: /****************************************************************************************/
2835: /****************************************************************************************/
2836: t1 = 0.3141592654e1 * 0.3141592654e1;
2837: t2 = t1 * 0.3141592654e1;
2838: t3 = _PC1 * t2;
2839: t4 = t3 * Z;
2840: t5 = nz * nz;
2841: t6 = t5 * t5;
2842: t7 = t6 * nz;
2843: t8 = x * t7;
2844: t9 = x * nz;
2845: t11 = PetscExpReal(t9 * 0.3141592654e1);
2846: t12 = t11 * t11;
2847: t13 = t8 * t12;
2848: t16 = t5 * nz;
2849: t17 = x * t16;
2850: t18 = t17 * t2;
2851: t19 = _PC4 * t12;
2852: t20 = nx * nx;
2853: t24 = t2 * _PC4;
2854: t28 = _PC3 * t2;
2855: t29 = t28 * x;
2856: t30 = t12 * nz;
2857: t31 = t20 * t20;
2858: t40 = _PC2 * Z;
2859: t44 = t9 * t2;
2860: t48 = t12 * t20;
2861: t52 = t17 * t20;
2862: 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;
2863: t58 = t9 * t31;
2864: t61 = _PC3 * t1;
2865: t62 = t12 * t31;
2866: t73 = t5 * t20;
2867: t78 = _PC1 * t1;
2868: t90 = Z * t12;
2869: 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;
2870: t101 = PetscCosReal(nx * 0.3141592654e1 * x);
2871: t102 = t11 * t101;
2872: t109 = t12 * t5;
2873: t110 = t109 * t20;
2874: 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;
2875: 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;
2876: t159 = t1 * t11;
2878: u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31);
2879: /****************************************************************************************/
2880: /****************************************************************************************/
2881: t1 = _PC2 * Z;
2882: t2 = 0.3141592654e1 * 0.3141592654e1;
2883: t3 = t2 * 0.3141592654e1;
2884: t4 = nz * nz;
2885: t5 = t4 * t4;
2886: t6 = t5 * t4;
2887: t8 = t3 * t6 * x;
2888: t11 = x * t4;
2889: t12 = t11 * t3;
2890: t15 = PetscExpReal(x * nz * 0.3141592654e1);
2891: t16 = t15 * t15;
2892: t17 = _PC3 * t16;
2893: t18 = nx * nx;
2894: t19 = t18 * t18;
2895: t23 = t5 * nz;
2896: t24 = t2 * t23;
2897: t28 = t1 * t3;
2898: t29 = t6 * x;
2899: t30 = t29 * t16;
2900: t33 = _PC4 * t3;
2901: t34 = t5 * x;
2902: t35 = t34 * t18;
2903: t41 = PetscSinReal(nx * 0.3141592654e1 * x);
2904: t47 = t11 * t19;
2905: t54 = t3 * _PC3;
2906: 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;
2907: t58 = 0.3141592654e1 * t16;
2908: t60 = t2 * _PC4;
2909: t69 = t4 * nz;
2910: t73 = t1 * t2;
2911: t75 = t69 * t16 * t18;
2912: t79 = x * t16;
2913: t83 = nz * t16;
2914: t84 = t83 * t19;
2915: 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;
2916: t97 = t34 * t3;
2917: t101 = Z * _PC1;
2918: t102 = t16 * t19;
2919: t106 = t16 * t18;
2920: t127 = t2 * t69;
2921: t131 = t2 * nz;
2922: 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;
2923: 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;
2925: u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19);
2927: /****************************************************************************************/
2928: /****************************************************************************************/
2930: u5 = (-2 * Z * nz * PETSC_PI * u2 - u3 * 2 * nz * PETSC_PI) * PetscCosReal(nz * PETSC_PI * z); /* pressure */
2932: u6 = (u3 * 2 * nz * PETSC_PI + 4 * Z * nz * PETSC_PI * u2) * PetscCosReal(nz * PETSC_PI * z); /* zz stress */
2933: sum5 += u5;
2934: sum6 += u6;
2936: u1 *= PetscCosReal(nz * PETSC_PI * z); /* x velocity */
2937: sum1 += u1;
2938: u2 *= PetscSinReal(nz * PETSC_PI * z); /* z velocity */
2939: sum2 += u2;
2940: u3 *= 2 * nz * PETSC_PI * PetscCosReal(nz * PETSC_PI * z); /* xx stress */
2941: sum3 += u3;
2942: u4 *= 2 * nz * PETSC_PI * PetscSinReal(nz * PETSC_PI * z); /* zx stress */
2943: sum4 += u4;
2945: /* Output */
2946: if (mu) *mu = Z;
2947: if (vel) {
2948: vel[0] = sum1;
2949: vel[1] = sum2;
2950: }
2951: if (p) (*p) = sum5;
2952: if (s) {
2953: s[0] = sum3;
2954: s[1] = sum4;
2955: s[2] = sum6;
2956: }
2957: if (gamma) {
2958: /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
2959: gamma[0] = (sum3 + sum5) / (2.0 * Z);
2960: gamma[1] = (sum4) / (2.0 * Z);
2961: gamma[2] = (sum6 + sum5) / (2.0 * Z);
2962: }
2963: PetscFunctionReturn(PETSC_SUCCESS);
2964: }
2966: static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], PetscCtx ctx)
2967: {
2968: Parameter *s = (Parameter *)ctx;
2970: PetscFunctionBegin;
2971: PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL));
2972: PetscFunctionReturn(PETSC_SUCCESS);
2973: }
2975: static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], PetscCtx ctx)
2976: {
2977: Parameter *s = (Parameter *)ctx;
