Actual source code: ex69.c
1: static char help[] = "The variable-viscosity Stokes Problem in 2d with finite elements.\n\
2: We solve the Stokes problem in a square domain\n\
3: and compare against exact solutions from Mirko Velic.\n\n\n";
5: /* We discretize the variable-viscosity Stokes problem using the finite element method on an unstructured mesh. The weak form equations are
6: \begin{align*}
7: (\nabla v, \mu (\nabla u + {\nabla u}^T)) - (\nabla\cdot v, p) + (v, f) &= 0 \\
8: (q, \nabla\cdot u) &= 0
9: \end{align*}
10: Free slip conditions for velocity are enforced on every wall. The pressure is constrained to have zero integral over the domain.
12: To produce nice output, use
14: -dm_refine 3 -show_error -dm_view hdf5:sol1.h5 -error_vec_view hdf5:sol1.h5::append -sol_vec_view hdf5:sol1.h5::append -exact_vec_view hdf5:sol1.h5::append
15: */
17: #include <petscdmplex.h>
18: #include <petscsnes.h>
19: #include <petscds.h>
20: #include <petscbag.h>
22: typedef enum {
23: SOLKX,
24: SOLCX,
25: NUM_SOL_TYPES
26: } SolutionType;
27: const char *solTypes[NUM_SOL_TYPES + 1] = {"solkx", "solcx", "unknown"};
29: typedef struct {
30: PetscInt n, m; /* x- and y-wavelengths for variation across the domain */
31: /* SolKx */
32: PetscReal B; /* Exponential scale for viscosity variation */
33: /* SolCx */
34: PetscReal etaA, etaB; /* Two viscosities for discontinuous change */
35: PetscReal xc; /* The location of viscosity jump */
36: } Parameter;
38: typedef struct {
39: SolutionType solType; /* The type of exact solution */
40: PetscBag bag; /* Holds problem parameters */
41: } AppCtx;
43: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
44: {
45: PetscInt c;
46: for (c = 0; c < Nc; ++c) u[c] = 0.0;
47: return PETSC_SUCCESS;
48: }
49: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
50: {
51: PetscInt c;
52: for (c = 0; c < Nc; ++c) u[c] = 1.0;
53: return PETSC_SUCCESS;
54: }
56: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
57: {
58: f0[0] = 0.0;
59: f0[1] = -PetscSinScalar(constants[1] * PETSC_PI * x[1]) * PetscCosScalar(constants[0] * PETSC_PI * x[0]);
60: }
62: static void stokes_momentum_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
63: {
64: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
65: PetscInt c, d;
67: for (c = 0; c < dim; ++c) {
68: for (d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
69: f1[c * dim + c] -= u[dim];
70: }
71: }
73: static void stokes_momentum_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
74: {
75: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
76: PetscInt c, d;
78: for (c = 0; c < dim; ++c) {
79: for (d = 0; d < dim; ++d) f1[c * dim + d] = mu * (u_x[c * dim + d] + u_x[d * dim + c]);
80: f1[c * dim + c] -= u[dim];
81: }
82: }
84: static void stokes_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
85: {
86: PetscInt d;
87: f0[0] = 0.0;
88: for (d = 0; d < dim; ++d) f0[0] -= u_x[d * dim + d];
89: }
91: static void f1_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
92: {
93: PetscInt d;
94: for (d = 0; d < dim * dim; ++d) f1[d] = 0.0;
95: }
97: /* < q, \nabla\cdot u >, J_{pu} */
98: static void stokes_mass_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
99: {
100: PetscInt d;
101: for (d = 0; d < dim; ++d) g1[d * dim + d] = -1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
102: }
104: /* -< \nabla\cdot v, p >, J_{up} */
105: static void stokes_momentum_pres_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
106: {
107: PetscInt d;
108: for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
109: }
111: /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu}
112: This just gives \nabla u, give the perdiagonal for the transpose */
113: static void stokes_momentum_vel_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
114: {
115: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
116: PetscInt cI, d;
118: for (cI = 0; cI < dim; ++cI) {
119: for (d = 0; d < dim; ++d) {
120: g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
121: g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
122: }
123: }
124: }
125: static void stokes_momentum_vel_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
126: {
127: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
128: PetscInt cI, d;
130: for (cI = 0; cI < dim; ++cI) {
131: for (d = 0; d < dim; ++d) {
132: g3[((cI * dim + cI) * dim + d) * dim + d] += mu; /*g3[cI, cI, d, d]*/
133: g3[((cI * dim + d) * dim + d) * dim + cI] += mu; /*g3[cI, d, d, cI]*/
134: }
135: }
136: }
138: /* 1/mu < q, I q >, Jp_{pp} */
139: static void stokes_identity_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
140: {
141: const PetscReal mu = PetscExpReal(2.0 * PetscRealPart(constants[2]) * x[0]);
142: g0[0] = 1.0 / mu;
143: }
145: static void stokes_identity_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
146: {
147: const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
148: g0[0] = 1.0 / mu;
149: }
151: /*
152: SolKxSolution - Exact Stokes solutions for exponentially varying viscosity
154: Input Parameters:
155: + pos - The (x,z) coordinate at which to evaluate the solution
156: . n - The constant defining the x-dependence of the forcing function
157: . m - The constant defining the z-dependence of the forcing function
158: - B - The viscosity coefficient
160: Output Parameters:
161: + vel - The (x,z)-velocity at (x,z), or NULL
162: . p - The pressure at (x,z), or NULL
163: . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
164: . gamma - The strain rate, or NULL
165: - mu - The viscosity at (x,z), or NULL
167: Note:
168: .vb
169: The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
170: conditions everywhere. The forcing term f is given by
172: fx = 0
173: fz = sigma*sin(km*z)*cos(kn*x)
175: where
177: km = m*Pi (m may be non-integral)
178: kn = n*Pi
180: meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
181: The viscosity eta is exp(2*B*x).
182: .ve
184: */
185: static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
186: {
187: PetscReal sigma = 1.0;
188: PetscReal Z;
189: PetscReal u1, u2, u3, u4, u5, u6;
190: PetscReal sum1, sum2, sum3, sum4, sum5, sum6;
191: PetscReal kn, km, x, z;
192: PetscReal _PC1, _PC2, _PC3, _PC4;
193: PetscReal Rp, UU, VV;
194: PetscReal a, b, r, _aa, _bb, AA, BB, Rm;
195: PetscReal num1, num2, num3, num4, den1;
197: PetscReal t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
198: PetscReal t11, t12, t13, t14, t15, t16, t17, t18, t19, t20;
199: PetscReal t21, t22, t23, t24, t25, t26, t27, t28, t29, t30;
200: PetscReal t31, t32, t33, t34, t35, t36, t37, t38, t39, t40;
201: PetscReal t41, t42, t43, t44, t45, t46, t47, t49, t51, t53;
202: PetscReal t56, t58, t61, t62, t63, t64, t65, t66, t67, t68;
203: PetscReal t69, t70, t71, t72, t73, t74, t75, t76, t77, t78;
204: PetscReal t79, t80, t81, t82, t83, t84, t85, t86, t87, t88;
205: PetscReal t89, t90, t91, t92, t93, t94, t95, t96, t97, t99;
206: PetscReal t100, t101, t103, t104, t105, t106, t107, t108, t109, t110;
207: PetscReal t111, t112, t113, t114, t115, t116, t117, t118, t119, t120;
208: PetscReal t121, t124, t125, t126, t127, t129, t130, t132, t133, t135;
209: PetscReal t136, t138, t140, t141, t142, t143, t152, t160, t162;
211: PetscFunctionBegin;
212: /*************************************************************************/
213: /*************************************************************************/
214: /* rho = -sin(km*z)*cos(kn*x) */
215: x = pos[0];
216: z = pos[1];
217: Z = PetscExpReal(2.0 * B * x);
218: km = m * PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */
219: kn = (PetscReal)n * PETSC_PI;
220: /*************************************************************************/
221: /*************************************************************************/
222: a = B * B + km * km;
223: b = 2.0 * km * B;
224: r = PetscSqrtReal(a * a + b * b);
225: Rp = PetscSqrtReal((r + a) / 2.0);
226: Rm = PetscSqrtReal((r - a) / 2.0);
227: UU = Rp - B;
228: VV = Rp + B;
230: sum1 = 0.0;
231: sum2 = 0.0;
232: sum3 = 0.0;
233: sum4 = 0.0;
234: sum5 = 0.0;
235: sum6 = 0.0;
236: /*sum7=0.0;*/
238: /*******************************************/
239: /* calculate the constants */
240: /*******************************************/
242: t1 = kn * kn;
243: t4 = km * km;
244: t5 = t4 + t1;
245: t6 = t5 * t5;
246: t8 = pow(km + kn, 0.2e1);
247: t9 = B * B;
248: t16 = pow(km - kn, 0.2e1);
249: _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9);
251: t2 = km * km;
252: t3 = kn * kn;
253: t5 = pow(t2 + t3, 0.2e1);
254: t6 = km - kn;
255: t7 = km + kn;
256: t9 = B * B;
257: t13 = t7 * t7;
258: t19 = t6 * t6;
259: _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9);
261: AA = _aa;
262: BB = _bb;
264: /*******************************************/
265: /* calculate the velocities etc */
266: /*******************************************/
267: t1 = Rm * Rm;
268: t2 = B - Rp;
269: t4 = Rp + B;
270: t6 = UU * x;
271: t9 = PetscExpReal(t6 - 0.4e1 * Rp);
272: t13 = B * B;
273: t16 = Rp * t1;
274: t18 = Rp * Rp;
275: t19 = B * t18;
276: t20 = t13 * Rp;
277: t22 = kn * kn;
278: t24 = B * t1;
279: t32 = 0.8e1 * t13 * BB * kn * Rp;
280: t34 = 0.2e1 * Rm;
281: t35 = PetscCosReal(t34);
282: t37 = Rp * Rm;
283: t49 = PetscSinReal(t34);
284: t63 = PetscExpReal(t6 - 0.2e1 * Rp);
285: t65 = Rm * t2;
286: t67 = 0.2e1 * B * kn;
287: t68 = B * Rm;
288: t69 = t67 + t68 + t37;
289: t73 = 0.3e1 * t13;
290: t75 = 0.2e1 * B * Rp;
291: t76 = t73 - t75 + t1 - t22 - t18;
292: t78 = t65 * t76 * BB;
293: t80 = Rm - kn;
294: t81 = PetscCosReal(t80);
295: t83 = -t67 + t68 + t37;
296: t88 = Rm + kn;
297: t89 = PetscCosReal(t88);
298: t92 = t65 * t76 * AA;
299: t97 = PetscSinReal(t80);
300: t103 = PetscSinReal(t88);
301: t108 = PetscExpReal(t6 - 0.3e1 * Rp - B);
302: t110 = Rm * t4;
303: t111 = t67 + t68 - t37;
304: t115 = t73 + t75 + t1 - t22 - t18;
305: t117 = t110 * t115 * BB;
306: t120 = -t67 + t68 - t37;
307: t127 = t110 * t115 * AA;
308: t140 = PetscExpReal(t6 - Rp - B);
309: num1 = -0.4e1 * t1 * t2 * t4 * AA * t9 + ((0.2e1 * Rp * (0.3e1 * t13 * B - 0.2e1 * t16 - t19 - 0.2e1 * t20 - B * t22 - t24) * AA - t32) * t35 + (0.2e1 * t37 * (t1 + 0.5e1 * t13 - t22 - t18) * AA - 0.8e1 * B * BB * kn * Rm * Rp) * t49 - 0.2e1 * B * (0.3e1 * t20 - Rp * t22 - t18 * Rp - 0.2e1 * t19 - t16 - 0.2e1 * t24) * AA + t32) * t63 + ((0.2e1 * t65 * t69 * AA + t78) * t81 + (0.2e1 * t65 * t83 * AA - t78) * t89 + (t92 - 0.2e1 * t65 * t69 * BB) * t97 + (t92 + 0.2e1 * t65 * t83 * BB) * t103) * t108 + ((-0.2e1 * t110 * t111 * AA - t117) * t81 + (-0.2e1 * t110 * t120 * AA + t117) * t89 + (-t127 + 0.2e1 * t110 * t111 * BB) * t97 + (-t127 - 0.2e1 * t110 * t120 * BB) * t103) * t140;
311: t1 = Rp + B;
312: t2 = Rm * t1;
313: t3 = B * B;
314: t4 = 0.3e1 * t3;
315: t5 = B * Rp;
316: t7 = Rm * Rm;
317: t8 = kn * kn;
318: t9 = Rp * Rp;
319: t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9;
320: t12 = t2 * t10 * AA;
321: t14 = B * Rm;
322: t20 = UU * x;
323: t23 = PetscExpReal(t20 - 0.4e1 * Rp);
324: t25 = Rp * Rm;
325: t32 = Rm * kn;
326: t37 = 0.2e1 * Rm;
327: t38 = PetscCosReal(t37);
328: t40 = t3 * B;
329: t44 = B * t9;
330: t45 = t3 * Rp;
331: t53 = t3 * BB;
332: t58 = PetscSinReal(t37);
333: t69 = PetscExpReal(t20 - 0.2e1 * Rp);
334: t72 = 0.3e1 * t40 * Rm;
335: t73 = t9 * Rp;
336: t74 = t73 * Rm;
337: t75 = t7 * Rm;
338: t76 = B * t75;
339: t77 = t14 * t8;
340: t78 = Rp * t75;
341: t80 = 0.8e1 * t45 * kn;
342: t81 = t25 * t8;
343: t83 = 0.5e1 * t45 * Rm;
344: t84 = t44 * Rm;
345: t85 = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84;
346: t88 = 0.2e1 * t9 * t3;
347: t90 = 0.3e1 * t40 * Rp;
348: t91 = t7 * t3;
349: t93 = 0.2e1 * t5 * t32;
350: t94 = t5 * t7;
351: t95 = t5 * t8;
352: t96 = B * t73;
353: t97 = t7 * t9;
354: t100 = 0.2e1 * t3 * Rm * kn;
355: t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100;
356: t105 = Rm - kn;
357: t106 = PetscCosReal(t105);
358: t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77;
359: t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94;
360: t114 = Rm + kn;
361: t115 = PetscCosReal(t114);
362: t121 = PetscSinReal(t105);
363: t127 = PetscSinReal(t114);
364: t132 = PetscExpReal(t20 - 0.3e1 * Rp - B);
365: t135 = 0.2e1 * B * kn;
366: t136 = t135 + t14 - t25;
367: t142 = -t135 + t14 - t25;
368: t152 = t2 * t10 * BB;
369: t162 = PetscExpReal(t20 - Rp - B);
370: num2 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t23 + ((-0.2e1 * t25 * (t7 + 0.5e1 * t3 - t8 - t9) * AA + 0.8e1 * B * BB * t32 * Rp) * t38 + (0.2e1 * Rp * (0.3e1 * t40 - 0.2e1 * Rp * t7 - t44 - 0.2e1 * t45 - B * t8 - B * t7) * AA - 0.8e1 * t53 * kn * Rp) * t58 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t53 * t32) * t69 + ((-t85 * AA - 0.2e1 * t101 * BB) * t106 + (-t108 * AA + 0.2e1 * t110 * BB) * t115 + (-0.2e1 * t101 * AA + t85 * BB) * t121 + (-0.2e1 * t110 * AA - t108 * BB) * t127) * t132 + ((t12 - 0.2e1 * t2 * t136 * BB) * t106 + (t12 + 0.2e1 * t2 * t142 * BB) * t115 + (-0.2e1 * t2 * t136 * AA - t152) * t121 + (-0.2e1 * t2 * t142 * AA + t152) * t127) * t162;
372: t1 = Rm * Rm;
373: t2 = B - Rp;
374: t4 = Rp + B;
375: t6 = VV * x;
376: t7 = PetscExpReal(-t6);
377: t11 = kn * kn;
378: t13 = B * t1;
379: t14 = Rp * Rp;
380: t15 = B * t14;
381: t16 = B * B;
382: t17 = t16 * Rp;
383: t21 = Rp * t1;
384: t30 = 0.8e1 * t16 * BB * kn * Rp;
385: t32 = 0.2e1 * Rm;
386: t33 = PetscCosReal(t32);
387: t35 = Rp * Rm;
388: t47 = PetscSinReal(t32);
389: t61 = PetscExpReal(-t6 - 0.2e1 * Rp);
390: t63 = Rm * t2;
391: t65 = 0.2e1 * B * kn;
392: t66 = B * Rm;
393: t67 = t65 + t66 + t35;
394: t71 = 0.3e1 * t16;
395: t73 = 0.2e1 * B * Rp;
396: t74 = t71 - t73 + t1 - t11 - t14;
397: t76 = t63 * t74 * BB;
398: t78 = Rm - kn;
399: t79 = PetscCosReal(t78);