2979: PetscFunctionBegin;
2980: PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL));
2981: PetscFunctionReturn(PETSC_SUCCESS);
2982: }
2984: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
2985: {
2986: PetscInt sol;
2988: PetscFunctionBeginUser;
2989: options->solType = SOLKX;
2990: PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");
2991: sol = options->solType;
2992: PetscCall(PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL));
2993: options->solType = (SolutionType)sol;
2994: PetscOptionsEnd();
2995: PetscFunctionReturn(PETSC_SUCCESS);
2996: }
2998: static PetscErrorCode SetUpParameters(AppCtx *user)
2999: {
3000: PetscBag bag;
3001: Parameter *p;
3003: PetscFunctionBeginUser;
3004: /* setup PETSc parameter bag */
3005: PetscCall(PetscBagGetData(user->bag, &p));
3006: PetscCall(PetscBagSetName(user->bag, "par", "Problem parameters"));
3007: bag = user->bag;
3008: switch (user->solType) {
3009: case SOLKX:
3010: PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3011: PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3012: PetscCall(PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation"));
3013: break;
3014: case SOLCX:
3015: case SOLZERO:
3016: PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3017: PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3018: PetscCall(PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc"));
3019: PetscCall(PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc"));
3020: PetscCall(PetscBagRegisterReal(bag, &p->xc, 0.5, "xc", "x-coordinate of the viscosity jump"));
3021: break;
3022: default:
3023: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3024: }
3025: PetscCall(PetscBagSetFromOptions(bag));
3026: PetscCall(PetscBagViewFromOptions(bag, NULL, "-param_view"));
3027: PetscFunctionReturn(PETSC_SUCCESS);
3028: }
3030: /* Make split labels so that we can have corners in multiple labels */
3031: static PetscErrorCode CreateSplitLabels(DM dm)
3032: {
3033: const char *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"};
3034: PetscInt ids[4] = {1, 2, 3, 4};
3035: DMLabel label;
3036: IS is;
3038: PetscFunctionBeginUser;
3039: for (PetscInt f = 0; f < 4; ++f) {
3040: PetscCall(DMCreateLabel(dm, names[f]));
3041: PetscCall(DMGetStratumIS(dm, "marker", ids[f], &is));
3042: if (!is) continue;
3043: PetscCall(DMGetLabel(dm, names[f], &label));
3044: PetscCall(DMLabelInsertIS(label, is, 1));
3045: PetscCall(ISDestroy(&is));
3046: }
3047: PetscFunctionReturn(PETSC_SUCCESS);
3048: }
3050: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
3051: {
3052: DM cdm;
3054: PetscFunctionBeginUser;
3055: PetscCall(DMCreate(comm, dm));
3056: PetscCall(DMSetType(*dm, DMPLEX));
3057: PetscCall(DMSetFromOptions(*dm));
3058: cdm = *dm;
3059: while (cdm) {
3060: PetscCall(CreateSplitLabels(cdm));
3061: PetscCall(DMGetCoarseDM(cdm, &cdm));
3062: }
3063: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
3064: PetscFunctionReturn(PETSC_SUCCESS);
3065: }
3067: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
3068: {
3069: PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, PetscCtx ctx);
3070: PetscDS prob;
3071: DMLabel label;
3072: const PetscInt id = 1;
3073: PetscInt dim, comp;
3074: Parameter *ctx;
3075: void *data;
3077: PetscFunctionBeginUser;
3078: PetscCall(DMGetDimension(dm, &dim));
3079: PetscCall(DMGetDS(dm, &prob));
3080: switch (user->solType) {
3081: case SOLKX:
3082: PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx));
3083: PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3084: PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3085: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3086: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3087: PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3088: PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL));
3089: break;
3090: case SOLCX:
3091: PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx));
3092: PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3093: PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3094: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3095: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3096: PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3097: PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL));
3098: break;
3099: case SOLZERO:
3100: PetscCall(PetscDSSetResidual(prob, 0, f0_zero, stokes_momentum_cx));