400: t81 = -t65 + t66 + t35;
401: t86 = Rm + kn;
402: t87 = PetscCosReal(t86);
403: t90 = t63 * t74 * AA;
404: t95 = PetscSinReal(t78);
405: t101 = PetscSinReal(t86);
406: t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B);
407: t108 = Rm * t4;
408: t109 = t65 + t66 - t35;
409: t113 = t71 + t73 + t1 - t11 - t14;
410: t115 = t108 * t113 * BB;
411: t118 = -t65 + t66 - t35;
412: t125 = t108 * t113 * AA;
413: t138 = PetscExpReal(-t6 - Rp - B);
414: num3 = -0.4e1 * t1 * t2 * t4 * AA * t7 + ((-0.2e1 * Rp * (-B * t11 - t13 - t15 + 0.2e1 * t17 + 0.3e1 * t16 * B + 0.2e1 * t21) * AA + t30) * t33 + (-0.2e1 * t35 * (t1 + 0.5e1 * t16 - t11 - t14) * AA + 0.8e1 * B * BB * kn * Rm * Rp) * t47 + 0.2e1 * B * (0.3e1 * t17 - t21 + 0.2e1 * t15 + 0.2e1 * t13 - Rp * t11 - t14 * Rp) * AA - t30) * t61 + ((-0.2e1 * t63 * t67 * AA - t76) * t79 + (-0.2e1 * t63 * t81 * AA + t76) * t87 + (-t90 + 0.2e1 * t63 * t67 * BB) * t95 + (-t90 - 0.2e1 * t63 * t81 * BB) * t101) * t106 + ((0.2e1 * t108 * t109 * AA + t115) * t79 + (0.2e1 * t108 * t118 * AA - t115) * t87 + (t125 - 0.2e1 * t108 * t109 * BB) * t95 + (t125 + 0.2e1 * t108 * t118 * BB) * t101) * t138;
416: t1 = B - Rp;
417: t2 = Rm * t1;
418: t3 = B * B;
419: t4 = 0.3e1 * t3;
420: t5 = B * Rp;
421: t7 = Rm * Rm;
422: t8 = kn * kn;
423: t9 = Rp * Rp;
424: t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9;
425: t12 = t2 * t10 * AA;
426: t14 = B * Rm;
427: t20 = VV * x;
428: t21 = PetscExpReal(-t20);
429: t23 = Rp * Rm;
430: t30 = Rm * kn;
431: t35 = 0.2e1 * Rm;
432: t36 = PetscCosReal(t35);
433: t40 = B * t9;
434: t41 = t3 * Rp;
435: t43 = t3 * B;
436: t51 = t3 * BB;
437: t56 = PetscSinReal(t35);
438: t67 = PetscExpReal(-t20 - 0.2e1 * Rp);
439: t70 = 0.2e1 * B * kn;
440: t71 = t70 + t14 + t23;
441: t76 = Rm - kn;
442: t77 = PetscCosReal(t76);
443: t79 = -t70 + t14 + t23;
444: t84 = Rm + kn;
445: t85 = PetscCosReal(t84);
446: t91 = t2 * t10 * BB;
447: t93 = PetscSinReal(t76);
448: t99 = PetscSinReal(t84);
449: t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B);
450: t107 = 0.3e1 * t43 * Rm;
451: t108 = t9 * Rp;
452: t109 = t108 * Rm;
453: t110 = t7 * Rm;
454: t111 = B * t110;
455: t112 = t14 * t8;
456: t113 = Rp * t110;
457: t115 = 0.8e1 * t41 * kn;
458: t116 = t23 * t8;
459: t118 = 0.5e1 * t41 * Rm;
460: t119 = t40 * Rm;
461: t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119;
462: t124 = 0.2e1 * t3 * Rm * kn;
463: t125 = t5 * t8;
464: t126 = B * t108;
465: t127 = t7 * t9;
466: t129 = 0.2e1 * t9 * t3;
467: t130 = t5 * t7;
468: t132 = 0.3e1 * t43 * Rp;
469: t133 = t7 * t3;
470: t135 = 0.2e1 * t5 * t30;
471: t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135;
472: t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112;
473: t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135;
474: t160 = PetscExpReal(-t20 - Rp - B);
475: num4 = (0.2e1 * t12 - 0.8e1 * t14 * kn * t1 * BB) * t21 + ((0.2e1 * t23 * (t7 + 0.5e1 * t3 - t8 - t9) * AA - 0.8e1 * B * BB * t30 * Rp) * t36 + (-0.2e1 * Rp * (-B * t8 - B * t7 - t40 + 0.2e1 * t41 + 0.3e1 * t43 + 0.2e1 * Rp * t7) * AA + 0.8e1 * t51 * kn * Rp) * t56 - 0.2e1 * t14 * (-t8 + t9 + t4 + t7) * AA + 0.8e1 * t51 * t30) * t67 + ((t12 - 0.2e1 * t2 * t71 * BB) * t77 + (t12 + 0.2e1 * t2 * t79 * BB) * t85 + (-0.2e1 * t2 * t71 * AA - t91) * t93 + (-0.2e1 * t2 * t79 * AA + t91) * t99) * t104 + ((-t120 * AA + 0.2e1 * t136 * BB) * t77 + (-t141 * AA - 0.2e1 * t143 * BB) * t85 + (0.2e1 * t136 * AA + t120 * BB) * t93 + (0.2e1 * t143 * AA - t141 * BB) * t99) * t160;
477: t1 = Rm * Rm;
478: t2 = Rp * Rp;
479: t3 = t1 * t2;
480: t4 = B * B;
481: t5 = t1 * t4;
482: t9 = PetscExpReal(-0.4e1 * Rp);
483: t15 = PetscCosReal(0.2e1 * Rm);
484: t22 = PetscExpReal(-0.2e1 * Rp);
485: den1 = (-0.4e1 * t3 + 0.4e1 * t5) * t9 + ((0.8e1 * t1 + 0.8e1 * t4) * t2 * t15 - 0.8e1 * t5 - 0.8e1 * t2 * t4) * t22 - 0.4e1 * t3 + 0.4e1 * t5;
487: _PC1 = num1 / den1;
488: _PC2 = num2 / den1;
489: _PC3 = num3 / den1;
490: _PC4 = num4 / den1;
492: t1 = Rm * x;
493: t2 = PetscCosReal(t1);
494: t4 = PetscSinReal(t1);
495: t10 = PetscExpReal(-0.2e1 * x * B);
496: t12 = kn * x;
497: t13 = PetscCosReal(t12);
498: t16 = PetscSinReal(t12);
499: u1 = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16);
501: t2 = Rm * x;
502: t3 = PetscCosReal(t2);
503: t6 = PetscSinReal(t2);
504: t22 = PetscExpReal(-0.2e1 * x * B);
505: t23 = B * t22;
506: t24 = kn * x;
507: t25 = PetscCosReal(t24);
508: t29 = PetscSinReal(t24);
509: u2 = UU * _PC1 * t3 + UU * _PC2 * t6 - _PC1 * t6 * Rm + _PC2 * t3 * Rm - VV * _PC3 * t3 - VV * _PC4 * t6 - _PC3 * t6 * Rm + _PC4 * t3 * Rm - 0.2e1 * t23 * AA * t25 - 0.2e1 * t23 * BB * t29 - t22 * AA * t29 * kn + t22 * BB * t25 * kn;
511: t3 = PetscExpReal(0.2e1 * x * B);
512: t4 = t3 * B;
513: t8 = km * km;
514: t9 = t3 * t8;
515: t11 = 0.3e1 * t9 * Rm;
516: t12 = Rm * Rm;
517: t14 = t3 * t12 * Rm;
518: t15 = UU * UU;
519: t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm;
520: t20 = Rm * x;
521: t21 = PetscSinReal(t20);
522: t27 = 0.2e1 * B * t9;
523: t33 = 0.2e1 * t4 * t12;
524: t36 = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU;
525: t37 = PetscCosReal(t20);
526: t49 = VV * VV;
527: t53 = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14;
528: t64 = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12;
529: t76 = B * t8;
530: t80 = kn * kn;
531: t83 = B * B;
532: t87 = t80 * kn;
533: t90 = kn * x;
534: t91 = PetscSinReal(t90);
535: t106 = PetscCosReal(t90);
536: u3 = -((t19 * t21 + t36 * t37) * _PC1 + (t36 * t21 - t19 * t37) * _PC2 + (t53 * t21 + t64 * t37) * _PC3 + (t64 * t21 - t53 * t37) * _PC4 + (-0.3e1 * t8 * AA * kn - 0.8e1 * t76 * BB - 0.4e1 * BB * B * t80 + 0.4e1 * AA * t83 * kn - AA * t87) * t91 + (-0.4e1 * AA * t80 * B - 0.4e1 * t83 * BB * kn + 0.3e1 * t8 * BB * kn - sigma + BB * t87 - 0.8e1 * t76 * AA) * t106) / km;
538: t3 = PetscExpReal(0.2e1 * x * B);
539: t4 = km * km;
540: t5 = t3 * t4;
541: t6 = Rm * x;
542: t7 = PetscCosReal(t6);
543: t8 = _PC1 * t7;
544: t10 = PetscSinReal(t6);
545: t11 = _PC2 * t10;
546: t13 = _PC3 * t7;
547: t15 = _PC4 * t10;
548: t18 = kn * x;
549: t19 = PetscCosReal(t18);
550: t22 = PetscSinReal(t18);
551: t24 = UU * UU;
552: t25 = t3 * t24;
553: t28 = t3 * UU;
554: t38 = Rm * Rm;
555: t39 = t7 * t38;
556: t42 = t10 * t38;
557: t44 = t5 * t8 + t5 * t11 + t5 * t13 + t5 * t15 + t4 * AA * t19 + t4 * BB * t22 + t25 * t8 + t25 * t11 - 0.2e1 * t28 * _PC1 * t10 * Rm + 0.2e1 * t28 * _PC2 * t7 * Rm - t3 * _PC1 * t39 - t3 * _PC2 * t42;
558: t45 = VV * VV;
559: t46 = t3 * t45;
560: t49 = t3 * VV;
561: t62 = B * B;
562: t78 = kn * kn;
563: t82 = t46 * t13 + t46 * t15 + 0.2e1 * t49 * _PC3 * t10 * Rm - 0.2e1 * t49 * _PC4 * t7 * Rm - t3 * _PC3 * t39 - t3 * _PC4 * t42 + 0.4e1 * t62 * AA * t19 + 0.4e1 * t62 * BB * t22 + 0.4e1 * B * AA * t22 * kn - 0.4e1 * B * BB * t19 * kn - AA * t19 * t78 - BB * t22 * t78;
564: u4 = t44 + t82;
566: t3 = PetscExpReal(0.2e1 * x * B);
567: t4 = t3 * B;
568: t8 = km * km;
569: t9 = t3 * t8;
570: t10 = t9 * Rm;
571: t11 = Rm * Rm;
572: t13 = t3 * t11 * Rm;
573: t14 = UU * UU;
574: t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm;
575: t19 = Rm * x;
576: t20 = PetscSinReal(t19);
577: t26 = 0.2e1 * B * t9;
578: t31 = 0.2e1 * t4 * t11;
579: t34 = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU;
580: t35 = PetscCosReal(t19);
581: t47 = VV * VV;
582: t51 = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13;
583: t61 = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11;
584: t72 = B * t8;
585: t76 = kn * kn;
586: t79 = B * B;
587: t83 = t76 * kn;
588: t86 = kn * x;
589: t87 = PetscSinReal(t86);
590: t101 = PetscCosReal(t86);
591: u5 = ((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-t8 * AA * kn - 0.4e1 * t72 * BB - 0.4e1 * BB * B * t76 + 0.4e1 * AA * t79 * kn - AA * t83) * t87 + (-0.4e1 * AA * t76 * B - 0.4e1 * t79 * BB * kn + t8 * BB * kn - sigma + BB * t83 - 0.4e1 * t72 * AA) * t101) / km;
593: t3 = PetscExpReal(0.2e1 * x * B);
594: t4 = UU * UU;
595: t8 = km * km;
596: t9 = t3 * t8;
597: t10 = t9 * Rm;
598: t11 = Rm * Rm;
599: t13 = t3 * t11 * Rm;
600: t14 = t3 * B;
601: t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm;
602: t19 = Rm * x;
603: t20 = PetscSinReal(t19);
604: t28 = 0.2e1 * B * t9;
605: t33 = 0.2e1 * t14 * t11;
606: t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33;
607: t35 = PetscCosReal(t19);
608: t47 = VV * VV;
609: t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm;
610: t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28;
611: t71 = kn * kn;
612: t74 = B * B;
613: t80 = t71 * kn;
614: t83 = kn * x;
615: t84 = PetscSinReal(t83);
616: t96 = PetscCosReal(t83);
617: u6 = -((t18 * t20 + t34 * t35) * _PC1 + (t34 * t20 - t18 * t35) * _PC2 + (t51 * t20 + t61 * t35) * _PC3 + (t61 * t20 - t51 * t35) * _PC4 + (-0.4e1 * BB * B * t71 + 0.4e1 * AA * t74 * kn + t8 * AA * kn - AA * t80) * t84 + (-0.4e1 * AA * t71 * B - t8 * BB * kn - 0.4e1 * t74 * BB * kn - sigma + BB * t80) * t96) / km;
619: /* SS = sin(km*z)*(exp(UU*x)*(_PC1*cos(Rm*x)+_PC2*sin(Rm*x)) + exp(-VV*x)*(_PC3*cos(Rm*x)+_PC4*sin(Rm*x)) + exp(-2*x*B)*(AA*cos(kn*x)+BB*sin(kn*x))); */
621: /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */
623: sum5 += u5 * PetscCosReal(km * z); /* pressure */
624: sum6 += u6 * PetscCosReal(km * z); /* zz total stress */
626: u1 *= PetscCosReal(km * z); /* x velocity */
627: sum1 += u1;
628: u2 *= PetscSinReal(km * z); /* z velocity */
629: sum2 += u2;
631: u3 *= PetscCosReal(km * z); /* xx total stress */
632: sum3 += u3;
633: u4 *= PetscSinReal(km * z); /* zx stress */
634: sum4 += u4;
636: /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */
637: /* sum7 += rho; */
639: /* Output */
640: if (mu) *mu = Z;
641: if (vel) {
642: vel[0] = sum1;
643: vel[1] = sum2;
644: }
645: if (p) (*p) = sum5;
646: if (s) {
647: s[0] = sum3;
648: s[1] = sum4;
649: s[2] = sum6;
650: }
651: if (gamma) {
652: /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
653: gamma[0] = (sum3 + sum5) / (2.0 * Z);
654: gamma[1] = (sum4) / (2.0 * Z);
655: gamma[2] = (sum6 + sum5) / (2.0 * Z);
656: }
657: PetscFunctionReturn(PETSC_SUCCESS);
658: }
660: static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
661: {
662: Parameter *s = (Parameter *)ctx;
664: PetscFunctionBegin;
665: PetscCall(SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL));
666: PetscFunctionReturn(PETSC_SUCCESS);
667: }
669: static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
670: {
671: Parameter *s = (Parameter *)ctx;
673: PetscFunctionBegin;
674: PetscCall(SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL));
675: PetscFunctionReturn(PETSC_SUCCESS);
676: }
678: /*
679: SolCxSolution - Exact Stokes solutions for discontinuous viscosity
681: Input Parameters:
682: + pos - The (x,z) coordinate at which to evaluate the solution
683: . n - The constant defining the x-dependence of the forcing function
684: . m - The constant defining the z-dependence of the forcing function
685: . xc - The x coordinate at which the viscosity is discontinuous
686: . etaA - The viscosity coefficient for x < xc
687: - etaB - The viscosity coefficient for x > xc
689: Output Parameters:
690: + vel - The (x,z)-velocity at (x,z), or NULL
691: . p - The pressure at (x,z), or NULL
692: . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
693: . gamma - The strain rate, or NULL
694: - mu - The viscosity at (x,z), or NULL
696: Note:
697: .vb
698: The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
699: conditions everywhere. The forcing term f is given by
701: fx = 0
702: fz = sigma*sin(km*z)*cos(kn*x)
704: where
706: km = m*Pi (m may be non-integral)
707: kn = n*Pi
709: meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
710: The viscosity eta jumps from etaA to etaB at x = xc.
711: .ve
712: */
713: static PetscErrorCode SolCxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal xc, PetscReal etaA, PetscReal etaB, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
714: {
715: PetscReal _PC1A, _PC2A, _PC3A, _PC4A, _PC1B, _PC2B, _PC3B, _PC4B, _PC1, _PC2, _PC3, _PC4;
716: PetscReal t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21, t22, t23, t24, t25, t26, t27, t28, t29, t30, t31, t32, t33, t34, t35, t36, t37, t38, t39, t40;
717: PetscReal t41, t42, t43, t44, t45, t46, t47, t48, t49, t50, t51, t52, t53, t54, t55, t56, t57, t58, t59, t60, t61, t62, t63, t64, t65, t66, t67, t68, t69, t70, t71, t72, t73, t74, t75, t76, t77, t78, t79, t80;
718: PetscReal t81, t82, t83, t84, t85, t86, t87, t88, t89, t90, t91, t92, t93, t94, t95, t96, t97, t98, t99, t100, t101, t102, t103, t104, t105, t106, t107, t108, t109, t110, t111, t112, t113, t115, t116, t117, t118, t119, t120;
719: PetscReal t121, t122, t123, t124, t125, t126, t127, t128, t129, t130, t131, t132, t133, t134, t135, t136, t137, t138, t139, t140, t141, t142, t143, t144, t145, t146, t147, t148, t149, t150, t151, t152, t153, t154, t155, t156, t157, t158, t159, t160;
720: PetscReal t161, t162, t163, t164, t165, t166, t167, t168, t169, t170, t171, t172, t173, t174, t175, t176, t177, t178, t179, t180, t181, t182, t183, t184, t186, t187, t188, t189, t190, t191, t192, t193, t194, t195, t196, t197, t198, t199;
721: PetscReal t201, t202, t203, t204, t206, t207, t208, t209, t210, t211, t212, t213, t215, t216, t217, t218, t219, t220, t221, t222, t223, t224, t225, t226, t227, t228, t229, t230, t231, t232, t233, t234, t235, t236, t237, t238, t239, t240;
722: PetscReal t241, t242, t243, t244, t245, t246, t247, t248, t249, t250, t251, t252, t253, t254, t255, t256, t257, t258, t259, t260, t261, t262, t263, t264, t265, t267, t268, t269, t270, t272, t273, t274, t275, t276, t277, t278, t279, t280;