3101: PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3102: PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3103: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3104: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3105: PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3106: PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL));
3107: break;
3108: default:
3109: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3110: }
3111: PetscCall(PetscBagGetData(user->bag, &data));
3112: switch (dim) {
3113: case 2:
3114: switch (user->solType) {
3115: case SOLKX:
3116: PetscCall(PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data));
3117: PetscCall(PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data));
3118: break;
3119: case SOLCX:
3120: PetscCall(PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data));
3121: PetscCall(PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data));
3122: break;
3123: case SOLZERO:
3124: PetscCall(PetscDSSetExactSolution(prob, 0, zero, NULL));
3125: PetscCall(PetscDSSetExactSolution(prob, 1, zero, NULL));
3126: break;
3127: default:
3128: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3129: }
3130: break;
3131: default:
3132: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %" PetscInt_FMT, dim);
3133: }
3134: /* Setup constants */
3135: {
3136: Parameter *param;
3138: PetscCall(PetscBagGetData(user->bag, ¶m));
3139: switch (user->solType) {
3140: case SOLKX: {
3141: PetscScalar constants[3];
3143: constants[0] = param->m;
3144: constants[1] = param->n;
3145: constants[2] = param->B;
3146: PetscCall(PetscDSSetConstants(prob, 3, constants));
3147: } break;
3148: case SOLZERO:
3149: case SOLCX: {
3150: PetscScalar constants[5];
3152: constants[0] = param->m;
3153: constants[1] = param->n;
3154: constants[2] = param->etaA;
3155: constants[3] = param->etaB;
3156: constants[4] = param->xc;
3157: PetscCall(PetscDSSetConstants(prob, 5, constants));
3158: } break;
3159: default:
3160: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType);
3161: }
3162: }
3163: /* Setup Boundary Conditions */
3164: PetscCall(PetscDSGetExactSolution(prob, 0, &exactFunc, (void **)&ctx));
3165: if (user->solType == SOLZERO) {
3166: PetscCall(DMGetLabel(dm, "markerBottom", &label));
3167: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 0, NULL, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3168: PetscCall(DMGetLabel(dm, "markerTop", &label));
3169: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 0, NULL, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3170: } else {
3171: comp = 1;
3172: PetscCall(DMGetLabel(dm, "markerBottom", &label));
3173: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 1, &comp, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3174: comp = 0;
3175: PetscCall(DMGetLabel(dm, "markerRight", &label));
3176: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", label, 1, &id, 0, 1, &comp, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3177: comp = 1;
3178: PetscCall(DMGetLabel(dm, "markerTop", &label));
3179: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 1, &comp, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3180: comp = 0;
3181: PetscCall(DMGetLabel(dm, "markerLeft", &label));
3182: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", label, 1, &id, 0, 1, &comp, (PetscVoidFn *)exactFunc, NULL, ctx, NULL));
3183: }
3184: PetscFunctionReturn(PETSC_SUCCESS);
3185: }
3187: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
3188: {
3189: Vec vec;
3190: PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, PetscCtx ctx) = {zero, one};
3192: PetscFunctionBeginUser;
3193: PetscCheck(origField == 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Field %" PetscInt_FMT " should be 1 for pressure", origField);
3194: funcs[field] = one;
3195: {
3196: PetscDS ds;
3197: PetscCall(DMGetDS(dm, &ds));
3198: PetscCall(PetscObjectViewFromOptions((PetscObject)ds, NULL, "-ds_view"));
3199: }
3200: PetscCall(DMCreateGlobalVector(dm, &vec));
3201: PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec));
3202: PetscCall(VecNormalize(vec, NULL));
3203: PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace));
3204: PetscCall(VecDestroy(&vec));
3205: /* New style for field null spaces */
3206: {
3207: PetscObject pressure;
3208: MatNullSpace nullspacePres;
3210: PetscCall(DMGetField(dm, field, NULL, &pressure));
3211: PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres));
3212: PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullspacePres));
3213: PetscCall(MatNullSpaceDestroy(&nullspacePres));
3214: }
3215: PetscFunctionReturn(PETSC_SUCCESS);
3216: }
3218: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
3219: {
3220: DM cdm = dm;
3221: PetscFE fe[2];