723: PetscReal t281, t282, t283, t284, t285, t286, t288, t289, t290, t291, t292, t295, t296, t297, t298, t299, t300, t301, t303, t304, t305, t307, t308, t310, t311, t312, t313, t314, t315, t316, t317, t318, t319, t320;
724: PetscReal t321, t322, t323, t324, t325, t326, t327, t328, t329, t330, t331, t332, t334, t335, t336, t337, t338, t339, t340, t341, t342, t344, t345, t346, t347, t348, t349, t350, t351, t352, t353, t354, t355, t356, t358, t359, t360;
725: PetscReal t361, t362, t363, t364, t365, t366, t367, t368, t369, t370, t371, t372, t373, t374, t375, t376, t377, t378, t379, t380, t381, t382, t383, t384, t385, t386, t387, t389, t390, t391, t393, t394, t395, t396, t397, t398;
726: PetscReal t401, t402, t403, t404, t405, t406, t407, t408, t409, t410, t411, t412, t413, t414, t415, t416, t417, t418, t419, t421, t422, t423, t424, t425, t426, t427, t428, t429, t430, t431, t432, t433, t434, t436, t437, t438, t439, t440;
727: PetscReal t441, t442, t443, t444, t445, t446, t447, t448, t450, t451, t453, t454, t455, t456, t457, t458, t459, t461, t462, t463, t464, t465, t466, t468, t469, t470, t471, t474, t475, t478, t480;
728: PetscReal t482, t483, t484, t485, t488, t489, t490, t492, t493, t495, t497, t498, t499, t501, t502, t503, t504, t505, t507, t508, t509, t510, t511, t512, t513, t515, t518, t520;
729: PetscReal t522, t525, t527, t528, t529, t530, t532, t533, t534, t535, t536, t538, t539, t541, t542, t544, t545, t546, t547, t548, t549, t550, t551, t552, t553, t554, t555, t556, t557, t560;
730: PetscReal t561, t562, t563, t564, t567, t568, t571, t573, t575, t576, t578, t579, t583, t590, t591, t594, t595, t596, t597, t598, t600;
731: PetscReal t601, t602, t604, t606, t607, t608, t611, t613, t615, t616, t617, t619, t621, t623, t624, t625, t626, t627, t629, t630, t632, t633, t634, t638, t639, t640;
732: PetscReal t641, t642, t643, t644, t645, t647, t648, t649, t650, t651, t652, t653, t654, t655, t656, t657, t658, t659, t660, t662, t663, t665, t666, t667, t668, t670, t671, t672, t673, t674, t675, t676, t679, t680;
733: PetscReal t682, t683, t684, t685, t686, t688, t689, t690, t691, t693, t694, t695, t696, t697, t698, t699, t700, t701, t702, t704, t705, t708, t709, t711, t712, t713, t714, t717, t718, t719;
734: PetscReal t721, t722, t723, t726, t727, t728, t730, t733, t734, t735, t736, t737, t738, t739, t740, t741, t744, t745, t746, t749, t750, t752, t753, t754, t755, t757, t758, t759, t760;
735: PetscReal t761, t762, t763, t764, t766, t767, t768, t770, t771, t772, t773, t774, t775, t776, t777, t778, t780, t781, t782, t785, t786, t789, t790, t791, t792, t793, t794, t795, t796, t797, t798, t800;
736: PetscReal t801, t806, t807, t808, t809, t811, t812, t817, t818, t819, t821, t822, t824, t827, t828, t830, t834, t835, t837, t840;
737: PetscReal t842, t843, t844, t845, t846, t849, t850, t853, t854, t855, t857, t858, t859, t860, t863, t864, t867, t868, t869, t873, t874, t877, t878, t879, t880;
738: PetscReal t884, t888, t891, t894, t900, t901, t903, t904, t907, t908, t909, t911, t914, t915, t916, t919, t920;
739: PetscReal t923, t924, t925, t926, t927, t929, t932, t935, t937, t939, t942, t943, t944, t945, t947, t948, t949, t950, t952, t953, t954, t955, t956, t957;
740: PetscReal t961, t964, t965, t966, t967, t968, t969, t971, t972, t974, t977, t978, t981, t983, t987, t988, t992, t993, t994, t997, t998;
741: PetscReal t1001, t1003, t1005, t1006, t1009, t1010, t1012, t1013, t1015, t1016, t1017, t1018, t1020, t1021, t1029, t1031, t1032, t1033, t1040;
742: PetscReal t1041, t1042, t1044, t1047, t1050, t1054, t1055, t1057, t1058, t1063, t1068, t1069, t1070, t1079, t1080;
743: PetscReal t1088, t1089, t1091, t1092, t1094, t1096, t1101, t1102, t1103, t1104, t1105, t1108, t1112, t1113, t1118, t1119, t1120;
744: PetscReal t1121, t1122, t1123, t1124, t1125, t1126, t1127, t1128, t1129, t1130, t1132, t1133, t1134, t1135, t1138, t1139, t1140, t1141, t1142, t1145, t1146, t1148, t1149, t1150, t1153, t1154, t1156, t1157, t1158, t1159;
745: PetscReal t1161, t1162, t1165, t1166, t1170, t1171, t1172, t1173, t1175, t1176, t1178, t1180, t1181, t1182, t1185, t1189, t1192, t1193, t1195, t1196, t1199;
746: PetscReal t1201, t1203, t1209, t1210, t1211, t1213, t1214, t1218, t1221, t1224, t1225, t1226, t1228, t1233, t1234, t1235, t1236, t1237, t1240;
747: PetscReal t1241, t1242, t1243, t1244, t1245, t1248, t1251, t1252, t1257, t1258, t1259, t1260, t1263, t1268, t1269, t1272, t1280;
748: PetscReal t1282, t1283, t1284, t1285, t1287, t1288, t1289, t1292, t1293, t1296, t1297, t1300, t1304, t1307, t1310, t1311, t1312, t1316, t1317, t1320;
749: PetscReal t1321, t1323, t1328, t1330, t1331, t1332, t1333, t1336, t1338, t1343, t1344, t1346, t1349, t1350, t1354;
750: PetscReal t1366, t1369, t1370, t1371, t1376, t1378, t1380, t1383, t1386, t1387, t1388, t1391, t1393, t1399;
751: PetscReal t1411, t1412, t1420, t1427;
752: PetscReal t1450, t1456, t1468, t1472, t1474, t1478;
753: PetscReal t1504, t1511;
754: PetscReal t1545;
755: PetscReal t1564, t1583;
757: PetscReal sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, sum6 = 0.0;
758: PetscReal ZA = etaA, ZB = etaB;
759: PetscInt nz = m, nx = n;
760: PetscReal u1, u2, u3, u4, u5, u6, Z, x = pos[0], z = pos[1];
762: PetscFunctionBegin;
763: /* Note that there is no Fourier sum here. */
764: /****************************************************************************************/
765: _PC1A = 0;
766: /****************************************************************************************/
767: t1 = nx * 0.3141592654e1;
768: t2 = PetscSinReal(t1);
769: t3 = nx * t2;
770: t4 = nz * nz;
771: t5 = t4 * t4;
772: t6 = 0.3141592654e1 * 0.3141592654e1;
773: t8 = t3 * t5 * t6;
774: t9 = ZA * xc;
775: t12 = PetscExpReal(xc * nz * 0.3141592654e1);
776: t13 = t12 * t12;
777: t15 = nz * 0.3141592654e1;
778: t16 = PetscExpReal(t15);
779: t17 = t16 * t16;
780: t18 = t17 * t16;
781: t19 = ZB * t13 * t18;
782: t20 = t9 * t19;
783: t23 = ZA * ZA;
784: t24 = nx * nx;
785: t25 = t24 * nx;
786: t26 = t23 * t25;
787: t28 = t13 * t13;
788: t29 = t28 * t13;
789: t33 = nx * ZB;
790: t34 = t1 * xc;
791: t35 = PetscSinReal(t34);
792: t36 = t4 * nz;
793: t37 = t35 * t36;
794: t38 = t33 * t37;
795: t39 = 0.3141592654e1 * ZA;
796: t40 = t13 * t12;
797: t41 = t17 * t40;
798: t45 = ZB * ZB;
799: t46 = t45 * t24;
800: t47 = t46 * t4;
801: t48 = 0.3141592654e1 * xc;
802: t49 = t13 * t17;
803: t53 = xc * xc;
804: t54 = t36 * t53;
805: t56 = t54 * t6 * t45;
806: t57 = PetscCosReal(t34);
807: t58 = t57 * t24;
808: t59 = t28 * t12;
809: t60 = t17 * t59;
810: t61 = t58 * t60;
811: t64 = t25 * t2;
812: t65 = t64 * t15;
813: t72 = nx * t23;
814: t74 = t72 * t2 * t5;
815: t75 = t6 * t53;
816: t76 = t16 * t29;
817: t80 = t23 * nz;
818: t81 = t80 * 0.3141592654e1;
819: t82 = t18 * t28;
820: t86 = nx * t5;
821: t87 = t23 * t6;
822: t89 = xc * t2;
823: t90 = t13 * t18;
824: t91 = t89 * t90;
825: t94 = t28 * t28;
826: t96 = t24 * nz;
827: t98 = t4 * t45;
828: t99 = t98 * 0.3141592654e1;
829: t100 = t58 * t41;
830: t104 = 0.3141592654e1 * t25;
831: t105 = ZA * nz * t104;
832: t106 = t2 * ZB;
833: t110 = t17 * t17;
834: t111 = ZA * t110;
835: t116 = nz * t28;
836: t122 = t64 * t4 * t6;
837: t126 = t23 * t29 * t4;
838: t128 = t24 * xc;
839: t132 = t36 * t23;
840: t133 = t6 * t57;
841: t135 = t128 * t41;
842: t138 = t6 * xc;
843: t142 = t72 * t2;
844: t147 = 0.4e1 * t8 * t20 - 0.2e1 * t26 * t2 * t16 * t29 - 0.8e1 * t38 * t39 * t41 + 0.4e1 * t47 * t48 * t49 - 0.8e1 * t56 * t61 - 0.4e1 * t65 * t20 + 0.2e1 * t26 * t2 * t18 * t28 - 0.4e1 * t74 * t75 * t76 - 0.2e1 * t81 * t64 * t82 - 0.4e1 * t86 * t87 * t91 - t23 * t94 * t96 + 0.8e1 * t99 * t100 - 0.2e1 * t105 * t106 * t82 - 0.4e1 * t38 * t48 * t111 * t12 + 0.2e1 * t116 * ZB * t111 * t24 + 0.4e1 * t122 * t20 + 0.4e1 * t126 * 0.3141592654e1 * t17 * t128 + 0.8e1 * t132 * t133 * t135 + 0.4e1 * t74 * t138 * t76 - 0.2e1 * t142 * t4 * t18 * t28;
845: t149 = ZA * t25 * t2;
846: t150 = ZB * t28;
847: t154 = t35 * t5;
848: t155 = t72 * t154;
849: t156 = t75 * t41;
850: t159 = nx * ZA;
851: t160 = t2 * t36;
852: t161 = t159 * t160;
853: t162 = 0.3141592654e1 * ZB;
854: t163 = t28 * t16;
855: t167 = t23 * t57;
856: t168 = t167 * t24;
857: t169 = nz * t110;
858: t170 = t169 * t40;
859: t173 = ZA * ZB;
860: t174 = t173 * t90;
861: t177 = t36 * 0.3141592654e1;
862: t181 = t80 * t104;
863: t184 = nz * t17;
864: t188 = t17 * t29;
865: t190 = t4 * 0.3141592654e1;
866: t191 = t190 * t24;
867: t206 = t138 * t60;
868: t209 = t23 * t4;
869: t211 = t209 * t6 * t25;
870: t212 = t89 * t76;
871: t216 = ZB * t16 * t29;
872: t217 = t9 * t216;
873: t220 = ZB * t110;
874: t221 = ZA * t24;
875: t222 = t221 * nz;
876: t225 = t132 * t75;
877: t232 = t45 * t28;
878: t233 = t110 * t24;
879: t234 = t233 * nz;
880: t236 = t209 * 0.3141592654e1;
881: t237 = t17 * xc;
882: t239 = t237 * t13 * t24;
883: t242 = -0.2e1 * t149 * t150 * t16 - 0.8e1 * t155 * t156 - 0.2e1 * t161 * t162 * t163 + 0.2e1 * t168 * t170 + 0.2e1 * t65 * t174 - 0.2e1 * t142 * t177 * t76 + 0.4e1 * t181 * t91 - 0.4e1 * t168 * t184 * t59 - 0.4e1 * t188 * t23 * t191 + 0.4e1 * t38 * t48 * ZA * t17 * t40 + 0.4e1 * t49 * t23 * t191 + 0.2e1 * t26 * t2 * t13 * t18 - 0.8e1 * t155 * t206 + 0.4e1 * t211 * t212 - 0.4e1 * t8 * t217 + 0.2e1 * t220 * t222 - 0.8e1 * t225 * t100 + 0.2e1 * t142 * t4 * t16 * t29 + t232 * t234 - 0.4e1 * t236 * t239;
884: t244 = nx * t45;
885: t245 = t244 * t37;
886: t246 = t110 * t40;
887: t251 = t237 * t59;
888: t256 = t64 * t90;
889: t260 = t36 * t45 * t133;
890: t263 = t45 * t57;
891: t264 = t263 * t24;
892: t265 = t169 * t12;
893: t269 = t6 * t36;
894: t270 = t17 * t24;
895: t274 = t110 * t13;
896: t276 = t190 * t128;
897: t279 = nx * t36;
898: t281 = t28 * t40;
899: t282 = t281 * t35;
900: t286 = t138 * t41;
901: t289 = t75 * t60;
902: t296 = t190 * t173;
903: t305 = t86 * t45 * t35;
904: t312 = t33 * t154;
905: t313 = t6 * ZA;
906: t324 = t232 * t270;
907: t327 = -0.2e1 * t245 * t48 * t246 + 0.4e1 * t159 * t37 * t162 * t251 + 0.4e1 * t209 * t75 * t256 + 0.8e1 * t260 * t135 + 0.2e1 * t264 * t265 + 0.32e2 * t9 * t150 * t269 * t270 + 0.4e1 * t274 * t23 * t276 + 0.2e1 * t279 * t45 * t282 * t48 + 0.8e1 * t155 * t286 + 0.8e1 * t155 * t289 - 0.8e1 * t150 * ZA * t96 * t17 + 0.8e1 * t296 * t61 - 0.2e1 * t105 * t106 * t163 - 0.2e1 * t81 * t256 - 0.8e1 * t305 * t156 - 0.4e1 * t33 * t282 * t177 * t9 - 0.16e2 * t312 * t313 * t237 * t40 - 0.4e1 * t168 * t184 * t40 + 0.2e1 * t168 * t265 + 0.16e2 * t269 * t53 * t324;
908: t328 = t3 * t4;
909: t331 = t72 * t37;
910: t332 = t48 * t60;
911: t335 = nz * t94;
912: t345 = t72 * t35;
913: t349 = t173 * t57;
914: t355 = t53 * t17;
915: t364 = t54 * t6 * ZB;
916: t365 = t28 * t17;
917: t369 = xc * ZB;
918: t370 = t269 * t369;
919: t371 = ZA * t57;
920: t373 = t371 * t270 * t40;
921: t385 = nx * t35;
922: t396 = t4 * xc;
923: t397 = t396 * t162;
924: t415 = t37 * t48;
925: t418 = -0.32e2 * t364 * t365 * t221 - 0.16e2 * t370 * t373 - 0.4e1 * t331 * t48 * t41 + 0.4e1 * t86 * t23 * t53 * t6 * t2 * t90 + 0.2e1 * t385 * t177 * t23 * xc * t246 + 0.16e2 * t132 * t53 * t6 * t28 * t270 - 0.4e1 * t397 * t371 * t233 * t12 - 0.12e2 * t173 * t58 * t190 * t251 + 0.2e1 * t385 * t36 * 0.3141592654e1 * t23 * xc * t59 - 0.8e1 * t99 * t61 - 0.2e1 * t244 * t59 * t415;
926: t427 = t371 * t270 * t59;
927: t439 = t209 * t48;
928: t440 = t110 * t12;
929: t441 = t58 * t440;
930: t447 = t36 * xc;
931: t455 = t48 * t440;
932: t471 = ZB * t17;
933: t492 = 0.12e2 * t397 * t373 - 0.4e1 * t122 * t217 + 0.16e2 * t364 * t427 + 0.16e2 * t312 * t313 * t355 * t40 - 0.8e1 * t279 * t39 * t35 * ZB * t60 + 0.2e1 * t439 * t441 - 0.2e1 * t81 * t64 * t163 + 0.8e1 * t447 * t87 * t61 + 0.2e1 * t23 * t59 * t57 * t276 + 0.2e1 * t245 * t455 - 0.4e1 * t349 * t96 * t440 - 0.16e2 * t370 * t427 + 0.4e1 * t181 * t212 - 0.16e2 * t365 * t23 * t269 * t128 + 0.16e2 * t86 * t138 * ZA * t35 * t471 * t59 + 0.8e1 * t305 * t289 - 0.4e1 * t439 * t100 + 0.2e1 * ZB * t25 * t2 * ZA * t18 * t28 + 0.2e1 * t142 * t4 * t28 * t16 - 0.8e1 * t56 * t100;
934: t499 = ZA * t53 * t19;
935: t505 = t396 * 0.3141592654e1;
936: t518 = t173 * t53 * t16 * t29;
937: t533 = t23 * t28;
938: t535 = t188 * t45;
939: t538 = t24 * t4;
940: t545 = t3 * t177;
941: t546 = t173 * t76;
942: t555 = t45 * t110;
943: t557 = t72 * t160;
944: t561 = -0.8e1 * t225 * t61 - 0.2e1 * t161 * t162 * t82 + t533 * t234 + 0.4e1 * t535 * t191 + 0.4e1 * t167 * t538 * t332 + 0.4e1 * t349 * t96 * t60 + 0.2e1 * t545 * t546 - 0.2e1 * t264 * t170 + 0.4e1 * t397 * t281 * ZA * t58 - t555 * t96 - 0.4e1 * t557 * t48 * t76;
945: t567 = t396 * 0.3141592654e1 * t45;
946: t568 = t58 * t246;
947: t597 = t58 * nz;
948: t615 = t13 * t45;
949: t616 = t615 * t233;
950: t619 = t94 * t45;
951: t621 = t45 * t59;
952: t625 = 0.2e1 * t149 * t216 + 0.2e1 * t567 * t568 - 0.16e2 * t269 * xc * t324 - 0.2e1 * t236 * xc * t281 * t58 - 0.2e1 * t142 * t177 * t90 - 0.8e1 * t567 * t100 + 0.2e1 * t65 * t546 - 0.8e1 * t305 * t206 + 0.2e1 * nz * t45 * t281 * t57 * t24 - t23 * t110 * t96 - 0.8e1 * t296 * t100 + 0.2e1 * t23 * t281 * t597 + 0.4e1 * t545 * t20 + 0.2e1 * t159 * t2 * t4 * ZB * t163 - 0.4e1 * t557 * t48 * t90 + 0.4e1 * t122 * t518 + 0.8e1 * t263 * t538 * t332 - 0.4e1 * t505 * t616 - t619 * t96 - 0.2e1 * t621 * t57 * t276;
953: t626 = t49 * t45;
954: t660 = t29 * t45;
955: t685 = 0.2e1 * t545 * t174 - 0.4e1 * t126 * 0.3141592654e1 * t24 * xc - 0.4e1 * t47 * t48 * t188 + 0.4e1 * t505 * t660 * t24 - 0.2e1 * t142 * t177 * t163 - 0.2e1 * t142 * t4 * t13 * t18 + 0.8e1 * t260 * t128 * t60 - 0.2e1 * t328 * t546 - 0.2e1 * t26 * t2 * t28 * t16 + 0.4e1 * t545 * t217 - 0.4e1 * t209 * t138 * t256;
956: t690 = t6 * 0.3141592654e1;
957: t691 = ZA * t690;
958: t693 = t24 * t24;
959: t694 = t693 * xc;
960: t695 = t188 * t694;
961: t698 = t23 * ZA;
962: t699 = t698 * t690;
963: t700 = t699 * t5;