3222: DMPolytopeType ct;
3223: PetscInt dim, cStart;
3224: PetscBool simplex;
3226: PetscFunctionBeginUser;
3227: PetscCall(DMGetDimension(dm, &dim));
3228: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
3229: PetscCall(DMPlexGetCellType(dm, cStart, &ct));
3230: simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
3231: /* Create discretization of solution fields */
3232: PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]));
3233: PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity"));
3234: PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]));
3235: PetscCall(PetscFECopyQuadrature(fe[0], fe[1]));
3236: PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure"));
3237: /* Set discretization and boundary conditions for each mesh */
3238: PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0]));
3239: PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1]));
3240: PetscCall(DMCreateDS(dm));
3241: PetscCall(SetupProblem(dm, user));
3242: while (cdm) {
3243: PetscCall(DMCopyDisc(dm, cdm));
3244: if (user->solType != SOLZERO) PetscCall(DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace));
3245: PetscCall(DMGetCoarseDM(cdm, &cdm));
3246: }
3247: PetscCall(PetscFEDestroy(&fe[0]));
3248: PetscCall(PetscFEDestroy(&fe[1]));
3249: if (user->solType != SOLZERO) {
3250: PetscObject pressure;
3251: MatNullSpace nullSpacePres;
3253: PetscCall(DMGetField(dm, 1, NULL, &pressure));
3254: PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres));
3255: PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullSpacePres));
3256: PetscCall(MatNullSpaceDestroy(&nullSpacePres));
3257: }
3258: PetscFunctionReturn(PETSC_SUCCESS);
3259: }
3261: /* Add a vector in the nullspace to make the continuum integral 0.
3263: If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0
3264: */
3265: 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[])
3266: {
3267: p[0] = u[uOff[1]];
3268: }
3270: static PetscErrorCode CorrectDiscretePressure(DM dm, MatNullSpace nullspace, Vec u, AppCtx *user)
3271: {
3272: PetscDS ds;
3273: const Vec *nullvecs;
3274: PetscScalar pintd, intc[2], intn[2];
3275: MPI_Comm comm;
3277: PetscFunctionBeginUser;
3278: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
3279: PetscCall(DMGetDS(dm, &ds));
3280: PetscCall(PetscDSSetObjective(ds, 1, pressure));
3281: PetscCall(MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs));
3282: PetscCall(VecDot(nullvecs[0], u, &pintd));
3283: PetscCheck(PetscAbsScalar(pintd) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g", (double)PetscRealPart(pintd));
3284: PetscCall(DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, user));
3285: PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3286: PetscCall(VecAXPY(u, -intc[1] / intn[1], nullvecs[0]));
3287: PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3288: PetscCheck(PetscAbsScalar(intc[1]) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g", (double)PetscRealPart(intc[1]));
3289: PetscFunctionReturn(PETSC_SUCCESS);
3290: }
3292: static PetscErrorCode SNESConvergenceCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, PetscCtx ctx)
3293: {
3294: AppCtx *user = (AppCtx *)ctx;
3296: PetscFunctionBeginUser;
3297: PetscCall(SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, NULL));
3298: if (*reason > 0) {
3299: DM dm;
3300: Mat J;
3301: Vec u;
3302: MatNullSpace nullspace;
3304: PetscCall(SNESGetDM(snes, &dm));
3305: PetscCall(SNESGetSolution(snes, &u));
3306: PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
3307: PetscCall(MatGetNullSpace(J, &nullspace));
3308: PetscCheck(user->solType == SOLZERO || nullspace, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "SNES Jacobian has no attached null space");
3309: if (nullspace) PetscCall(CorrectDiscretePressure(dm, nullspace, u, user));
3310: }
3311: PetscFunctionReturn(PETSC_SUCCESS);
3312: }
3314: int main(int argc, char **argv)
3315: {
3316: SNES snes; /* nonlinear solver */
3317: DM dm; /* problem definition */
3318: Vec u, r; /* solution, residual vectors */
3319: Mat J, M; /* Jacobian and preconditiong matrix */
3320: MatNullSpace nullSpace = NULL; /* May be necessary for pressure */
3321: AppCtx user; /* user-defined work context */
3322: PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, PetscCtx ctx) = {zero, zero};
3324: PetscFunctionBeginUser;
3325: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
3326: PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
3327: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
3328: PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
3329: PetscCall(SNESSetDM(snes, dm));
3330: PetscCall(DMSetApplicationContext(dm, &user));
3331: /* Setup problem parameters */
3332: PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag));
3333: PetscCall(SetUpParameters(&user));
3334: /* Setup problem */
3335: PetscCall(SetupDiscretization(dm, &user));
3336: PetscCall(DMPlexCreateClosureIndex(dm, NULL));
3338: PetscCall(DMCreateGlobalVector(dm, &u));
3339: PetscCall(VecDuplicate(u, &r));
3341: PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
3342: if (user.solType != SOLZERO) PetscCall(CreatePressureNullSpace(dm, 1, 1, &nullSpace));
3344: { /* set tolerances */
3345: KSP ksp;
3347: PetscCall(SNESGetKSP(snes, &ksp));
3348: PetscCall(KSPSetTolerances(ksp, 1.e-2 * PETSC_SMALL, PETSC_SMALL, PETSC_CURRENT, PETSC_CURRENT));
3349: }
3351: /* There should be a way to express this using the DM */
3352: PetscCall(SNESSetFromOptions(snes));
3353: PetscCall(SNESSetUp(snes));
3354: PetscCall(SNESGetJacobian(snes, &J, &M, NULL, NULL));
3355: PetscCall(MatSetNullSpace(J, nullSpace));
3356: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "prec_"));
3357: PetscCall(MatSetFromOptions(M));
3358: PetscCall(SNESSetConvergenceTest(snes, SNESConvergenceCorrectPressure, &user, NULL));
3360: PetscCall(DMSNESCheckFromOptions(snes, u));
3361: PetscCall(DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u));
3362: if (user.solType == SOLZERO) PetscCall(VecSetRandom(u, NULL));
3363: PetscCall(PetscObjectSetName((PetscObject)u, "Solution"));
3364: PetscCall(SNESSolve(snes, NULL, u));
3365: {
3366: PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, PetscCtx ctx);
3367: void *ectxs[2];
3368: PetscDS ds;
3369: Vec e;
3371: PetscCall(DMGetDS(dm, &ds));
3372: PetscCall(PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]));
3373: PetscCall(PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]));
3375: PetscCall(DMGetGlobalVector(dm, &e));
3376: PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", (PetscObject)dm));
3377: PetscCall(DMPlexComputeL2DiffVec(dm, 0.0, exacts, ectxs, u, e));
3378: PetscCall(PetscObjectSetName((PetscObject)e, "Solution Error"));
3379: PetscCall(VecViewFromOptions(e, NULL, "-error_vec_view"));
3380: PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", NULL));
3381: PetscCall(DMRestoreGlobalVector(dm, &e));
3382: }
3383: PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view"));
3385: PetscCall(MatNullSpaceDestroy(&nullSpace));
3386: PetscCall(VecDestroy(&u));
3387: PetscCall(VecDestroy(&r));
3388: PetscCall(SNESDestroy(&snes));
3389: PetscCall(DMDestroy(&dm));
3390: PetscCall(PetscBagDestroy(&user.bag));
3391: PetscCall(PetscFinalize());
3392: return 0;
3393: }
3395: /*TEST
3397: # 2D serial discretization tests
3398: test:
3399: suffix: p2p1
3400: requires: triangle
3401: args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3402: -snes_error_if_not_converged -dmsnes_check .001 \
3403: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3404: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3405: -fieldsplit_velocity_pc_type lu \
3406: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3407: test:
3408: suffix: p2p1_zero
3409: requires: triangle
3410: args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3411: -snes_error_if_not_converged -dmsnes_check .001 \
3412: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3413: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3414: -fieldsplit_velocity_pc_type lu \
3415: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu -sol_type zero -dm_plex_box_faces 16,1 -dm_plex_box_crisscross -dm_plex_box_lower 0,0 -dm_plex_box_upper 1,0.01
3416: test:
3417: suffix: p2p1_gmg
3418: TODO: broken (requires subDMs hooks)
3419: requires: triangle
3420: args: -dm_plex_separate_marker -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3421: -snes_error_if_not_converged -dmsnes_check .001 \
3422: -ksp_type fgmres -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3423: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3424: -fieldsplit_velocity_pc_type mg \
3425: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3426: test:
3427: suffix: p2p1_conv
3428: requires: triangle
3429: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.2]
3430: args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3431: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3432: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3433: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3434: -fieldsplit_velocity_pc_type lu \
3435: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3436: test:
3437: suffix: q2q1_conv
3438: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.1]
3439: args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3440: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3441: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3442: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3443: -fieldsplit_velocity_pc_type lu \
3444: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3445: test:
3446: suffix: q1p0_conv
3447: # -dm_refine 2 gives L_2 convergence rate: [2.0, 1.0]
3448: args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
3449: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3450: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3451: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3452: -fieldsplit_velocity_pc_type lu \
3453: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3454: test:
3455: suffix: q2p1_conv
3456: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.0]
3457: args: -dm_plex_simplex 0 -dm_plex_separate_marker \
3458: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 \
3459: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3460: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3461: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3462: -fieldsplit_velocity_pc_type lu \
3463: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3465: # FETI-DP tests
3466: testset:
3467: output_file: output/ex69_q2p1fetidp.out
3468: suffix: q2p1fetidp
3469: requires: !single
3470: nsize: 5
3471: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3472: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3473: -snes_error_if_not_converged \
3474: -ksp_error_if_not_converged \
3475: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3476: -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
3477: test:
3478: suffix: aij
3479: args: -mat_is_localmat_type aij
3480: test:
3481: requires: viennacl !CUDA_VERSION_11PLUS
3482: TODO: broken
3483: suffix: aijviennacl
3484: args: -mat_is_localmat_type aijviennacl
3485: test:
3486: requires: cuda
3487: suffix: aijcusparse
3488: args: -mat_is_localmat_type aijcusparse
3490: testset:
3491: suffix: q2p1fetidp_deluxe
3492: output_file: output/ex69_q2p1fetidp_deluxe.out
3493: requires: mumps double
3494: nsize: 5
3495: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3496: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3497: -snes_error_if_not_converged \
3498: -ksp_error_if_not_converged \
3499: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3500: -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 \
3501: -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
3502: test:
3503: suffix: aij
3504: args: -mat_is_localmat_type aij
3505: test:
3506: suffix: aij_seqdense
3507: args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3508: test:
3509: requires: viennacl !CUDA_VERSION_11PLUS
3510: suffix: aijviennacl
3511: args: -mat_is_localmat_type aijviennacl
3512: test:
3513: requires: cuda
3514: suffix: aijcusparse
3515: args: -mat_is_localmat_type aijcusparse
3517: testset:
3518: suffix: q2p1fetidp_deluxe_adaptive
3519: output_file: output/ex69_q2p1fetidp_deluxe_adaptive.out
3520: requires: mumps double
3521: nsize: 5
3522: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3523: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3524: -snes_error_if_not_converged \
3525: -ksp_error_if_not_converged \
3526: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3527: -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 \
3528: -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
3529: test:
3530: suffix: aij
3531: args: -mat_is_localmat_type aij
3532: test:
3533: suffix: aij_seqdense
3534: args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3535: test:
3536: requires: viennacl !CUDA_VERSION_11PLUS
3537: suffix: aijviennacl
3538: args: -mat_is_localmat_type aijviennacl
3539: test:
3540: requires: cuda
3541: suffix: aijcusparse
3542: args: -mat_is_localmat_type aijcusparse
3544: test:
3545: suffix: p2p1fetidp
3546: requires: triangle
3547: nsize: 4
3548: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3549: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3550: -snes_error_if_not_converged \
3551: -ksp_error_if_not_converged \
3552: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3553: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3554: -fetidp_fieldsplit_lag_ksp_type preonly \
3555: -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
3557: test:
3558: suffix: p2p1fetidp_allp
3559: requires: triangle