964: t704 = t5 * t4;
965: t705 = t691 * t704;
966: t709 = t691 * t5;
967: t713 = t5 * nz;
968: t714 = t713 * ZB;
969: t718 = t698 * t6;
970: t719 = t713 * t28;
971: t722 = t699 * t704;
972: t726 = t713 * t94;
973: t733 = t713 * t45;
974: t736 = t87 * t36;
975: t740 = -0.4e1 * t691 * t98 * t695 + 0.8e1 * t700 * t270 * t13 + 0.4e1 * t705 * t660 * xc + 0.8e1 * t709 * t660 * t128 + 0.2e1 * t87 * t714 * t110 + t718 * t719 * t110 - 0.4e1 * t722 * t237 * t13 - t313 * t726 * t45 - 0.4e1 * t699 * t704 * xc * t29 + t313 * t733 * t28 + 0.4e1 * t736 * t150 * t233;
976: t746 = t313 * t36;
977: t752 = t6 * t6;
978: t753 = t23 * t752;
979: t759 = t698 * t752;
980: t760 = t759 * t36;
981: t761 = t17 * t693;
982: t762 = xc * t28;
983: t763 = t761 * t762;
984: t766 = t87 * t713;
985: t773 = t699 * t4;
986: t774 = t110 * t693;
987: t775 = xc * t13;
988: t785 = t704 * t17;
989: t789 = -0.16e2 * t736 * t150 * t270 + t718 * t116 * t693 - 0.2e1 * t746 * t555 * t24 + 0.4e1 * t705 * t535 + 0.64e2 * t753 * t713 * t17 * t150 * t128 - 0.16e2 * t760 * t763 + 0.2e1 * t766 * t150 * t110 + 0.4e1 * t722 * t274 * xc + 0.4e1 * t773 * t774 * t775 - 0.8e1 * t766 * t150 * t17 + 0.8e1 * t700 * t233 * t775 + 0.4e1 * t699 * t785 * t13;
990: t791 = t691 * t4;
991: t792 = t45 * t693;
992: t793 = t49 * t792;
993: t796 = t759 * t713;
994: t797 = t53 * t28;
995: t798 = t270 * t797;
996: t801 = t87 * nz;
997: t818 = t5 * t36;
998: t819 = t753 * t818;
999: t827 = t753 * t36 * ZB;
1000: t830 = xc * t45;
1001: t834 = -0.4e1 * t791 * t793 + 0.32e2 * t796 * t798 + 0.2e1 * t801 * ZB * t693 * t110 + 0.2e1 * t718 * t36 * t28 * t24 - 0.8e1 * t700 * t128 * t29 - 0.8e1 * t700 * t239 - 0.8e1 * t801 * t150 * t761 + 0.32e2 * t819 * t365 * t369 - 0.64e2 * t753 * t714 * t798 + 0.32e2 * t827 * t763 + 0.4e1 * t705 * t830 * t49;
1002: t842 = xc * t29;
1003: t843 = t270 * t842;
1004: t849 = t759 * t818;
1005: t853 = t691 * t396;
1006: t857 = t691 * t5 * t45;
1007: t869 = t313 * nz;
1008: t874 = -0.2e1 * t718 * t36 * t94 * t24 - 0.4e1 * t773 * t761 * t29 + 0.8e1 * t700 * t843 + 0.2e1 * t87 * t726 * ZB + 0.16e2 * t849 * t797 * t17 + 0.4e1 * t853 * t793 + 0.8e1 * t857 * t239 + 0.2e1 * t801 * t150 * t693 - 0.8e1 * t700 * t270 * t29 - 0.8e1 * t709 * t49 * t46 - t869 * t619 * t693 + t869 * t232 * t693;
1009: t877 = ZA * t752;
1010: t878 = t877 * t818;
1011: t911 = 0.16e2 * t878 * t53 * t45 * t365 - 0.4e1 * t699 * t785 * t29 - 0.4e1 * t705 * t188 * t830 + 0.2e1 * t801 * t94 * t693 * ZB - 0.8e1 * t857 * t843 - t718 * t726 + 0.4e1 * t773 * t761 * t13 - 0.4e1 * t705 * t775 * t555 + 0.2e1 * t746 * t232 * t233 - 0.16e2 * t878 * t830 * t365 - 0.2e1 * t746 * t619 * t24;
1012: t916 = t110 * t28;
1013: t945 = t28 * t693 * t45 * t17;
1014: t948 = 0.32e2 * t877 * t733 * t798 + 0.2e1 * t718 * t36 * t916 * t24 - 0.4e1 * t705 * t626 + t718 * nz * t916 * t693 - t869 * t792 * t110 - 0.4e1 * t773 * t761 * t775 + t718 * t719 + 0.2e1 * t746 * t232 * t24 - 0.16e2 * t849 * t365 * xc - t718 * t713 * t110 - 0.4e1 * t773 * t694 * t29 + 0.16e2 * t877 * t54 * t945;
1015: t974 = t761 * t797;
1016: t987 = 0.4e1 * t773 * t695 + 0.4e1 * t736 * t150 * t24 + 0.4e1 * t722 * t842 * t17 - 0.16e2 * t877 * t447 * t945 + 0.2e1 * t87 * t714 * t28 + t313 * t713 * t916 * t45 - 0.4e1 * t853 * t615 * t774 - 0.32e2 * t877 * t713 * xc * t324 + 0.16e2 * t760 * t974 + 0.4e1 * t736 * t94 * t24 * ZB + t869 * t792 * t916 - 0.8e1 * t691 * t5 * xc * t616;
1017: t1021 = -t718 * t169 * t693 - 0.32e2 * t827 * t974 + 0.2e1 * t801 * t150 * t774 + 0.4e1 * t791 * t188 * t792 + 0.4e1 * t736 * t220 * t24 + 0.4e1 * t791 * t842 * t792 + 0.8e1 * t709 * t660 * t270 - t718 * t335 * t693 - 0.2e1 * t718 * t36 * t110 * t24 - 0.32e2 * t819 * t797 * t471 - t313 * t733 * t110 - 0.32e2 * t796 * t270 * t762;
1019: _PC2A = (t147 - 0.4e1 * t65 * t217 + t418 + 0.2e1 * t150 * t222 + t327 - 0.2e1 * t149 * t19 + 0.2e1 * t335 * ZB * t24 * ZA - 0.16e2 * t312 * t313 * t355 * t59 - 0.4e1 * t281 * ZB * ZA * t597 - 0.2e1 * t505 * t45 * t281 * t58 - 0.4e1 * t211 * t2 * t53 * t76 + 0.8e1 * t305 * t286 - 0.4e1 * t122 * t499 - 0.4e1 * t331 * t332 + 0.8e1 * t345 * t177 * t60 - 0.2e1 * t142 * t177 * t82 + 0.2e1 * t72 * t281 * t415 + 0.4e1 * t349 * t96 * t41 - 0.2e1 * t81 * t64 * t76 + 0.2e1 * t58 * t80 * t59 + 0.8e1 * t345 * t177 * t41 - 0.4e1 * t8 * t499 + t242 + 0.4e1 * t8 * t518 + t625 + t685 + 0.2e1 * t328 * t174 + 0.2e1 * t331 * t455 - 0.2e1 * t33 * t2 * t4 * ZA * t82 - 0.4e1 * t626 * t191 + 0.16e2 * t364 * t373 - 0.2e1 * t621 * t597 - 0.2e1 * t439 * t568 + t492 + t533 * t96 + t232 * t96 + 0.2e1 * t567 * t441 + t561) / (t740 + t789 + t834 + t874 + t911 + t948 + t987 + t1021);
1020: /****************************************************************************************/
1021: t1 = nz * nz;
1022: t2 = t1 * nz;
1023: t3 = t2 * 0.3141592654e1;
1024: t4 = t3 * xc;
1025: t5 = ZB * ZB;
1026: t7 = PetscExpReal(nz * 0.3141592654e1);
1027: t8 = t7 * t7;
1028: t9 = t5 * t8;
1029: t12 = PetscExpReal(xc * nz * 0.3141592654e1);
1030: t13 = t12 * t12;
1031: t14 = t13 * t13;
1032: t15 = t14 * t13;
1033: t19 = nx * nx;
1034: t21 = nx * 0.3141592654e1;
1035: t22 = PetscSinReal(t21);
1036: t23 = t19 * nx * t22;
1037: t24 = t23 * 0.3141592654e1;
1038: t25 = ZA * ZB;
1039: t26 = t7 * t15;
1040: t27 = t25 * t26;
1041: t30 = t21 * xc;
1042: t31 = PetscSinReal(t30);
1043: t32 = t31 * nx;
1044: t33 = t32 * nz;
1045: t34 = ZA * ZA;
1046: t35 = t8 * t8;
1047: t36 = t34 * t35;
1048: t40 = t2 * t34;
1049: t41 = 0.3141592654e1 * t8;
1050: t42 = t41 * t15;
1051: t45 = t1 * t5;
1052: t46 = t14 * t14;
1053: t49 = t19 * t5;
1054: t51 = t19 * t46;
1055: t53 = t19 * t34;
1056: t55 = t8 * t7;
1057: t56 = t13 * t55;
1058: t57 = t25 * t56;
1059: t60 = t2 * nx;
1060: t61 = 0.3141592654e1 * 0.3141592654e1;
1061: t63 = t60 * t31 * t61;
1062: t64 = xc * xc;
1063: t65 = ZA * t64;
1064: t66 = ZB * t8;
1065: t67 = t14 * t12;
1066: t68 = t66 * t67;
1067: t69 = t65 * t68;
1068: t72 = -0.4e1 * t4 * t9 * t15 + 0.4e1 * t24 * t27 + 0.4e1 * t33 * t36 * t12 - 0.4e1 * t40 * t42 - t45 * t46 + t45 * t14 - t49 * t14 + t51 * t5 - t53 * t14 + 0.4e1 * t24 * t57 + 0.32e2 * t63 * t69;
1069: t73 = t1 * nx;
1070: t75 = t73 * t31 * 0.3141592654e1;
1071: t76 = t8 * t67;
1072: t77 = t25 * t76;
1073: t80 = t1 * t1;
1074: t81 = t80 * t34;
1075: t83 = t61 * t14;
1076: t87 = t1 * t19;
1077: t88 = PetscCosReal(t30);
1078: t90 = t87 * t88 * t61;
1079: t91 = t5 * t64;
1080: t92 = t13 * t12;
1081: t93 = t8 * t92;
1082: t94 = t91 * t93;
1083: t100 = ZB * t64 * ZA * t8 * t92;
1084: t103 = nz * t19;
1085: t105 = t103 * t88 * 0.3141592654e1;
1086: t106 = ZA * xc;
1087: t107 = ZB * t35;
1088: t109 = t106 * t107 * t12;
1089: t112 = t34 * xc;
1090: t113 = t112 * t93;
1091: t116 = t35 * t14;
1092: t118 = t1 * ZA;
1093: t119 = ZB * t14;
1094: t122 = t1 * t46;
1095: t125 = t19 * ZB;
1096: t126 = t35 * ZA;
1097: t127 = t125 * t126;
1098: t129 = t1 * ZB;
1099: t132 = -0.16e2 * t75 * t77 + 0.16e2 * t81 * t64 * t83 * t8 + 0.16e2 * t90 * t94 - 0.32e2 * t90 * t100 + 0.8e1 * t105 * t109 - 0.8e1 * t75 * t113 + t45 * t116 + 0.2e1 * t118 * t119 + 0.2e1 * t122 * t25 - 0.2e1 * t127 + 0.2e1 * t129 * t126;
1100: t134 = t1 * t34;
1101: t136 = t34 * t64;
1102: t137 = t136 * t76;
1103: t141 = t91 * t76;
1104: t145 = t103 * t34;
1105: t146 = 0.3141592654e1 * xc;
1106: t147 = t8 * t13;
1107: t153 = t14 * ZA;
1108: t156 = xc * t5;
1109: t157 = t156 * t93;
1110: t160 = t103 * t5;
1111: t162 = t146 * t8 * t15;
1112: t166 = t34 * t7 * t15;
1113: t169 = t134 * t116 - 0.16e2 * t63 * t137 - t49 * t116 - 0.16e2 * t63 * t141 - t53 * t116 + 0.4e1 * t145 * t146 * t147 - 0.2e1 * t51 * t25 - 0.2e1 * t125 * t153 - 0.16e2 * t75 * t157 + 0.4e1 * t160 * t162 - 0.4e1 * t24 * t166;
1114: t170 = t106 * t68;
1115: t177 = t35 * t92;
1116: t178 = t112 * t177;
1117: t181 = t156 * t76;
1118: t186 = t35 * t12;
1119: t187 = t112 * t186;
1120: t193 = t5 * 0.3141592654e1;
1121: t206 = t34 * t14;
1122: t207 = t206 * t7;
1123: t210 = -0.32e2 * t63 * t170 + 0.32e2 * t90 * t170 + 0.8e1 * t75 * t109 + 0.4e1 * t105 * t178 - 0.16e2 * t75 * t181 - 0.16e2 * t90 * t113 - 0.4e1 * t75 * t187 + 0.16e2 * t90 * t141 - 0.4e1 * t103 * t15 * t193 * xc + 0.16e2 * t73 * t22 * t34 * t146 * t26 + 0.4e1 * t32 * nz * t34 * t67 + 0.4e1 * t24 * t207;
1124: t217 = t106 * t66 * t92;
1125: t226 = t88 * t19 * nz;
1126: t227 = 0.3141592654e1 * t34;
1127: t229 = t227 * xc * t67;
1128: t232 = t73 * t31;
1129: t234 = t146 * t5 * t67;
1130: t238 = t61 * ZB;
1131: t239 = t14 * t8;
1132: t240 = t238 * t239;
1133: t243 = t136 * t93;
1134: t246 = -0.8e1 * t33 * t25 * t186 + 0.32e2 * t90 * t217 - t45 * t35 + t53 * t35 - t134 * t35 - t134 * t46 + t134 * t14 - 0.4e1 * t226 * t229 + 0.4e1 * t232 * t234 + 0.32e2 * t87 * t65 * t240 + 0.16e2 * t63 * t243;
1135: t247 = t14 * t92;
1136: t249 = t227 * t247 * xc;
1137: t254 = t73 * t22;
1138: t259 = t60 * t22 * t61;
1139: t260 = t112 * t26;
1140: t264 = t146 * t247 * t5;
1141: t268 = xc * t14;
1142: t274 = t5 * t14;
1143: t275 = t274 * t8;
1144: t280 = nz * nx;
1145: t281 = t280 * t22;
1146: t282 = t55 * t14;
1147: t283 = t25 * t282;
1148: t290 = ZA * t247 * xc * ZB;
1149: t295 = t22 * nx * t1 * 0.3141592654e1;
1150: t298 = -0.4e1 * t232 * t249 + 0.8e1 * t105 * t217 - 0.4e1 * t254 * t227 * t26 - 0.8e1 * t259 * t260 - 0.4e1 * t232 * t264 - 0.16e2 * t81 * t61 * t268 * t8 + 0.16e2 * t80 * t64 * t61 * t275 - 0.4e1 * t232 * t229 + 0.8e1 * t281 * t283 - 0.4e1 * t105 * t187 + 0.8e1 * t75 * t290 + 0.4e1 * t295 * t27;
1151: t301 = t61 * t5;
1152: t307 = t87 * t34;
1153: t312 = t61 * xc;
1154: t313 = t312 * t239;
1155: t317 = t34 * t55 * t14;
1156: t329 = ZB * t13 * t55;
1157: t330 = t65 * t329;
1158: t337 = -0.16e2 * t87 * t64 * t301 * t239 - 0.32e2 * t90 * t69 - 0.16e2 * t307 * t64 * t61 * t239 + 0.16e2 * t307 * t313 + 0.4e1 * t24 * t317 + t53 * t46 + t49 * t35 - 0.32e2 * t63 * t100 - 0.4e1 * t280 * t31 * t34 * t247 + 0.8e1 * t259 * t330 - 0.4e1 * t280 * t31 * t247 * t5;
1159: t340 = t5 * t35;
1160: t344 = t25 * t93;
1161: t356 = t41 * t13;
1162: t360 = t23 * nz * t61;
1163: t363 = t25 * t64 * t7 * t15;
1164: t366 = t156 * t177;
1165: t369 = t14 * t7;
1166: t370 = t25 * t369;
1167: t373 = t156 * t186;
1168: t378 = 0.4e1 * t24 * t283 + 0.4e1 * t33 * t340 * t12 - 0.16e2 * t75 * t344 - 0.4e1 * t280 * t31 * t5 * t67 + 0.8e1 * t33 * t25 * t247 + 0.32e2 * t63 * t217 + 0.4e1 * t40 * t356 - 0.8e1 * t360 * t363 + 0.4e1 * t75 * t366 + 0.4e1 * t295 * t370 - 0.4e1 * t75 * t373 - 0.4e1 * t105 * t366;
1169: t382 = t112 * t76;
1170: t387 = t80 * t61;
1171: t391 = t136 * t26;
1172: t409 = 0.16e2 * t63 * t382 + 0.4e1 * t226 * t234 - 0.16e2 * t387 * xc * t275 + 0.8e1 * t259 * t391 - 0.16e2 * t105 * t344 + 0.4e1 * t226 * t264 - 0.8e1 * t105 * t170 + 0.16e2 * t232 * t193 * t76 + 0.8e1 * t360 * t330 - 0.8e1 * t105 * t290 + 0.16e2 * t90 * t243;
1173: t423 = t153 * t8;
1174: t426 = t34 * t13;
1175: t427 = t426 * t55;
1176: t430 = t34 * t8;
1177: t437 = t80 * ZA;
1178: t441 = 0.4e1 * t145 * t42 - 0.16e2 * t90 * t157 + 0.24e2 * t75 * t217 + 0.4e1 * t226 * t249 + 0.4e1 * t254 * t227 * t282 + 0.4e1 * t160 * t356 - 0.8e1 * t129 * t423 - 0.8e1 * t281 * t427 - 0.8e1 * t33 * t430 * t67 + 0.8e1 * t33 * t430 * t92 + 0.32e2 * t437 * ZB * t313;
1179: t453 = t106 * ZB * t7 * t15;
1180: t456 = t2 * t5;
1181: t459 = t112 * t56;
1182: t462 = t126 * t14;
1183: t474 = t40 * 0.3141592654e1;
1184: t475 = xc * t8;
1185: t480 = t146 * t13 * t35;
1186: t483 = -0.4e1 * t103 * xc * t193 * t147 + 0.16e2 * t87 * t61 * t156 * t239 + 0.8e1 * t259 * t453 - 0.4e1 * t456 * t356 + 0.8e1 * t259 * t459 - 0.2e1 * t125 * t462 - 0.8e1 * t281 * t207 + 0.16e2 * t295 * t459 - 0.8e1 * t60 * t22 * ZA * t312 * t329 + 0.4e1 * t474 * t475 * t15 + 0.4e1 * t160 * t480;
1187: t497 = t136 * t56;
1188: t504 = t9 * t13;
1189: t509 = t475 * t13;
1190: t512 = -0.8e1 * t105 * t113 - 0.4e1 * t254 * t227 * t56 + 0.8e1 * t281 * t57 + 0.4e1 * t295 * t283 + 0.2e1 * t129 * t462 + 0.4e1 * t24 * t370 - 0.8e1 * t360 * t497 - 0.4e1 * t24 * t427 - 0.4e1 * t145 * t162 + 0.4e1 * t4 * t504 - 0.8e1 * t281 * t370 - 0.4e1 * t474 * t509;
1191: t528 = t5 * t13;
1192: t529 = t528 * t35;
1193: t532 = t106 * t329;
1194: t542 = -0.16e2 * t295 * t453 - 0.32e2 * t437 * t64 * t240 + 0.8e1 * t281 * t317 + 0.24e2 * t75 * t170 - 0.4e1 * t75 * t178 + 0.8e1 * t360 * t453 - 0.4e1 * t4 * t529 - 0.16e2 * t295 * t532 - 0.8e1 * t33 * t344 - 0.16e2 * t90 * t181 + 0.4e1 * t33 * t340 * t92;
1195: t557 = t146 * t15;
1196: t562 = xc * t15;
1197: t563 = t562 * t5;
1198: t573 = 0.16e2 * t232 * t193 * t93 - 0.8e1 * t259 * t363 - 0.8e1 * t259 * t497 + 0.8e1 * t33 * t77 + 0.8e1 * t360 * t391 + 0.4e1 * t254 * t227 * t369 + 0.4e1 * t145 * t557 + 0.8e1 * t281 * t166 + 0.4e1 * t3 * t563 + 0.8e1 * t105 * t382 - 0.4e1 * t145 * t480 - 0.4e1 * t33 * t36 * t92;
1199: t600 = 0.4e1 * t456 * t42 - 0.8e1 * t360 * t260 - 0.4e1 * t40 * t557 - 0.4e1 * t105 * t373 + 0.16e2 * t226 * t227 * t93 - 0.16e2 * t90 * t382 - 0.4e1 * t145 * t356 - 0.16e2 * t63 * t157 - 0.32e2 * t87 * t25 * t313 - 0.16e2 * t226 * t227 * t76 - 0.16e2 * t63 * t113;
1200: t623 = xc * t13;
1201: t627 = 0.8e1 * t125 * t423 - 0.8e1 * t360 * t532 + 0.16e2 * t90 * t137 - 0.4e1 * t160 * t42 + 0.16e2 * t63 * t94 + 0.16e2 * t63 * t181 - 0.8e1 * t281 * t27 - 0.8e1 * t75 * t382 + 0.8e1 * t360 * t459 + 0.4e1 * t295 * t57 + 0.16e2 * t105 * t77 + 0.4e1 * t474 * t623 * t35;
1202: t632 = t61 * 0.3141592654e1;
1203: t633 = t632 * t8;
1204: t634 = t80 * nz;
1205: t638 = t632 * t634;
1206: t639 = t638 * xc;
1207: t642 = t61 * t34;
1208: t643 = t122 * t19;
1209: t649 = t61 * t61;
1210: t650 = t649 * t1;
1211: t652 = t19 * t19;
1212: t653 = t14 * t652;
1213: t654 = t653 * t9;
1214: t657 = t14 * t1;
1215: t658 = t657 * t19;
1216: t665 = t632 * t34;
1217: t666 = t665 * t2;
1218: t667 = t8 * t19;
1219: t668 = t667 * t623;