3560: nsize: 4
3561: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3562: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3563: -snes_error_if_not_converged \
3564: -ksp_error_if_not_converged \
3565: -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 \
3566: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3567: -fetidp_fieldsplit_lag_ksp_type preonly \
3568: -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
3570: test:
3571: suffix: p2p1fetidp_discharm
3572: requires: triangle
3573: nsize: 4
3574: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3575: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3576: -snes_error_if_not_converged \
3577: -ksp_error_if_not_converged \
3578: -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 \
3579: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3580: -fetidp_fieldsplit_lag_ksp_type preonly \
3581: -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
3583: test:
3584: suffix: p2p1fetidp_lumped
3585: requires: triangle
3586: nsize: 4
3587: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3588: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3589: -snes_error_if_not_converged \
3590: -ksp_error_if_not_converged \
3591: -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 \
3592: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3593: -fetidp_fieldsplit_lag_ksp_type preonly \
3594: -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
3596: test:
3597: suffix: p2p1fetidp_deluxe
3598: requires: triangle mumps
3599: nsize: 4
3600: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3601: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3602: -snes_error_if_not_converged \
3603: -ksp_error_if_not_converged \
3604: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3605: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3606: -fetidp_fieldsplit_lag_ksp_type preonly \
3607: -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 \
3608: -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0
3610: test:
3611: suffix: p2p1fetidp_deluxe_discharm
3612: requires: triangle mumps
3613: nsize: 4
3614: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3615: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3616: -snes_error_if_not_converged \
3617: -ksp_error_if_not_converged \
3618: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3619: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3620: -fetidp_fieldsplit_lag_ksp_type preonly \
3621: -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 \
3622: -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
3624: testset:
3625: nsize: 4
3626: requires: triangle
3627: output_file: output/ex69_p2p1fetidp_olof.out
3628: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3629: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3630: -snes_error_if_not_converged \
3631: -ksp_error_if_not_converged \
3632: -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 \
3633: -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none -fetidp_fieldsplit_p_ksp_type preonly \
3634: -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 \
3635: -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
3636: test:
3637: suffix: p2p1fetidp_olof_full
3638: args: -fetidp_pc_fieldsplit_schur_fact_type full
3639: test:
3640: suffix: p2p1fetidp_olof_diag
3641: args: -fetidp_pc_fieldsplit_schur_fact_type diag
3642: test:
3643: suffix: p2p1fetidp_olof_additive
3644: args: -fetidp_pc_fieldsplit_type additive
3646: #BDDC with benign trick
3647: testset:
3648: suffix: q2p1bddc
3649: output_file: output/ex69_q2p1fetidp_deluxe.out
3650: nsize: 5
3651: 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
3652: test:
3653: requires: double
3654: suffix: benign_card
3655: # no native support for saddle point factorizations from PETSc
3656: args: -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd
3657: test:
3658: requires: mumps double
3659: suffix: benign_deluxe_mumps
3660: args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3661: test:
3662: requires: mumps double
3663: suffix: benign_deluxe_adaptive_mumps
3664: 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
3665: test:
3666: TODO: broken (INDEFINITE PC)
3667: requires: mkl_pardiso double !complex
3668: suffix: benign_deluxe_mkl
3669: args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3670: test:
3671: TODO: broken (INDEFINITE PC)
3672: requires: mkl_pardiso double !complex
3673: suffix: benign_deluxe_adaptive_mkl
3674: args: -pc_bddc_adaptive_threshold 1.7 -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3676: TEST*/