1220: t674 = t665 * nz;
1221: t675 = t652 * xc;
1222: t682 = 0.8e1 * t633 * t426 * t634 - 0.8e1 * t639 * t529 - 0.4e1 * t642 * t643 + 0.2e1 * t642 * t116 * t80 + 0.32e2 * t650 * t64 * t654 + 0.4e1 * t301 * t658 + 0.4e1 * t387 * t46 * ZA * ZB - 0.16e2 * t666 * t668 - 0.16e2 * t666 * t667 * t15 - 0.8e1 * t674 * t675 * t15 + 0.4e1 * t238 * t153 * t80;
1223: t683 = t46 * t652;
1224: t686 = t633 * t15;
1225: t691 = t35 * t80;
1226: t698 = t35 * t652;
1227: t705 = t14 * t80;
1228: t708 = t61 * t35;
1229: t717 = -0.2e1 * t642 * t683 - 0.8e1 * t686 * t5 * t634 * xc - 0.2e1 * t301 * t691 + 0.8e1 * t638 * t563 - 0.2e1 * t642 * t691 - 0.2e1 * t642 * t698 - 0.2e1 * t301 * t698 - 0.2e1 * t301 * t683 + 0.2e1 * t642 * t705 + 0.2e1 * t708 * t274 * t80 + 0.2e1 * t301 * t653 - 0.2e1 * t642 * t80 * t46;
1230: t727 = t61 * t46;
1231: t737 = t649 * t34;
1232: t738 = t737 * t1;
1233: t739 = t8 * t652;
1234: t740 = t739 * t268;
1235: t746 = t61 * ZA;
1236: t754 = t632 * nz * xc;
1237: t758 = 0.2e1 * t301 * t705 + 0.2e1 * t642 * t653 - 0.8e1 * t665 * xc * t634 * t15 - 0.2e1 * t727 * t5 * t80 - 0.32e2 * t650 * xc * t654 + 0.2e1 * t301 * t698 * t14 - 0.32e2 * t738 * t740 + 0.8e1 * t674 * t739 * t562 + 0.4e1 * t746 * t119 * t652 + 0.8e1 * t674 * t698 * t623 - 0.8e1 * t754 * t528 * t698;
1238: t762 = t633 * t13;
1239: t764 = t5 * nz * t652;
1240: t767 = t80 * t1;
1241: t768 = t649 * t767;
1242: t772 = t649 * ZA;
1243: t773 = t772 * t129;
1244: t777 = t35 * t1 * t19;
1245: t780 = t632 * t5;
1246: t781 = t780 * t15;
1247: t786 = t698 * ZA;
1248: t790 = t64 * t14;
1249: t800 = t649 * t8;
1250: t809 = 0.4e1 * t238 * t126 * t80 - 0.8e1 * t762 * t764 - 0.32e2 * t768 * xc * t275 + 0.64e2 * t773 * t740 - 0.4e1 * t301 * t777 - 0.8e1 * t781 * nz * t8 * t675 + 0.4e1 * t238 * t786 + 0.32e2 * t768 * t34 * t790 * t8 - 0.8e1 * t633 * t528 * t634 + 0.8e1 * t754 * t528 * t739 + 0.128e3 * t800 * t119 * t80 * t19 * t106 + 0.8e1 * t674 * t739 * t13;
1251: t812 = t649 * t80;
1252: t817 = t83 * ZB;
1253: t824 = t746 * ZB;
1254: t828 = t800 * t14;
1255: t855 = -0.64e2 * t812 * xc * t274 * t667 + 0.4e1 * t817 * t786 + 0.4e1 * t727 * ZA * t652 * ZB - 0.32e2 * t824 * t657 * t667 - 0.32e2 * t828 * t34 * t767 * xc - 0.8e1 * t633 * t15 * t34 * t634 - 0.8e1 * t674 * t739 * t15 + 0.32e2 * t768 * t64 * t275 + 0.4e1 * t708 * t14 * t307 + 0.2e1 * t708 * t206 * t652 + 0.8e1 * t632 * t35 * t13 * t34 * t634 * xc;
1256: t858 = t35 * t19;
1257: t873 = t2 * t8;
1258: t878 = t61 * t1;
1259: t901 = -0.16e2 * t632 * t2 * xc * t528 * t858 + 0.8e1 * t824 * t658 + 0.4e1 * t301 * t14 * t777 - 0.8e1 * t665 * t634 * t509 - 0.8e1 * t674 * t739 * t623 - 0.16e2 * t781 * t873 * t19 * xc + 0.8e1 * t878 * t14 * t127 + 0.8e1 * t878 * ZA * t51 * ZB + 0.8e1 * t686 * t764 + 0.8e1 * t665 * xc * t634 * t15 * t8 + 0.8e1 * t633 * t15 * t5 * t634 + 0.4e1 * t387 * t14 * t107 * ZA;
1260: t903 = t739 * t790;
1261: t923 = t737 * t80;
1262: t924 = t667 * t790;
1263: t927 = t780 * t2;
1264: t937 = t15 * t19 * xc;
1265: t943 = 0.32e2 * t738 * t903 + 0.16e2 * t781 * t873 * t19 + 0.8e1 * t754 * t15 * t652 * t5 + 0.16e2 * t666 * t858 * t623 + 0.64e2 * t828 * t25 * t767 * xc - 0.16e2 * t762 * t456 * t19 + 0.64e2 * t923 * t924 + 0.16e2 * t927 * t668 - 0.64e2 * t768 * ZA * t790 * t66 - 0.64e2 * t773 * t903 + 0.16e2 * t927 * t937 + 0.16e2 * t666 * t667 * t562;
1266: t977 = 0.64e2 * t812 * t5 * t924 + 0.8e1 * t639 * t504 + 0.8e1 * t238 * t35 * t118 * t19 + 0.4e1 * t642 * t658 - 0.16e2 * t817 * t437 * t8 - 0.128e3 * t772 * ZB * t80 * t924 + 0.16e2 * t666 * t667 * t13 - 0.4e1 * t301 * t643 - 0.16e2 * t824 * t653 * t8 - 0.4e1 * t642 * t777 - 0.64e2 * t923 * t667 * t268 - 0.16e2 * t666 * t937;
1268: _PC3A = (t72 + t132 + t169 + t210 + t246 + t298 + t337 + t378 + t409 + t441 + t483 + t512 + t542 + t573 + t600 + t627) / (t682 + t717 + t758 + t809 + t855 + t901 + t943 + t977);
1269: /****************************************************************************************/
1270: _PC4A = 0;
1271: /****************************************************************************************/
1272: t1 = nx * 0.3141592654e1;
1273: t2 = t1 * xc;
1274: t3 = PetscCosReal(t2);
1275: t4 = nx * nx;
1276: t6 = nz * 0.3141592654e1;
1277: t7 = t3 * t4 * t6;
1278: t8 = ZA * ZB;
1279: t9 = PetscExpReal(t6);
1280: t10 = t9 * t9;
1281: t11 = xc * nz;
1282: t13 = PetscExpReal(t11 * 0.3141592654e1);
1283: t14 = t13 * t13;
1284: t15 = t14 * t13;
1285: t16 = t14 * t14;
1286: t17 = t16 * t15;
1287: t18 = t10 * t17;
1288: t19 = t8 * t18;
1289: t22 = PetscSinReal(t2);
1290: t23 = nx * t22;
1291: t24 = t23 * nz;
1292: t25 = ZB * ZB;
1293: t30 = nz * nz;
1294: t31 = t30 * nz;
1295: t32 = t31 * nx;
1296: t33 = 0.3141592654e1 * 0.3141592654e1;
1297: t35 = t32 * t22 * t33;
1298: t36 = ZA * ZA;
1299: t37 = t36 * xc;
1300: t38 = t16 * t13;
1301: t39 = t10 * t38;
1302: t40 = t37 * t39;
1303: t43 = PetscSinReal(t1);
1304: t44 = nx * t43;
1305: t45 = t30 * 0.3141592654e1;
1306: t46 = t44 * t45;
1307: t47 = ZA * xc;
1308: t49 = ZB * t16 * t9;
1309: t54 = t4 * nx * t43;
1310: t55 = xc * xc;
1311: t57 = t54 * t30 * t55;
1312: t58 = t33 * 0.3141592654e1;
1313: t59 = t58 * t25;
1314: t60 = t16 * t9;
1315: t61 = t59 * t60;
1316: t64 = xc * t25;
1317: t65 = t14 * t9;
1318: t66 = t64 * t65;
1319: t70 = t44 * t31 * t33;
1320: t71 = t37 * t65;
1321: t74 = t10 * t15;
1322: t75 = t64 * t74;
1323: t78 = t25 * t10;
1324: t83 = t54 * nz * t33;
1325: t84 = t55 * t25;
1326: t85 = t10 * t9;
1327: t86 = t14 * t85;
1328: t87 = t84 * t86;
1329: t90 = t30 * t30;
1330: t92 = t44 * t90 * t58;
1331: t93 = t55 * xc;
1332: t94 = t93 * t25;
1333: t95 = t85 * t16;
1334: t96 = t94 * t95;
1335: t102 = t23 * t45;
1336: t103 = t10 * t10;
1337: t104 = ZB * t103;
1338: t106 = t47 * t104 * t15;
1339: t111 = t54 * 0.3141592654e1;
1340: t112 = t25 * t85;
1341: t113 = t112 * t16;
1342: t115 = t8 * t39;
1343: t118 = t16 * t14;
1344: t119 = t85 * t118;
1345: t120 = t37 * t119;
1346: t123 = t16 * t16;
1347: t124 = t36 * t123;
1348: t125 = t124 * t9;
1349: t127 = -0.8e1 * t7 * t19 + 0.2e1 * t24 * t25 * t13 * t10 - 0.16e2 * t35 * t40 - 0.16e2 * t46 * t47 * t49 - 0.8e1 * t57 * t61 + 0.4e1 * t46 * t66 + 0.2e1 * t70 * t71 - 0.16e2 * t35 * t75 + 0.6e1 * t24 * t78 * t38 - 0.2e1 * t83 * t87 - 0.8e1 * t92 * t96 - 0.8e1 * t46 * t37 * t95 - 0.12e2 * t102 * t106 + 0.2e1 * t83 * t71 + t111 * t113 + 0.8e1 * t7 * t115 + 0.2e1 * t83 * t120 + t111 * t125;
1350: t128 = t37 * t74;
1351: t131 = t44 * nz;
1352: t133 = t25 * t9 * t118;
1353: t136 = t36 * t14;
1354: t137 = t136 * t9;
1355: t140 = t30 * t4;
1356: t142 = t140 * t3 * t33;
1357: t143 = t64 * t39;
1358: t147 = t30 * nx * t43;
1359: t148 = 0.3141592654e1 * t36;
1360: t149 = t9 * t118;
1361: t153 = t44 * t31 * ZA;
1362: t154 = t33 * xc;
1363: t155 = t154 * t49;
1364: t160 = ZA * t17 * xc * ZB;
1365: t163 = t103 * t13;
1366: t164 = t64 * t163;
1367: t170 = t44 * t90 * t55;
1368: t171 = t58 * ZB;
1369: t172 = ZA * t16;
1370: t174 = t171 * t172 * t9;
1371: t177 = t36 * t55;
1372: t178 = t177 * t149;
1373: t181 = t54 * t11;
1374: t182 = t33 * t25;
1375: t186 = t25 * t14;
1376: t187 = t186 * t9;
1377: t193 = t186 * t85;
1378: t198 = ZB * t55;
1379: t199 = ZA * t103;
1380: t201 = t198 * t199 * t15;
1381: t204 = 0.2e1 * t7 * t128 - 0.2e1 * t131 * t133 - 0.2e1 * t131 * t137 + 0.16e2 * t142 * t143 - t147 * t148 * t149 + 0.8e1 * t153 * t155 - 0.4e1 * t7 * t160 + 0.2e1 * t7 * t164 + 0.10e2 * t102 * t40 + 0.16e2 * t170 * t174 + 0.2e1 * t83 * t178 - 0.2e1 * t181 * t182 * t65 - t111 * t187 - 0.2e1 * t70 * t87 + 0.4e1 * t102 * t160 - 0.2e1 * t131 * t193 - 0.16e2 * t142 * t75 + 0.16e2 * t35 * t201;
1382: t210 = t32 * t22;
1383: t211 = t33 * t55;
1384: t212 = t25 * t38;
1385: t213 = t211 * t212;
1386: t216 = nz * nx;
1387: t217 = t22 * t25;
1388: t222 = ZB * t85 * t16;
1389: t226 = t23 * t30;
1390: t227 = t13 * t10;
1391: t228 = t148 * t227;
1392: t233 = t37 * t163;
1393: t237 = nz * t4 * t3;
1394: t238 = t148 * t74;
1395: t241 = t64 * t86;
1396: t245 = t148 * xc * t15;
1397: t248 = t112 * t118;
1398: t250 = t22 * t36;
1399: t256 = 0.3141592654e1 * t25;
1400: t257 = t256 * t39;
1401: t262 = t38 * t103;
1402: t263 = t37 * t262;
1403: t267 = t148 * t17 * xc;
1404: t270 = -0.6e1 * t7 * t143 - 0.4e1 * t24 * t19 - 0.8e1 * t210 * t213 - 0.2e1 * t216 * t217 * t15 - 0.32e2 * t153 * t211 * t222 + 0.4e1 * t226 * t228 + 0.16e2 * t142 * t201 + 0.2e1 * t7 * t233 - 0.4e1 * t237 * t238 - 0.2e1 * t83 * t241 - 0.2e1 * t237 * t245 + t111 * t248 + 0.2e1 * t216 * t250 * t15 - 0.2e1 * t131 * t125 - 0.4e1 * t226 * t257 + t147 * t148 * t95 - 0.2e1 * t102 * t263 + 0.2e1 * t237 * t267;
1405: t273 = t37 * t149;
1406: t277 = t47 * t104 * t13;
1407: t285 = t31 * t36;
1408: t286 = t44 * t285;
1409: t291 = t25 * t123 * t9;
1410: t304 = 0.3141592654e1 * xc;
1411: t305 = t304 * t212;
1412: t312 = t256 * t18;
1413: t315 = t8 * t60;
1414: t319 = t54 * t30 * t58;
1415: t323 = t90 * t36;
1416: t324 = t44 * t323;
1417: t325 = t55 * t58;
1418: t326 = t325 * t60;
1419: t329 = 0.2e1 * t102 * t164 + 0.2e1 * t83 * t273 - 0.4e1 * t102 * t277 - 0.2e1 * t7 * t263 + 0.4e1 * t24 * t8 * t17 - 0.4e1 * t286 * t154 * t60 - 0.2e1 * t131 * t291 - t147 * t148 * t119 + 0.2e1 * t24 * t78 * t17 + 0.2e1 * t54 * t85 * 0.3141592654e1 * ZA * ZB - 0.4e1 * t226 * t305 - 0.2e1 * t70 * t66 + t147 * t256 * t95 + 0.4e1 * t237 * t312 + 0.2e1 * t111 * t315 - 0.8e1 * t319 * t96 - t111 * t193 - 0.8e1 * t324 * t326;
1420: t332 = t8 * t95;
1421: t335 = t136 * t85;
1422: t337 = t256 * t227;
1423: t340 = t177 * t119;
1424: t346 = t37 * t86;
1425: t351 = t103 * t15;
1426: t352 = t177 * t351;
1427: t355 = t64 * t119;
1428: t358 = t8 * t227;
1429: t361 = t85 * 0.3141592654e1;
1430: t365 = t84 * t39;
1431: t372 = ZB * t10;
1432: t373 = t372 * t38;
1433: t374 = t47 * t373;
1434: t379 = t177 * t39;
1435: t384 = -0.2e1 * t46 * t332 + t111 * t335 + 0.4e1 * t237 * t337 - 0.2e1 * t83 * t340 + 0.16e2 * t286 * t211 * t95 + 0.2e1 * t70 * t346 - 0.8e1 * t170 * t61 - 0.8e1 * t142 * t352 - 0.2e1 * t83 * t355 - 0.4e1 * t24 * t358 + 0.2e1 * t147 * t361 * t8 + 0.8e1 * t35 * t365 - 0.2e1 * t226 * t267 + 0.8e1 * t102 * t115 - 0.12e2 * t102 * t374 + 0.16e2 * t142 * t40 - 0.8e1 * t142 * t379 + 0.4e1 * t237 * t228;
1436: t386 = t54 * t30 * t93;
1437: t387 = ZA * t85;
1438: t389 = t171 * t387 * t16;
1439: t394 = t64 * t60;
1440: t398 = t304 * t25 * t15;
1441: t401 = t361 * t25;
1442: t405 = t84 * t65;
1443: t410 = t148 * t18;
1444: t414 = t25 * t16 * t9;
1445: t417 = t84 * t74;
1446: t422 = t177 * t86;
1447: t428 = ZB * t38;
1448: t429 = t47 * t428;
1449: t432 = t148 * t39;
1450: t439 = 0.16e2 * t386 * t389 - 0.16e2 * t386 * t174 + 0.8e1 * t46 * t394 + 0.2e1 * t237 * t398 - t147 * t401 + 0.4e1 * t7 * t374 + 0.2e1 * t83 * t405 - 0.4e1 * t46 * t241 - 0.4e1 * t226 * t410 + 0.2e1 * t131 * t414 + 0.8e1 * t35 * t417 - 0.8e1 * t142 * t365 + 0.2e1 * t70 * t422 - 0.4e1 * t181 * t182 * t60 + 0.12e2 * t102 * t429 - 0.4e1 * t226 * t432 + 0.32e2 * t35 * t374 - 0.4e1 * t7 * t106;
1451: t442 = t36 * t9 * t118;
1452: t444 = t123 * t9;
1453: t445 = t8 * t444;
1454: t448 = t361 * t36;
1455: t451 = t47 * t372 * t17;
1456: t454 = t94 * t60;
1457: t457 = t25 * t103;
1458: t465 = t47 * t372 * t15;
1459: t468 = t36 * t85;
1460: t469 = t468 * t16;
1461: t474 = t43 * t85;
1462: t478 = t8 * t74;
1463: t484 = t256 * t74;
1464: t489 = t198 * ZA * t10 * t15;
1465: t501 = -t111 * t442 + 0.4e1 * t131 * t445 - t147 * t448 + 0.4e1 * t7 * t451 + 0.8e1 * t92 * t454 - 0.2e1 * t24 * t457 * t13 - 0.2e1 * t286 * t211 * t65 + 0.4e1 * t7 * t465 + t111 * t469 - 0.2e1 * t216 * t250 * t17 - 0.2e1 * t216 * t474 * t25 - 0.4e1 * t24 * t478 + 0.4e1 * t24 * t8 * t38 + 0.4e1 * t226 * t484 - 0.16e2 * t142 * t489 - 0.2e1 * t24 * t212 * t103 - 0.2e1 * t216 * t22 * t17 * t25 + 0.2e1 * t70 * t120;
1466: t504 = t33 * t36 * t55 * t38;
1467: t507 = t37 * t18;
1468: t512 = t47 * ZB * t13 * t10;
1469: t518 = t59 * t95;
1470: t530 = t84 * t351;
1471: t534 = t37 * t227;
1472: t549 = -0.8e1 * t210 * t504 + 0.2e1 * t102 * t507 + 0.4e1 * t7 * t512 + t111 * t133 - 0.16e2 * t35 * t489 + 0.8e1 * t170 * t518 + 0.2e1 * t24 * t36 * t13 * t10 + 0.4e1 * t131 * t387 * ZB + 0.12e2 * t102 * t465 - 0.8e1 * t142 * t530 + t111 * t291 - 0.2e1 * t102 * t534 - 0.4e1 * t70 * t394 - 0.10e2 * t102 * t128 + 0.4e1 * t237 * t305 + 0.8e1 * t102 * t19 + 0.2e1 * t83 * t346 - 0.16e2 * t35 * t128;
1473: t557 = t468 * t118;
1474: t562 = t93 * t58;
1475: t563 = t562 * t60;
1476: t567 = t44 * t90 * t93;
1477: t575 = ZA * t55;
1478: t576 = t575 * t428;
1479: t583 = t37 * t60;
1480: t590 = t140 * t3;
1481: t601 = -0.2e1 * t226 * t398 - 0.2e1 * t70 * t340 - 0.2e1 * t131 * t557 - 0.4e1 * t24 * t115 + 0.8e1 * t324 * t563 + 0.16e2 * t567 * t389 + 0.16e2 * t70 * t84 * t95 + 0.2e1 * t70 * t178 - 0.16e2 * t142 * t576 - 0.4e1 * t237 * t257 - 0.4e1 * t226 * t312 + 0.8e1 * t46 * t583 + 0.2e1 * t24 * t36 * t38 * t103 + 0.8e1 * t590 * t213 + 0.2e1 * t102 * t143 - 0.16e2 * t35 * t143 + 0.2e1 * t131 * t248 + 0.4e1 * t46 * t346;
1482: t604 = nz * t36;
1483: t606 = t154 * t95;
1484: t625 = t36 * t103;
1485: t640 = t30 * t36;
1486: t641 = t54 * t640;
1487: t642 = t325 * t95;
1488: t647 = -0.4e1 * t131 * t315 - 0.4e1 * t54 * t604 * t606 - t147 * t148 * t60 + 0.16e2 * t35 * t576 - 0.8e1 * t102 * t478 + 0.32e2 * t142 * t465 - 0.4e1 * t237 * t484 - 0.2e1 * t70 * t355 + 0.2e1 * t70 * t273 + 0.2e1 * t102 * t233 - 0.2e1 * t24 * t625 * t13 - 0.8e1 * t7 * t358 - 0.2e1 * t111 * t445 - 0.4e1 * t7 * t429 + 0.16e2 * t46 * t47 * t222 + 0.2e1 * t131 * t113 + 0.8e1 * t641 * t642 - 0.2e1 * t7 * t534;
1489: t652 = t36 * t16;
1490: t653 = t652 * t9;
1491: t655 = t64 * t227;
1492: t658 = t182 * t95;
1493: t663 = t562 * t95;
1494: t684 = t64 * t351;
1495: t689 = t36 * t10;
1496: t695 = t154 * t222;
1497: t698 = -0.4e1 * t216 * t217 * t38 - t111 * t653 - 0.2e1 * t7 * t655 - 0.4e1 * t181 * t658 + 0.2e1 * t131 * t469 - 0.8e1 * t641 * t663 - 0.4e1 * t83 * t583 - 0.2e1 * t83 * t177 * t65 - 0.4e1 * t24 * t457 * t15 + 0.16e2 * t70 * t84 * t60 + 0.8e1 * t57 * t518 - 0.32e2 * t142 * t374 + 0.4e1 * t24 * t8 * t351 + 0.4e1 * t102 * t684 - t147 * t256 * t86 - 0.2e1 * t24 * t689 * t15 - 0.2e1 * t70 * t241 + 0.8e1 * t153 * t695;
1498: t711 = t575 * t373;
1499: t717 = t304 * t17 * t25;
1500: t736 = t177 * t74;
1501: t739 = 0.2e1 * t226 * t245 - 0.8e1 * t102 * t358 - 0.16e2 * t57 * t389 - 0.2e1 * t102 * t655 + 0.8e1 * t590 * t504 - 0.8e1 * t641 * t326 - 0.16e2 * t35 * t711 - t111 * t557 + t111 * t137 - 0.2e1 * t226 * t717 + 0.8e1 * t102 * t37 * t351 + 0.2e1 * t131 * t335 - 0.4e1 * t131 * t332 - 0.2e1 * t216 * t474 * t36 - 0.2e1 * t111 * t332 + 0.16e2 * t142 * t711 - t147 * t256 * t60 + 0.8e1 * t142 * t736;
1502: t750 = t64 * t262;
1503: t763 = t44 * t640;
1504: t770 = t84 * t119;
1505: t782 = 0.4e1 * t102 * t512 + 0.8e1 * t142 * t417 + 0.8e1 * t641 * t563 - 0.2e1 * t7 * t507 + 0.2e1 * t7 * t750 - 0.8e1 * t35 * t352 + 0.4e1 * t237 * t410 + 0.4e1 * t7 * t684 - 0.2e1 * t46 * t445 + t147 * t148 * t65 + 0.4e1 * t763 * t304 * t119 + 0.16e2 * t70 * t177 * t60 + 0.2e1 * t70 * t770 - t111 * t414 - 0.16e2 * t567 * t174 - 0.4e1 * t46 * t71 - 0.4e1 * t46 * t355 - 0.4e1 * t7 * t277;
1506: t797 = t64 * t149;
1507: t821 = -t54 * t448 + 0.2e1 * t131 * t442 + 0.8e1 * t7 * t478 + 0.8e1 * t35 * t379 - 0.2e1 * t181 * t182 * t149 + 0.2e1 * t70 * t405 + 0.2e1 * t83 * t770 - 0.2e1 * t70 * t797 - 0.6e1 * t7 * t75 - 0.4e1 * t286 * t606 - 0.4e1 * t237 * t432 + t147 * t256 * t149 - 0.4e1 * t763 * t304 * t149 - 0.2e1 * t102 * t75 + 0.2e1 * t237 * t717 + 0.8e1 * t324 * t642 - 0.16e2 * t170 * t389 + 0.2e1 * t83 * t422;
1508: t827 = t84 * t149;
1509: t846 = t54 * nz * ZA;
1510: t854 = t64 * t18;
1511: t867 = -0.16e2 * t142 * t128 + 0.32e2 * t35 * t465 - 0.2e1 * t83 * t827 + 0.2e1 * t46 * t315 + t147 * t148 * t86 - 0.4e1 * t102 * t451 - 0.8e1 * t226 * t148 * xc * t38 - 0.2e1 * t24 * t689 * t38 + 0.2e1 * t131 * t187 + 0.8e1 * t846 * t155 + 0.8e1 * t35 * t736 + 0.2e1 * t24 * t689 * t17 - 0.2e1 * t7 * t854 + t147 * t256 * t119 + 0.2e1 * t102 * t854 - 0.8e1 * t35 * t530 + 0.4e1 * t46 * t797 + 0.2e1 * t102 * t750;
1512: t909 = -0.8e1 * t324 * t663 + t147 * t256 * t444 - t147 * t256 * t65 + 0.4e1 * t226 * t238 + 0.2e1 * t7 * t40 - t54 * t401 + 0.16e2 * t57 * t174 + 0.4e1 * t226 * t337 + 0.4e1 * t24 * t8 * t163 + 0.8e1 * t846 * t695 + 0.8e1 * t319 * t454 + 0.2e1 * t131 * t653 - 0.8e1 * t46 * t64 * t95 + 0.6e1 * t24 * t78 * t15 - 0.4e1 * t44 * t31 * xc * t658 - 0.32e2 * t153 * t211 * t49 - 0.2e1 * t70 * t827 + t147 * t148 * t444;
1513: t914 = t25 * ZB;
1514: t915 = t33 * t914;
1515: t919 = t4 * t4;
1516: t920 = t16 * t919;
1517: t929 = t123 * t90;
1518: t932 = t919 * t103;
1519: t935 = t33 * ZB;
1520: t939 = t652 * t919;
1521: t942 = t16 * t30;
1522: t943 = t942 * t4;
1523: t949 = t103 * t16;
1524: t950 = t949 * t90;
1525: t953 = -0.2e1 * t915 * t103 * t90 + 0.2e1 * t915 * t920 - 0.2e1 * t915 * t123 * t919 + 0.2e1 * t915 * t16 * t90 - 0.2e1 * t915 * t929 - 0.2e1 * t915 * t932 - 0.2e1 * t935 * t323 * t123 + 0.2e1 * t935 * t939 + 0.4e1 * t915 * t943 + 0.4e1 * t182 * t172 * t90 + 0.2e1 * t915 * t950;
1526: t954 = t171 * t36;
1527: t955 = t90 * nz;
1528: t956 = xc * t955;
1529: t957 = t118 * t10;
1530: t964 = t33 * t33;
1531: t965 = t964 * ZB;
1532: t966 = t965 * t640;
1533: t967 = t10 * t919;
1534: t968 = t55 * t16;
1535: t969 = t967 * t968;
1536: t972 = t935 * t36;
1537: t974 = t103 * t30 * t4;
1538: t977 = xc * t16;
1539: t978 = t967 * t977;
1540: t981 = t90 * t30;
1541: t983 = t16 * t10;
1542: t987 = t182 * ZA;
1543: t988 = t4 * t10;
1544: t992 = t171 * t604;
1545: t993 = xc * t14;
1546: t994 = t932 * t993;
1547: t997 = t182 * t30;
1548: t1005 = t171 * t285;
1549: t1006 = t988 * t993;
1550: t1009 = t58 * t914;
1551: t1010 = t1009 * t31;
1552: t1013 = 0.8e1 * t954 * t956 * t957 + 0.2e1 * t915 * t932 * t16 + 0.32e2 * t966 * t969 - 0.4e1 * t972 * t974 - 0.32e2 * t966 * t978 + 0.32e2 * t965 * t981 * t177 * t983 - 0.32e2 * t987 * t942 * t988 + 0.8e1 * t992 * t994 + 0.8e1 * t997 * t949 * ZA * t4 - 0.2e1 * t935 * t124 * t919 - 0.16e2 * t1005 * t1006 + 0.16e2 * t1010 * t1006;
1553: t1015 = t964 * t25;
1554: t1016 = ZA * t30;
1555: t1017 = t1015 * t1016;
1556: t1020 = t967 * t993;
1557: t1031 = t1009 * t118;
1558: t1032 = t31 * t10;
1559: t1040 = t964 * t914;
1560: t1041 = t1040 * t90;
1561: t1044 = t55 * t10 * t4 * t16;
1562: t1047 = t1040 * t30;
1563: t1050 = t123 * ZA;
1564: t1054 = t977 * t988;
1565: t1057 = 0.64e2 * t1017 * t978 - 0.8e1 * t992 * t1020 + 0.2e1 * t972 * t950 + 0.4e1 * t182 * t929 * ZA + 0.4e1 * t182 * t199 * t90 - 0.16e2 * t1031 * t1032 * t4 * xc + 0.4e1 * t182 * t172 * t919 + 0.64e2 * t1041 * t1044 + 0.32e2 * t1047 * t969 + 0.4e1 * t182 * t1050 * t919 - 0.64e2 * t1041 * t1054;
1566: t1058 = t1009 * nz;
1567: t1063 = t932 * ZA;
1568: t1069 = t123 * t30 * t4;
1569: t1080 = t993 * t103 * t4;
1570: t1088 = t935 * t103;
1571: t1094 = -0.8e1 * t1058 * t994 - 0.32e2 * t1047 * t978 + 0.4e1 * t182 * t1063 - 0.4e1 * t915 * t974 - 0.4e1 * t915 * t1069 - 0.2e1 * t935 * t625 * t90 - 0.8e1 * t1009 * t10 * t14 * t955 - 0.16e2 * t1010 * t1080 - 0.2e1 * t935 * t625 * t919 - 0.64e2 * t1017 * t969 + 0.2e1 * t1088 * t939 + 0.8e1 * t1009 * t957 * t955;
1572: t1113 = t955 * t118 * xc;
1573: t1120 = t4 * t118;
1574: t1125 = t981 * xc;
1575: t1133 = nz * t10;
1576: t1140 = -0.8e1 * t954 * t955 * t10 * t993 + 0.2e1 * t935 * t652 * t90 - 0.64e2 * t1015 * t981 * t575 * t983 + 0.8e1 * t182 * t103 * t1016 * t4 + 0.8e1 * t1009 * t1113 + 0.16e2 * t954 * t1032 * t4 * t14 - 0.16e2 * t954 * t1032 * t1120 + 0.64e2 * t1015 * t10 * t172 * t1125 + 0.8e1 * t171 * t103 * t136 * t956 - 0.8e1 * t1031 * t1133 * t919 * xc + 0.8e1 * t1058 * t1020;
1577: t1153 = xc * t118;
1578: t1165 = t182 * t16;
1579: t1170 = t171 * t10;
1580: t1178 = ZA * t90;
1581: t1182 = 0.4e1 * t1088 * t652 * t140 + 0.8e1 * t954 * t1133 * t919 * t14 + 0.4e1 * t972 * t943 - 0.4e1 * t972 * t1069 - 0.16e2 * t954 * t31 * t4 * t1153 - 0.8e1 * t954 * nz * t919 * t1153 - 0.8e1 * t954 * t1133 * t919 * t118 + 0.4e1 * t1165 * t1063 + 0.16e2 * t1005 * t1080 - 0.8e1 * t1170 * t118 * t36 * t955 - 0.16e2 * t987 * t920 * t10 - 0.16e2 * t1165 * t1178 * t10;
1582: t1195 = t1040 * t981;
1583: t1199 = t1009 * t955;
1584: t1203 = t1009 * t10;
1585: t1211 = t965 * t323;
1586: t1225 = -0.32e2 * t965 * t10 * t652 * t1125 + 0.4e1 * t915 * t16 * t974 + 0.4e1 * t182 * t90 * t949 * ZA + 0.32e2 * t1195 * t968 * t10 - 0.8e1 * t1199 * t993 * t103 + 0.8e1 * t1203 * t118 * nz * t919 + 0.8e1 * t1170 * t136 * t955 + 0.64e2 * t1211 * t1044 + 0.16e2 * t1031 * t1032 * t4 + 0.8e1 * t987 * t943 + 0.8e1 * t1199 * t993 * t10 + 0.8e1 * t997 * t1050 * t4;
1587: t1263 = -0.128e3 * t1015 * t1178 * t1044 + 0.16e2 * t1005 * t988 * t1153 + 0.8e1 * t1058 * t1153 * t919 + 0.16e2 * t1010 * t1120 * xc - 0.8e1 * t954 * t1113 - 0.8e1 * t1203 * t14 * nz * t919 - 0.16e2 * t1203 * t14 * t31 * t4 - 0.8e1 * t1203 * t1113 - 0.32e2 * t1195 * t977 * t10 - 0.64e2 * t1211 * t1054 + 0.8e1 * t992 * t967 * t1153 + 0.128e3 * t1015 * t983 * t90 * t4 * t47;
1589: _PC1B = (t127 + t204 + t270 + t329 + t384 + t439 + t501 + t549 + t601 + t647 + t698 + t739 + t782 + t821 + t867 + t909) / (t953 + t1013 + t1057 + t1094 + t1140 + t1182 + t1225 + t1263);
1590: /****************************************************************************************/
1591: t1 = nz * nz;
1592: t2 = t1 * nz;
1593: t3 = nx * t2;
1594: t4 = 0.3141592654e1 * ZA;
1595: t5 = t3 * t4;
1596: t6 = nx * 0.3141592654e1;
1597: t7 = t6 * xc;
1598: t8 = PetscSinReal(t7);
1599: t9 = t8 * ZB;
1600: t10 = nz * 0.3141592654e1;
1601: t11 = PetscExpReal(t10);
1602: t12 = t11 * t11;
1603: t15 = PetscExpReal(xc * nz * 0.3141592654e1);
1604: t16 = t15 * t15;
1605: t17 = t16 * t16;
1606: t18 = t17 * t15;
1607: t19 = t12 * t18;
1608: t23 = t1 * t1;
1609: t24 = nx * t23;
1610: t25 = ZB * ZB;
1611: t27 = t18 * t8;
1612: t28 = 0.3141592654e1 * 0.3141592654e1;
1613: t29 = xc * xc;
1614: t30 = t28 * t29;
1615: t34 = t1 * xc;
1616: t35 = 0.3141592654e1 * ZB;
1617: t36 = t34 * t35;
1618: t37 = PetscCosReal(t7);
1619: t38 = ZA * t37;
1620: t39 = nx * nx;
1621: t40 = t39 * t12;
1622: t41 = t16 * t15;
1623: t43 = t38 * t40 * t41;
1624: t46 = t25 * nz;
1625: t47 = t46 * 0.3141592654e1;
1626: t48 = t39 * nx;
1627: t49 = PetscSinReal(t6);
1628: t50 = t48 * t49;
1629: t51 = t12 * t11;
1630: t52 = t51 * t17;
1631: t53 = t50 * t52;
1632: t56 = t34 * 0.3141592654e1 * t25;
1633: t57 = t37 * t39;
1634: t58 = t17 * t41;
1635: t59 = t12 * t58;
1636: t60 = t57 * t59;
1637: t63 = t25 * t18;
1638: t64 = t57 * nz;
1639: t67 = ZA * ZA;
1640: t68 = t67 * nz;
1641: t69 = 0.3141592654e1 * t48;
1642: t70 = t68 * t69;
1643: t71 = t49 * xc;
1644: t72 = t17 * t16;
1645: t73 = t11 * t72;
1646: t74 = t71 * t73;
1647: t77 = t1 * t67;
1648: t78 = t77 * 0.3141592654e1;
1649: t81 = nx * t25;
1650: t82 = t81 * t49;
1651: t83 = t17 * t17;
1652: t85 = t1 * t83 * t11;
1653: t87 = nx * ZB;
1654: t88 = t8 * t2;
1655: t89 = t87 * t88;
1656: t90 = 0.3141592654e1 * xc;
1657: t91 = t12 * t12;
1658: t92 = ZA * t91;
1659: t97 = ZB * ZA;
1660: t98 = t97 * t37;
1661: t99 = t39 * nz;
1662: t100 = t12 * t41;
1663: t104 = 0.8e1 * t5 * t9 * t19 + 0.8e1 * t24 * t25 * t27 * t30 + 0.12e2 * t36 * t43 - t47 * t53 - 0.2e1 * t56 * t60 - 0.4e1 * t63 * t64 + 0.6e1 * t70 * t74 + 0.4e1 * t78 * t60 - t82 * t85 + 0.4e1 * t89 * t90 * t92 * t41 + 0.4e1 * t98 * t99 * t100;
1664: t105 = t67 * t48;
1665: t106 = t49 * t51;
1666: t107 = t106 * t72;
1667: t109 = t1 * 0.3141592654e1;
1668: t110 = t109 * xc;
1669: t115 = nx * t67;
1670: t116 = t115 * t49;
1671: t117 = t1 * t16;
1672: t118 = t117 * t11;
1673: t120 = t2 * t25;
1674: t121 = t28 * 0.3141592654e1;
1675: t122 = t121 * t29;
1676: t123 = t120 * t122;
1677: t129 = t1 * ZB;
1678: t130 = t129 * t4;
1679: t131 = t57 * t100;
1680: t134 = t12 * t16;
1681: t136 = t109 * t39;
1682: t139 = ZB * t18;
1683: t141 = t39 * t1;
1684: t142 = t141 * t90;
1685: t145 = t77 * t90;
1686: t146 = t91 * t41;
1687: t147 = t57 * t146;
1688: t151 = t25 * t39 * t1;
1689: t152 = t72 * t12;
1690: t156 = t49 * t2;
1691: t158 = t83 * t11;
1692: t162 = -t105 * t107 + 0.8e1 * t110 * t72 * t25 * t39 - t116 * t118 + 0.8e1 * t123 * t53 + 0.8e1 * t5 * t9 * t59 - 0.8e1 * t130 * t131 - 0.8e1 * t134 * t25 * t136 - 0.12e2 * t139 * t38 * t142 - 0.8e1 * t145 * t147 - 0.8e1 * t151 * t90 * t152 - 0.2e1 * t87 * t156 * t4 * t158;
1693: t164 = t115 * t88;
1694: t165 = t90 * t19;
1695: t168 = t25 * t48;
1696: t169 = t49 * t16;
1697: t170 = t169 * t11;
1698: t174 = ZA * nz * t69;
1699: t175 = ZB * t51;
1700: t176 = t175 * t17;
1701: t177 = t71 * t176;
1702: t180 = t1 * t29;
1703: t181 = t28 * t25;
1704: t182 = t180 * t181;
1705: t183 = t50 * t73;
1706: t186 = ZA * t1;
1707: t187 = t28 * t48;
1708: t188 = t186 * t187;
1709: t189 = ZB * t17;
1710: t190 = t189 * t11;
1711: t191 = t71 * t190;
1712: t194 = t50 * t158;
1713: t196 = t115 * t156;
1714: t197 = t90 * t73;
1715: t201 = t49 * t17 * t11;
1716: t204 = t88 * t90;
1717: t207 = t68 * 0.3141592654e1;
1718: t208 = t17 * t11;
1719: t209 = t50 * t208;
1720: t211 = -0.2e1 * t164 * t165 - t168 * t170 + t168 * t107 + 0.8e1 * t174 * t177 + 0.2e1 * t182 * t183 + 0.8e1 * t188 * t191 + t47 * t194 - 0.6e1 * t196 * t197 - t168 * t201 - 0.4e1 * t81 * t18 * t204 - t207 * t209;
1721: t212 = t2 * 0.3141592654e1;
1722: t213 = t212 * t52;
1723: t215 = t81 * t8;
1724: t216 = t212 * t59;
1725: t219 = t3 * t90;
1726: t220 = t25 * t8;
1727: t221 = t18 * t91;
1728: t225 = t71 * t52;
1729: t231 = t16 * t51;
1730: t232 = t50 * t231;
1731: t237 = ZA * t12;
1732: t243 = t67 * t28;
1733: t244 = t24 * t243;
1734: t245 = t71 * t231;
1735: t249 = -t116 * t213 - 0.4e1 * t215 * t216 + 0.2e1 * t219 * t220 * t221 - 0.4e1 * t70 * t225 + 0.4e1 * t98 * t99 * t146 + t47 * t232 - 0.2e1 * t145 * t57 * t221 + 0.4e1 * t89 * t90 * t237 * t41 - t105 * t201 - 0.6e1 * t244 * t245 + t105 * t170;
1736: t252 = t25 * t37;
1737: t253 = t252 * t39;
1738: t255 = nz * t15 * t12;
1739: t258 = t2 * t29;
1740: t259 = ZB * t28;
1741: t260 = t258 * t259;
1742: t263 = t106 * t17;
1743: t265 = xc * t25;
1744: t269 = t25 * t49;
1745: t270 = t269 * t52;
1746: t273 = t1 * t25;
1747: t274 = t273 * 0.3141592654e1;
1748: t275 = t57 * t19;
1749: t278 = t24 * t30;
1750: t288 = t1 * t11 * t72;
1751: t290 = t212 * t208;
1752: t292 = t2 * xc;
1753: t296 = 0.2e1 * t253 * t255 + 0.16e2 * t260 * t43 + t105 * t263 - 0.4e1 * t10 * t265 * t53 + 0.4e1 * t219 * t270 - 0.12e2 * t274 * t275 + 0.8e1 * t278 * t270 - 0.2e1 * ZB * nz * t69 * t49 * ZA * t158 - t82 * t288 - t116 * t290 + 0.16e2 * t292 * t243 * t275;
1754: t301 = t50 * t176;
1755: t304 = t51 * t72;
1756: t305 = t71 * t304;
1757: t308 = t25 * t41;
1758: t311 = ZA * t48;
1759: t312 = t311 * t49;
1760: t317 = t91 * t15;
1761: t318 = t57 * t317;
1762: t321 = t81 * t88;
1763: t322 = t90 * t59;
1764: t325 = t212 * t231;
1765: t327 = t15 * t12;
1766: t328 = t57 * t327;
1767: t331 = t77 * t187;
1768: t334 = t2 * ZA;
1769: t335 = t334 * t122;
1770: t336 = t50 * t190;
1771: t339 = 0.8e1 * t151 * t90 * t134 + 0.16e2 * t186 * t30 * t301 - 0.2e1 * t70 * t305 + 0.2e1 * t308 * t64 - 0.2e1 * t312 * ZB * t83 * t11 + 0.2e1 * t56 * t318 + 0.2e1 * t321 * t322 - t116 * t325 - 0.4e1 * t274 * t328 + 0.2e1 * t331 * t305 - 0.16e2 * t335 * t336;
1772: t341 = t169 * t51;
1773: t344 = t49 * t11 * t72;
1774: t346 = t77 * t30;
1775: t347 = t50 * t304;
1776: t350 = t25 * t51;
1777: t352 = nx * ZA;
1778: t353 = t49 * t23;
1779: t354 = t352 * t353;
1780: t355 = t28 * xc;
1781: t362 = t25 * t91;
1782: t365 = t23 * nz;
1783: t366 = nx * t365;
1784: t367 = t366 * t122;
1785: t368 = ZB * t49;
1786: t369 = ZA * t51;
1787: t370 = t369 * t17;
1788: t371 = t368 * t370;
1789: t374 = t115 * t353;
1790: t375 = t355 * t73;
1791: t381 = t105 * t341 - t105 * t344 - 0.2e1 * t346 * t347 - t350 * t50 - 0.8e1 * t354 * t355 * t176 - 0.4e1 * t98 * t99 * t317 - 0.2e1 * t362 * t99 - 0.16e2 * t367 * t371 + 0.6e1 * t374 * t375 - 0.8e1 * t182 * t53 - t82 * t290;
1792: t382 = t71 * t208;
1793: t394 = t2 * t67;
1794: t395 = t394 * t122;
1795: t398 = t352 * t156;
1796: t402 = t17 * t12;
1797: t403 = t39 * ZA;
1798: t404 = t402 * t403;
1799: t407 = t269 * t208;
1800: t411 = t49 * t83 * t11;
1801: t413 = t46 * t69;
1802: t419 = -0.4e1 * t331 * t382 + 0.2e1 * t115 * t58 * t204 - 0.2e1 * t145 * t60 + 0.12e2 * t274 * t131 + 0.2e1 * t346 * t232 + 0.8e1 * t395 * t53 - 0.8e1 * t398 * t90 * t176 - 0.64e2 * t260 * t404 + 0.4e1 * t219 * t407 + t168 * t411 - 0.6e1 * t413 * t74 - 0.2e1 * t110 * t308 * t57;
1803: t424 = t16 * t11;
1804: t425 = t212 * t424;
1805: t427 = t258 * t181;
1806: t430 = t67 * t29;
1807: t431 = t366 * t430;
1808: t432 = t121 * t49;
1809: t433 = t432 * t52;
1810: t436 = nz * t12;
1811: t437 = t436 * t18;
1812: t440 = t29 * xc;
1813: t441 = t440 * t121;
1814: t442 = t394 * t441;
1815: t445 = t67 * t37;
1816: t446 = t445 * t39;
1817: t448 = nz * t18 * t91;
1818: t453 = t352 * t49;
1819: t458 = t8 * t23;
1820: t462 = t81 * t458;
1821: t463 = t30 * t19;
1822: t466 = -t47 * t209 + t116 * t425 - 0.8e1 * t427 * t275 + 0.8e1 * t431 * t433 - 0.2e1 * t253 * t437 - 0.8e1 * t442 * t53 - 0.2e1 * t446 * t448 + 0.2e1 * t175 * t312 + 0.6e1 * t453 * t129 * t208 + 0.8e1 * t115 * t18 * t458 * t30 + 0.8e1 * t462 * t463;
1823: t470 = t436 * t58;
1824: t475 = t2 * t121 * t440 * t25;
1825: t485 = t212 * t73;
1826: t488 = t67 * t72 * t1;
1827: t490 = t39 * xc;
1828: t501 = 0.4e1 * t374 * t355 * t52 + 0.2e1 * t446 * t470 - 0.8e1 * t475 * t53 - 0.2e1 * t446 * t437 - 0.4e1 * t36 * t38 * t39 * t15 * t12 - t116 * t485 + 0.8e1 * t488 * 0.3141592654e1 * t12 * t490 - t207 * t183 - 0.2e1 * t182 * t232 - 0.6e1 * t413 * t245 - 0.4e1 * t413 * t382;
1829: t503 = t115 * t8;
1830: t510 = t355 * t19;
1831: t513 = t432 * t208;
1832: t525 = t38 * t40 * t18;
1833: t533 = -0.4e1 * t503 * t216 - 0.4e1 * t89 * t90 * t92 * t15 - 0.16e2 * t462 * t510 + 0.8e1 * t431 * t513 - 0.4e1 * t78 * t131 + t47 * t183 - 0.2e1 * t67 * t83 * t99 + 0.4e1 * t331 * t225 + 0.16e2 * t260 * t525 - 0.4e1 * t89 * t90 * t237 * t58 - t207 * t53;
1834: t536 = t28 * t37;
1835: t538 = t490 * t100;
1836: t541 = t334 * t441;
1837: t547 = t394 * t30;
1838: t550 = t212 * t19;
1839: t553 = t366 * t441;
1840: t556 = nz * t17;
1841: t571 = -0.8e1 * t427 * t131 + 0.16e2 * t394 * t536 * t538 + 0.16e2 * t541 * t336 + 0.2e1 * t453 * t129 * t158 - 0.8e1 * t547 * t147 + 0.4e1 * t503 * t550 - 0.8e1 * t553 * t270 + 0.4e1 * t556 * ZB * t92 * t39 - 0.2e1 * t67 * t91 * t99 - t82 * t425 + 0.4e1 * t78 * t275 + 0.2e1 * t78 * xc * t41 * t57;
1842: t583 = t90 * t317;
1843: t594 = t212 * t158;
1844: t596 = t152 * t67;
1845: t602 = t67 * t17;
1846: t607 = 0.8e1 * t367 * t407 - 0.4e1 * t98 * t99 * t59 + 0.16e2 * t260 * t18 * ZA * t57 + 0.2e1 * t321 * t583 - 0.6e1 * t174 * t368 * t52 - 0.4e1 * t89 * t90 * ZA * t15 * t12 + t116 * t594 - 0.8e1 * t596 * t136 - 0.4e1 * t98 * t99 * t327 + 0.2e1 * t602 * t99 + 0.2e1 * t164 * t583;
1847: t613 = t83 * t25;
1848: t616 = t81 * t156;
1849: t627 = t90 * t231;
1850: t630 = t91 * t16;
1851: t638 = 0.4e1 * t196 * t90 * t208 - 0.8e1 * t130 * t60 - 0.2e1 * t613 * t99 + 0.6e1 * t616 * t197 - 0.8e1 * t547 * t131 + 0.8e1 * t67 * t18 * t37 * t142 + 0.2e1 * t145 * t328 - 0.6e1 * t196 * t627 + 0.8e1 * t630 * t67 * t142 - 0.8e1 * t547 * t275 + 0.8e1 * t395 * t209;
1852: t643 = t77 * t355;
1853: t648 = t115 * t458;
1854: t651 = t134 * t67;
1855: t657 = t30 * t304;
1856: t660 = t30 * t146;
1857: t665 = t25 * t17;
1858: t668 = t50 * t424;
1859: t671 = -0.4e1 * t321 * t90 * t146 - 0.6e1 * t643 * t232 + 0.8e1 * t182 * t209 - 0.16e2 * t648 * t510 + 0.8e1 * t651 * t136 + 0.8e1 * t89 * t4 * t100 - 0.2e1 * t374 * t657 - 0.8e1 * t648 * t660 + 0.8e1 * t130 * t328 + 0.2e1 * t665 * t99 + 0.2e1 * t346 * t668;
1860: t672 = t90 * t424;
1861: t676 = t120 * t536;
1862: t680 = t436 * t41;
1863: t688 = t366 * t67 * t440;
1864: t696 = xc * t12;
1865: t697 = t696 * t18;
1866: t701 = t252 * t141;
1867: t702 = t90 * t221;
1868: t705 = 0.2e1 * t196 * t672 - t47 * t347 + 0.16e2 * t676 * t538 - t116 * t85 - 0.2e1 * t253 * t680 + t207 * t194 + 0.4e1 * t98 * t99 * t19 - 0.8e1 * t688 * t433 + 0.16e2 * t541 * t301 - 0.6e1 * t312 * t190 + 0.4e1 * t352 * t88 * t35 * t697 + 0.2e1 * t701 * t702;
1869: t712 = t24 * t430;
1870: t713 = t28 * t49;
1871: t721 = t1 * t17 * t11;
1872: t726 = ZB * xc;
1873: t737 = nz * t91;
1874: t741 = 0.8e1 * t346 * t209 + 0.2e1 * t712 * t713 * t424 + 0.8e1 * t130 * t275 - t47 * t668 + t116 * t721 - 0.8e1 * t688 * t513 + 0.4e1 * t352 * t27 * t212 * t726 + 0.8e1 * t648 * t463 + 0.4e1 * t274 * t60 - 0.4e1 * t374 * t355 * t208 - 0.4e1 * t253 * t737 * t41;
1875: t745 = t269 * t231;
1876: t749 = t1 * t28 * t265;
1877: t757 = t16 * t39;
1878: t758 = t696 * t757;
1879: t762 = t69 * t49;
1880: t772 = t355 * t100;
1881: t775 = t81 * t353;
1882: t778 = -0.8e1 * t398 * t90 * t190 - 0.2e1 * t278 * t745 + 0.4e1 * t749 * t53 + 0.32e2 * t394 * t29 * t28 * t17 * t40 - 0.8e1 * t78 * t758 + t350 * nz * t762 - 0.6e1 * t87 * t49 * t186 * t52 - 0.8e1 * t553 * t407 - 0.4e1 * t749 * t209 + 0.16e2 * t648 * t772 - 0.6e1 * t775 * t375;
1883: t790 = t212 * t304;
1884: t793 = t156 * 0.3141592654e1;
1885: t795 = t355 * t304;
1886: t800 = t91 * t39;
1887: t801 = t800 * nz;
1888: t807 = t2 * t28;
1889: t808 = t807 * t726;
1890: t811 = -0.2e1 * t616 * t672 - 0.2e1 * t446 * t680 - 0.2e1 * t78 * xc * t58 * t57 + 0.8e1 * t367 * t270 - t82 * t790 + t115 * t51 * t793 - 0.2e1 * t775 * t795 + 0.8e1 * t123 * t209 + 0.2e1 * t665 * t801 - 0.2e1 * t67 * t41 * t64 - 0.32e2 * t808 * t43;
1891: t812 = t117 * t51;
1892: t821 = t24 * t355;
1893: t827 = t90 * t304;
1894: t840 = t800 * t41;
1895: t844 = -t116 * t812 - 0.2e1 * t110 * t25 * t58 * t57 - 0.4e1 * t78 * t328 + t82 * t485 - 0.4e1 * t821 * t407 + 0.4e1 * t196 * t90 * t52 + 0.2e1 * t196 * t827 + t82 * t325 + 0.2e1 * t253 * t448 - 0.32e2 * t402 * t67 * t807 * t490 - t207 * t232 + 0.12e2 * t186 * t90 * ZB * t37 * t840;
1896: t849 = t1 * t51;
1897: t850 = t849 * t17;
1898: t860 = t269 * t424;
1899: t863 = t273 * t187;
1900: t874 = 0.16e2 * t462 * t772 - t116 * t850 + 0.16e2 * t553 * t371 + t116 * t288 - 0.12e2 * t97 * t57 * t109 * t697 + t82 * t594 - 0.2e1 * t278 * t860 - 0.2e1 * t863 * t305 - 0.16e2 * t180 * t259 * t311 * t201 - 0.6e1 * t863 * t74 + 0.8e1 * t174 * t191;
1901: t879 = xc * ZA;
1902: t888 = t67 * t51;
1903: t901 = ZA * t17;
1904: t903 = t368 * t901 * t11;
1905: t908 = -0.2e1 * t352 * t51 * t156 * t35 + 0.64e2 * t879 * t189 * t807 * t40 + 0.2e1 * t46 * t58 * t37 * t39 - t888 * t50 + t105 * t411 - 0.16e2 * t335 * t301 + 0.8e1 * t152 * t25 * t136 - 0.8e1 * t278 * t407 + 0.2e1 * t712 * t713 * t231 - 0.16e2 * t367 * t903 + 0.2e1 * t145 * t318;
1906: t923 = t71 * t424;
1907: t926 = t87 * t458;
1908: t927 = t28 * ZA;
1909: t944 = 0.8e1 * t354 * t355 * t190 - 0.8e1 * t110 * t16 * t25 * t800 - 0.2e1 * t374 * t30 * t73 - 0.16e2 * t354 * t30 * t176 - 0.2e1 * t244 * t923 - 0.32e2 * t926 * t927 * t696 * t41 - 0.32e2 * t808 * t525 + 0.6e1 * t749 * t232 - 0.8e1 * t188 * t177 + 0.4e1 * t36 * t58 * ZA * t57 + 0.4e1 * t821 * t270;
1910: t948 = t90 * t327;
1911: t961 = t30 * t100;
1912: t964 = t29 * t49;
1913: t981 = t106 * t1;
1914: t983 = -0.2e1 * t219 * t220 * t100 + 0.2e1 * t321 * t948 - 0.16e2 * t189 * ZA * t99 * t12 - 0.2e1 * t369 * nz * t69 * t368 + 0.2e1 * t374 * t795 - 0.8e1 * t462 * t961 - 0.8e1 * t244 * t964 * t208 + 0.2e1 * t413 * t923 + 0.4e1 * t36 * t38 * t40 * t58 - 0.2e1 * t87 * t51 * t49 * t1 * ZA + t888 * nz * t762 + t115 * t981;
1915: t1012 = 0.6e1 * t616 * t627 - t82 * t213 + 0.2e1 * t775 * t657 - 0.12e2 * t215 * t550 - 0.6e1 * t145 * t131 + 0.2e1 * t81 * t41 * t204 + 0.6e1 * ZB * t48 * t49 * t370 - 0.4e1 * t70 * t382 + 0.2e1 * t446 * t255 + 0.8e1 * t89 * t4 * t327 - 0.4e1 * t56 * t147;
1916: t1018 = t212 * t100;
1917: t1029 = t212 * t327;
1918: t1040 = 0.6e1 * t70 * t245 + 0.2e1 * t56 * t328 + t207 * t668 + 0.4e1 * t503 * t1018 + 0.2e1 * t253 * t470 - 0.6e1 * t398 * t35 * t208 - 0.8e1 * t331 * t964 * t52 - 0.4e1 * t503 * t1029 + 0.6e1 * t821 * t745 + 0.4e1 * t63 * t37 * t142 + 0.16e2 * t260 * t38 * t840;
1919: t1068 = t207 * t347 - 0.2e1 * t164 * t702 - 0.2e1 * t331 * t964 * t73 + 0.8e1 * t374 * t30 * t52 + 0.16e2 * t278 * t903 + 0.2e1 * t863 * t923 + 0.6e1 * t445 * t141 * t165 - 0.2e1 * t164 * t90 * t100 + 0.6e1 * t331 * t74 - 0.2e1 * t182 * t668 - 0.2e1 * t115 * t41 * t204;
1920: t1079 = t58 * t8;
1921: t1091 = t807 * t29;
1922: t1092 = t665 * t40;
1923: t1101 = ZB * t91;
1924: t1102 = t403 * nz;
1925: t1105 = -0.4e1 * t58 * ZB * ZA * t64 - t82 * t850 + 0.2e1 * t821 * t860 + t81 * t51 * t793 + 0.2e1 * t3 * t25 * t1079 * t90 + t82 * t721 - 0.2e1 * t643 * t668 + 0.16e2 * t926 * t927 * t29 * t91 * t41 + 0.32e2 * t1091 * t1092 - 0.2e1 * t219 * t220 * t19 + 0.4e1 * t139 * ZA * t64 + 0.4e1 * t1101 * t1102;
1926: t1108 = t849 * t72;
1927: t1121 = t737 * t15;
1928: t1124 = t29 * t12;
1929: t1133 = t116 * t1108 - 0.8e1 * t475 * t209 - 0.32e2 * t807 * xc * t1092 + 0.2e1 * t278 * t269 * t73 + t82 * t812 - 0.6e1 * t56 * t131 + 0.2e1 * t253 * t1121 + 0.16e2 * t926 * t927 * t1124 * t41 + t168 * t263 - 0.2e1 * t616 * t827 + t81 * t981;
1930: t1134 = t394 * t28;
1931: t1159 = -0.8e1 * t1134 * t29 * t18 * t57 + t82 * t118 - 0.12e2 * t215 * t1018 + 0.2e1 * t602 * t801 - t168 * t341 + 0.2e1 * t67 * t58 * t64 + t168 * t344 - 0.6e1 * t174 * t368 * t208 + 0.16e2 * t553 * t903 + t116 * t790 - 0.4e1 * t36 * t38 * t800 * t15;
1932: t1161 = nz * t83;
1933: t1173 = ZB * t12;
1934: t1196 = 0.4e1 * t1161 * ZB * t39 * ZA - 0.4e1 * t215 * t1029 - 0.8e1 * t488 * 0.3141592654e1 * t39 * xc + 0.32e2 * t821 * ZA * t8 * t1173 * t18 - 0.8e1 * t427 * t147 + 0.6e1 * t701 * t165 - 0.16e2 * t926 * t927 * t1124 * t18 - 0.8e1 * t1091 * t63 * t57 - 0.8e1 * t442 * t209 - 0.8e1 * t462 * t660 - 0.6e1 * t398 * t35 * t52;
1935: t1228 = 0.2e1 * t413 * t305 - 0.8e1 * t648 * t961 - 0.16e2 * t87 * t27 * t23 * t28 * ZA * t29 + 0.4e1 * t189 * t1102 - 0.4e1 * t87 * t1079 * t212 * t879 + 0.2e1 * t164 * t948 - 0.2e1 * t70 * t923 + 0.2e1 * t164 * t322 + 0.2e1 * t446 * t1121 + 0.2e1 * t863 * t964 * t304 - t82 * t1108 + 0.16e2 * t676 * t490 * t19;
1936: t1234 = t25 * ZB;
1937: t1235 = t1234 * t28;
1938: t1236 = t365 * t91;
1939: t1240 = ZB * t121;
1940: t1241 = t1240 * t77;
1941: t1242 = t39 * t39;
1942: t1243 = t12 * t1242;
1943: t1244 = xc * t72;
1944: t1245 = t1243 * t1244;
1945: t1248 = t365 * t25;
1946: t1252 = t243 * nz;
1947: t1257 = t23 * t1;
1948: t1258 = t1240 * t1257;
1949: t1259 = t67 * t12;
1950: t1260 = xc * t16;
1951: t1268 = t1234 * t121;
1952: t1269 = t1268 * t23;
1953: t1272 = t1242 * t91;
1954: t1280 = t67 * xc;
1955: t1284 = t28 * t28;
1956: t1285 = t67 * t1284;
1957: t1287 = t1285 * t2 * ZB;
1958: t1288 = t17 * xc;
1959: t1289 = t1243 * t1288;
1960: t1292 = 0.2e1 * t1235 * t1236 * t17 + 0.8e1 * t1241 * t1245 + 0.4e1 * t927 * t1248 * t91 - 0.2e1 * t1252 * ZB * t1242 * t91 - 0.8e1 * t1258 * t1259 * t1260 - 0.4e1 * t1235 * t2 * t83 * t39 + 0.16e2 * t1269 * t758 + 0.2e1 * t1252 * t189 * t1272 - 0.2e1 * t1252 * t83 * t1242 * ZB + 0.8e1 * t1258 * t630 * t1280 - 0.32e2 * t1287 * t1289;
1961: t1293 = t365 * t83;
1962: t1300 = ZA * t1284;
1963: t1304 = t17 * t1242 * t25 * t12;
1964: t1307 = t927 * t2;
1965: t1311 = t23 * t2;
1966: t1312 = t1300 * t1311;
1967: t1316 = t1234 * t1284;
1968: t1317 = t1316 * t1311;
1969: t1321 = t1240 * t23;
1970: t1331 = t1240 * t23 * t67;
1971: t1332 = t40 * t1244;
1972: t1338 = t1243 * t1260;
1973: t1344 = -0.2e1 * t1235 * t1293 - 0.16e2 * t181 * t365 * t901 * t12 - 0.64e2 * t1300 * t258 * t1304 + 0.8e1 * t1307 * t613 * t39 + 0.64e2 * t1312 * t265 * t402 - 0.32e2 * t1317 * t1288 * t12 - 0.16e2 * t1321 * t67 * t39 * t1244 + 0.2e1 * t1235 * nz * t1272 * t17 + 0.16e2 * t1331 * t1332 + 0.64e2 * t1300 * t292 * t1304 - 0.8e1 * t1241 * t1338 - 0.2e1 * t243 * t1293 * ZB;
1974: t1346 = t1316 * t2;
1975: t1349 = t927 * nz;
1976: t1350 = t25 * t1242;
1977: t1354 = t1268 * t1257;
1978: t1366 = t1268 * t1;
1979: t1370 = t29 * t17;
1980: t1371 = t1243 * t1370;
1981: t1386 = -0.32e2 * t1346 * t1289 + 0.4e1 * t1349 * t1350 * t91 + 0.8e1 * t1354 * t1260 * t12 - 0.16e2 * t181 * nz * t901 * t1243 - 0.4e1 * t1235 * t2 * t91 * t39 + 0.8e1 * t1366 * t152 * t1242 + 0.32e2 * t1287 * t1371 + 0.8e1 * t1258 * t1280 * t152 - 0.8e1 * t1354 * t1260 * t91 + 0.128e3 * t1300 * t365 * xc * t1092 + 0.8e1 * t1366 * t1338;
1982: t1387 = t1257 * t12;
1983: t1391 = t1240 * t1;
1984: t1399 = t1272 * t1260;
1985: t1412 = t1285 * t1311;
1986: t1427 = -0.8e1 * t1268 * t1387 * t16 - 0.8e1 * t1391 * t67 * t1242 * t1244 - 0.4e1 * t1134 * t1101 * t39 + 0.8e1 * t1241 * t1399 - 0.8e1 * t1258 * t596 + 0.4e1 * t927 * t1293 * t25 - 0.16e2 * t1331 * t758 + 0.8e1 * t1307 * t665 * t39 + 0.32e2 * t1412 * t1370 * t1173 + 0.8e1 * t1307 * t665 * t800 + 0.8e1 * t1391 * t1259 * t1242 * t16 - 0.8e1 * t1391 * t1259 * t1242 * t72;
1987: t1456 = t365 * ZB;
1988: t1468 = 0.4e1 * t927 * t1248 * t17 - 0.2e1 * t1235 * nz * t1242 * t91 + 0.8e1 * t1366 * t1244 * t1242 - 0.16e2 * t1269 * t134 * t39 + 0.8e1 * t1268 * t1257 * t72 * xc + 0.16e2 * t1321 * t1259 * t757 + 0.32e2 * t1317 * t1370 * t12 + 0.4e1 * t1349 * t613 * t1242 + 0.2e1 * t243 * t1456 * t17 - 0.64e2 * t1285 * t365 * t12 * t189 * t490 - 0.8e1 * t1354 * t152 * xc;
1989: t1472 = t1316 * t365;
1990: t1474 = t1124 * t39 * t17;
1991: t1478 = t17 * t91;
1992: t1504 = t72 * t39;
1993: t1511 = 0.4e1 * t1134 * t189 * t800 + 0.64e2 * t1472 * t1474 + 0.4e1 * t1235 * t2 * t1478 * t39 + 0.4e1 * t1349 * t665 * t1242 - 0.8e1 * t1258 * t1280 * t72 + 0.2e1 * t1252 * t189 * t1242 + 0.2e1 * t243 * t365 * t189 * t91 + 0.4e1 * t927 * t365 * t1478 * t25 - 0.128e3 * t1300 * t1248 * t1474 - 0.2e1 * t1235 * t1236 + 0.16e2 * t1269 * t1504 * xc + 0.2e1 * t1235 * t365 * t17;
1994: t1545 = -0.2e1 * t1235 * t1161 * t1242 + 0.4e1 * t1349 * t1350 * t1478 - 0.8e1 * t1366 * t1245 + 0.2e1 * t1235 * t556 * t1242 - 0.32e2 * t1412 * t402 * t726 - 0.8e1 * t1366 * t1399 + 0.8e1 * t1258 * t651 - 0.2e1 * t243 * t1456 * t91 + 0.8e1 * t1268 * t1387 * t72 - 0.16e2 * t1269 * t1332 + 0.4e1 * t1134 * t189 * t39 + 0.16e2 * t1269 * t152 * t39;
1995: t1564 = t1260 * t800;
1996: t1583 = 0.64e2 * t1285 * t1456 * t1474 - 0.64e2 * t1472 * t1288 * t40 - 0.8e1 * t1366 * t134 * t1242 + 0.8e1 * t1307 * t362 * t39 + 0.4e1 * t1235 * t2 * t17 * t39 + 0.32e2 * t1346 * t1371 - 0.16e2 * t1269 * t1564 - 0.16e2 * t1321 * t1259 * t1504 + 0.16e2 * t1331 * t1564 - 0.64e2 * t1312 * t29 * t25 * t402 - 0.4e1 * t1134 * t83 * t39 * ZB - 0.32e2 * t181 * t2 * t404;
1998: _PC2B = (t1133 + t1196 + t1068 + t811 + t466 + t1012 + t381 + t162 + t249 + t533 + t844 + t104 + t1159 + t571 + t211 + t874 + t607 + t339 + t296 + t638 + t908 + t671 + t419 + t983 + t705 + t1105 + t501 + t778 + t1040 + t1228 + t741 + t944) / (t1292 + t1344 + t1386 + t1427 + t1468 + t1511 + t1545 + t1583);
1999: /****************************************************************************************/
2000: t1 = nz * nz;
2001: t2 = t1 * nz;
2002: t3 = t2 * nx;
2003: t4 = nx * 0.3141592654e1;
2004: t5 = t4 * xc;
2005: t6 = PetscSinReal(t5);
2006: t7 = 0.3141592654e1 * 0.3141592654e1;
2007: t9 = t3 * t6 * t7;
2008: t10 = xc * xc;
2009: t11 = ZA * ZA;
2010: t12 = t10 * t11;
2011: t13 = nz * 0.3141592654e1;
2012: t14 = PetscExpReal(t13);
2013: t15 = t14 * t14;
2014: t16 = xc * nz;
2015: t18 = PetscExpReal(t16 * 0.3141592654e1);
2016: t19 = t18 * t18;
2017: t20 = t19 * t18;
2018: t21 = t15 * t20;
2019: t22 = t12 * t21;
2020: t25 = nx * t6;
2021: t26 = t1 * 0.3141592654e1;
2022: t27 = t25 * t26;
2023: t28 = ZA * ZB;
2024: t29 = t18 * t15;
2025: t30 = t28 * t29;
2026: t33 = t25 * nz;
2027: t34 = t11 * t15;
2028: t35 = t19 * t19;
2029: t36 = t35 * t18;
2030: t40 = t25 * t1;
2031: t41 = 0.3141592654e1 * t11;
2032: t42 = t15 * t36;
2033: t43 = t41 * t42;
2034: t46 = nx * nx;
2035: t47 = t1 * t46;
2036: t48 = t47 * t11;
2037: t49 = t7 * xc;
2038: t50 = t35 * t15;
2039: t51 = t49 * t50;
2040: t55 = PetscSinReal(t4);
2041: t56 = t46 * nx * t55;
2042: t58 = t56 * nz * t7;
2043: t59 = ZB * ZB;
2044: t60 = t10 * t59;
2045: t61 = t15 * t14;
2046: t62 = t19 * t61;
2047: t63 = t60 * t62;
2048: t66 = t19 * t14;
2049: t67 = t60 * t66;
2050: t70 = t28 * t42;
2051: t73 = PetscCosReal(t5);
2052: t74 = t47 * t73;
2053: t75 = t7 * t11;
2054: t77 = t75 * t10 * t36;
2055: t80 = t73 * t46;
2056: t81 = t80 * nz;
2057: t82 = 0.3141592654e1 * t59;
2058: t83 = t82 * t42;
2059: t87 = xc * t11;
2060: t88 = t87 * t62;
2061: t91 = nz * nx;
2062: t92 = t55 * t61;
2063: t96 = nx * t55;
2064: t98 = t96 * t2 * t7;
2065: t101 = xc * t59;
2066: t102 = t101 * t62;
2067: t108 = t1 * t1;
2068: t109 = t108 * t7;
2069: t111 = t59 * t35;
2070: t112 = t111 * t15;
2071: t115 = t35 * t20;
2072: t123 = t1 * nx * t55;
2073: t124 = t61 * t35;
2074: t127 = t35 * t19;
2075: t128 = t61 * t127;
2076: t129 = t60 * t128;
2077: t132 = t56 * t16;
2078: t133 = t7 * t59;
2079: t134 = t133 * t124;
2080: t137 = 0.6e1 * t58 * t88 - 0.2e1 * t91 * t92 * t11 + 0.2e1 * t98 * t63 - 0.6e1 * t58 * t102 - 0.2e1 * t91 * t92 * t59 - 0.16e2 * t109 * xc * t112 - 0.2e1 * t91 * t6 * t115 * t59 + 0.12e2 * t40 * t83 + t123 * t41 * t124 - 0.2e1 * t58 * t129 + 0.4e1 * t132 * t134;
2081: t139 = t56 * 0.3141592654e1;
2082: t140 = t111 * t14;
2083: t144 = t49 * t124;
2084: t147 = t91 * t55;
2085: t148 = t61 * ZA;
2086: t154 = ZA * t115 * xc * ZB;
2087: t157 = t7 * 0.3141592654e1;
2088: t159 = t96 * t108 * t157;
2089: t160 = t10 * xc;
2090: t161 = t160 * t59;
2091: t162 = t35 * t14;
2092: t163 = t161 * t162;
2093: t166 = t28 * t162;
2094: t169 = t80 * t13;
2095: t170 = t101 * t42;
2096: t173 = t2 * t11;
2097: t174 = t96 * t173;
2098: t175 = t7 * t10;
2099: t179 = t59 * t15;
2100: t184 = t15 * t15;
2101: t193 = t139 * t140 + 0.4e1 * t56 * nz * t11 * t144 + 0.4e1 * t147 * t148 * ZB + 0.4e1 * t27 * t154 + 0.8e1 * t159 * t163 - 0.12e2 * t147 * t166 + 0.2e1 * t169 * t170 - 0.16e2 * t174 * t175 * t124 + 0.2e1 * t33 * t179 * t20 - 0.2e1 * t33 * t11 * t36 * t184 + 0.2e1 * t56 * t61 * 0.3141592654e1 * ZA * ZB;
2102: t194 = t173 * 0.3141592654e1;
2103: t195 = xc * t15;
2104: t196 = t195 * t19;
2105: t202 = t15 * t115;
2106: t203 = t28 * t202;
2107: t206 = t96 * t26;
2108: t207 = t14 * t127;
2109: t208 = t101 * t207;
2110: t211 = t12 * t128;
2111: t218 = t11 * t61;
2112: t219 = t218 * t35;
2113: t221 = t108 * ZA;
2114: t223 = t7 * ZB;
2115: t224 = t223 * t50;
2116: t227 = ZA * xc;
2117: t228 = ZB * t15;
2118: t229 = t228 * t36;
2119: t230 = t227 * t229;
2120: t233 = t87 * t207;
2121: t236 = t6 * t11;
2122: t240 = -0.4e1 * t194 * t196 + 0.4e1 * t194 * t195 * t127 + 0.4e1 * t33 * t203 - 0.12e2 * t206 * t208 + 0.2e1 * t58 * t211 - 0.16e2 * t47 * t10 * t133 * t50 + t139 * t219 - 0.32e2 * t221 * t10 * t224 - 0.4e1 * t169 * t230 - 0.6e1 * t98 * t233 + 0.2e1 * t91 * t236 * t20;
2123: t244 = t227 * t228 * t20;
2124: t252 = t184 * t18;
2125: t253 = t101 * t252;
2126: t256 = t35 * t35;
2127: t257 = t256 * t14;
2128: t258 = t28 * t257;
2129: t261 = t108 * t11;
2130: t263 = t7 * t35;
2131: t268 = ZB * t61 * t35;
2132: t273 = t96 * t108 * t160;
2133: t274 = t157 * ZB;
2134: t276 = t274 * t148 * t35;
2135: t279 = t101 * t21;
2136: t282 = 0.3141592654e1 * xc;
2137: t283 = t59 * t36;
2138: t284 = t282 * t283;
2139: t289 = 0.4e1 * t169 * t244 - 0.4e1 * t132 * t133 * t162 - 0.2e1 * t147 * t140 - 0.2e1 * t27 * t253 + 0.2e1 * t139 * t258 + 0.16e2 * t261 * t10 * t263 * t15 - 0.16e2 * t206 * t227 * t268 - 0.16e2 * t273 * t276 - 0.6e1 * t27 * t279 - 0.4e1 * t40 * t284 - 0.32e2 * t9 * t230;
2140: t290 = t1 * t11;
2141: t291 = t96 * t290;
2142: t297 = t59 * t61;
2143: t298 = t297 * t127;
2144: t300 = ZB * t36;
2145: t301 = t227 * t300;
2146: t304 = t1 * t59;
2147: t305 = t184 * t35;
2148: t310 = t46 * ZB;
2149: t311 = t184 * ZA;
2150: t312 = t310 * t311;
2151: t314 = t60 * t21;
2152: t317 = t1 * ZA;
2153: t318 = ZB * t35;
2154: t321 = t1 * t256;
2155: t324 = t96 * t261;
2156: t325 = t10 * t157;
2157: t326 = t325 * t124;
2158: t329 = -0.4e1 * t291 * t282 * t128 + t123 * t82 * t62 - t139 * t298 + 0.12e2 * t27 * t301 + t304 * t305 - 0.2e1 * t58 * t12 * t66 - 0.2e1 * t312 + 0.8e1 * t9 * t314 + 0.2e1 * t317 * t318 + 0.2e1 * t321 * t28 - 0.8e1 * t324 * t326;
2159: t331 = t28 * t124;
2160: t334 = 0.3141592654e1 * t15;
2161: t335 = t334 * t127;
2162: t338 = t35 * ZA;
2163: t341 = t46 * t256;
2164: t344 = t46 * t11;
2165: t346 = t46 * t59;
2166: t348 = t297 * t35;
2167: t351 = ZA * t10;
2168: t352 = t351 * t300;
2169: t355 = t1 * ZB;
2170: t362 = 0.12e2 * t147 * t331 - 0.4e1 * t173 * t335 - 0.2e1 * t310 * t338 - 0.2e1 * t341 * t28 - t344 * t305 - t346 * t305 + 0.2e1 * t147 * t348 + 0.16e2 * t9 * t352 + 0.2e1 * t355 * t311 + t290 * t305 + 0.2e1 * t33 * t34 * t20;
2171: t363 = t36 * t184;
2172: t364 = t87 * t363;
2173: t368 = t47 * t73 * t7;
2174: t373 = t160 * t157;
2175: t374 = t373 * t124;
2176: t377 = t311 * t35;
2177: t380 = t12 * t62;
2178: t386 = ZB * t10 * ZA * t15 * t20;
2179: t389 = t87 * t66;
2180: t393 = t56 * t1 * t10;
2181: t401 = 0.2e1 * t27 * t364 - 0.16e2 * t368 * t279 - t123 * t41 * t257 + 0.8e1 * t324 * t374 + 0.2e1 * t355 * t377 - 0.2e1 * t98 * t380 - 0.16e2 * t9 * t386 + 0.2e1 * t58 * t389 + 0.16e2 * t393 * t276 + t123 * t82 * t162 - 0.2e1 * t33 * t179 * t36;
2182: t412 = t11 * t14 * t127;
2183: t416 = t11 * t19;
2184: t417 = t416 * t61;
2185: t421 = t96 * t2 * ZA;
2186: t426 = t56 * nz * ZA;
2187: t427 = t318 * t14;
2188: t428 = t49 * t427;
2189: t431 = t82 * t29;
2190: t434 = t87 * t21;
2191: t442 = 0.2e1 * t33 * t11 * t184 * t18 + 0.4e1 * t81 * t284 - t139 * t412 + 0.2e1 * t147 * t219 - 0.2e1 * t147 * t417 + 0.32e2 * t421 * t175 * t268 + 0.8e1 * t426 * t428 + 0.4e1 * t81 * t431 - 0.2e1 * t169 * t434 - 0.2e1 * t98 * t129 - 0.32e2 * t47 * t28 * t51;
2192: t443 = t184 * t20;
2193: t447 = t61 * 0.3141592654e1;
2194: t448 = t447 * t11;
2195: t450 = t49 * t268;
2196: t453 = t60 * t42;
2197: t456 = t41 * t202;
2198: t463 = t101 * t443;
2199: t469 = t41 * xc * t20;
2200: t474 = -0.8e1 * t27 * t87 * t443 - t56 * t448 - 0.8e1 * t426 * t450 + 0.8e1 * t368 * t453 + 0.4e1 * t40 * t456 + 0.4e1 * t40 * t431 - 0.4e1 * t81 * t456 - 0.4e1 * t27 * t463 + 0.6e1 * t139 * t331 + 0.2e1 * t40 * t469 - 0.16e2 * t9 * t434;
2201: t482 = t108 * t10;
2202: t492 = nz * t46;
2203: t493 = t492 * t11;
2204: t495 = t282 * t19 * t184;
2205: t498 = t56 * t290;
2206: t499 = t325 * t162;
2207: t502 = t416 * t14;
2208: t504 = t60 * t207;
2209: t507 = -t123 * t82 * t257 - 0.4e1 * t169 * t301 + t123 * t41 * t162 + 0.16e2 * t482 * t7 * t112 - 0.12e2 * t206 * t102 - t123 * t82 * t66 - 0.4e1 * t147 * t258 - 0.4e1 * t493 * t495 - 0.8e1 * t498 * t499 + t139 * t502 - 0.2e1 * t98 * t504;
2210: t508 = t101 * t162;
2211: t512 = t41 * t115 * xc;
2212: t515 = t87 * t42;
2213: t520 = ZB * t184;
2214: t522 = t227 * t520 * t18;
2215: t525 = t492 * t59;
2216: t528 = t6 * t59;
2217: t532 = t520 * t20;
2218: t533 = t351 * t532;
2219: t539 = t447 * t59;
2220: t544 = 0.8e1 * t206 * t508 - 0.2e1 * t40 * t512 - 0.16e2 * t368 * t515 + 0.12e2 * t206 * t88 + 0.4e1 * t27 * t522 + 0.4e1 * t525 * t495 - 0.4e1 * t91 * t528 * t36 - 0.16e2 * t368 * t533 - 0.16e2 * t206 * t227 * t427 - t56 * t539 - 0.2e1 * t132 * t133 * t66;
2221: t551 = t87 * t162;
2222: t554 = t351 * t229;
2223: t560 = t59 * t19;
2224: t561 = t560 * t14;
2225: t564 = t101 * t202;
2226: t567 = t87 * t252;
2227: t573 = t227 * t228 * t115;
2228: t578 = 0.4e1 * t33 * t70 + 0.4e1 * t493 * t335 - 0.4e1 * t58 * t551 + 0.16e2 * t9 * t554 - 0.4e1 * t33 * t28 * t252 + 0.2e1 * t147 * t561 + 0.2e1 * t169 * t564 - 0.2e1 * t27 * t567 - 0.8e1 * t324 * t499 - 0.4e1 * t169 * t573 + 0.12e2 * t27 * t244;
2229: t579 = t82 * t202;
2230: t591 = t282 * t115 * t59;
2231: t598 = t101 * t66;
2232: t606 = -0.4e1 * t81 * t579 - 0.2e1 * t169 * t567 - 0.6e1 * t27 * t170 + 0.8e1 * t169 * t203 + 0.2e1 * t98 * t67 + 0.2e1 * t81 * t591 + 0.32e2 * t368 * t244 - 0.2e1 * t27 * t564 + 0.4e1 * t206 * t598 + 0.16e2 * t9 * t170 + 0.2e1 * t33 * t283 * t184;
2233: t608 = t373 * t162;
2234: t611 = t59 * t184;
2235: t617 = t101 * t29;
2236: t624 = t227 * ZB * t18 * t15;
2237: t629 = t157 * t59;
2238: t630 = t629 * t124;
2239: t633 = t3 * t6;
2240: t634 = t175 * t283;
2241: t644 = 0.8e1 * t498 * t608 + 0.2e1 * t33 * t611 * t18 - 0.4e1 * t206 * t389 - 0.2e1 * t27 * t617 - 0.4e1 * t169 * t154 + 0.4e1 * t27 * t624 + 0.12e2 * t27 * t230 - 0.8e1 * t393 * t630 - 0.8e1 * t633 * t634 + 0.16e2 * t47 * t7 * t101 * t50 + 0.2e1 * t123 * t447 * t28;
2242: t645 = t41 * t29;
2243: t648 = t2 * 0.3141592654e1;
2244: t649 = t648 * xc;
2245: t650 = t560 * t184;
2246: t656 = t56 * t1 * t157;
2247: t659 = t87 * t128;
2248: t662 = t96 * t482;
2249: t663 = t629 * t162;
2250: t671 = t161 * t124;
2251: t674 = t218 * t127;
2252: t679 = 0.4e1 * t81 * t645 - 0.4e1 * t649 * t650 - 0.8e1 * t169 * t70 + 0.8e1 * t656 * t163 - 0.2e1 * t98 * t659 - 0.8e1 * t662 * t663 - 0.32e2 * t421 * t175 * t427 - 0.2e1 * t147 * t502 + 0.8e1 * t656 * t671 + 0.2e1 * t147 * t674 - 0.16e2 * t368 * t386;
2253: t714 = t334 * t19;
2254: t719 = t12 * t42;
2255: t722 = t304 * t35 - t346 * t35 + t341 * t59 - t344 * t35 + t344 * t256 + t346 * t184 - 0.16e2 * t368 * t554 - 0.16e2 * t48 * t175 * t50 + 0.4e1 * t525 * t714 - 0.2e1 * t58 * t659 + 0.8e1 * t368 * t719;
2256: t730 = xc * t19;
2257: t735 = t59 * t256 * t14;
2258: t752 = 0.4e1 * t173 * t714 - 0.6e1 * t27 * t515 - 0.16e2 * t9 * t279 + 0.4e1 * t194 * t730 * t184 - t139 * t735 - 0.4e1 * t492 * t127 * t82 * xc - 0.4e1 * t98 * t508 - t123 * t41 * t207 - 0.2e1 * t147 * t298 + 0.8e1 * t368 * t314 + 0.6e1 * t132 * t133 * t207;
2259: t755 = t28 * t21;
2260: t759 = t274 * t338 * t14;
2261: t767 = t11 * t35;
2262: t768 = t767 * t14;
2263: t778 = t560 * t61;
2264: t781 = -0.2e1 * t58 * t504 - 0.8e1 * t27 * t755 + 0.16e2 * t662 * t759 + 0.12e2 * t291 * t282 * t207 - 0.6e1 * t27 * t434 + t139 * t768 - 0.8e1 * t498 * t326 + 0.4e1 * t33 * t611 * t20 + 0.2e1 * t81 * t512 - t139 * t561 + 0.2e1 * t147 * t778;
2265: t786 = t12 * t443;
2266: t790 = t282 * t59 * t20;
2267: t796 = t59 * t14 * t127;
2268: t806 = t41 * t21;
2269: t811 = -0.8e1 * t393 * t663 + 0.8e1 * t368 * t786 + 0.2e1 * t81 * t790 + 0.4e1 * t169 * t624 + t139 * t796 + 0.2e1 * t206 * t258 - 0.2e1 * t40 * t591 - 0.8e1 * t662 * t630 - 0.4e1 * t33 * t30 - 0.4e1 * t40 * t806 + 0.8e1 * t9 * t786;
2270: t819 = t282 * t15 * t127;
2271: t822 = t101 * t363;
2272: t830 = t11 * t256 * t14;
2273: t835 = t227 * t532;
2274: t842 = 0.2e1 * t33 * t11 * t18 * t15 + t123 * t41 * t66 - 0.4e1 * t493 * t819 - 0.2e1 * t27 * t822 - 0.16e2 * t368 * t170 - 0.4e1 * t169 * t463 - t139 * t830 - 0.4e1 * t649 * t179 * t127 + 0.12e2 * t27 * t835 - 0.16e2 * t368 * t434 - 0.2e1 * t40 * t790;
2275: t845 = t87 * t202;
2276: t854 = t338 * t15;
2277: t859 = t12 * t207;
2278: t868 = t139 * t348 - 0.2e1 * t27 * t845 + 0.8e1 * t169 * t755 - 0.2e1 * t58 * t380 + 0.6e1 * t206 * t331 + 0.8e1 * t310 * t854 - 0.2e1 * t169 * t822 + 0.2e1 * t98 * t859 + 0.8e1 * t159 * t671 + 0.8e1 * t74 * t634 - 0.2e1 * t169 * t253;
2279: t880 = t60 * t443;
2280: t891 = t101 * t128;
2281: t894 = -t123 * t539 - 0.2e1 * t147 * t796 + 0.32e2 * t368 * t230 + t139 * t674 - 0.16e2 * t98 * t60 * t124 + 0.32e2 * t9 * t244 + 0.8e1 * t368 * t880 - 0.8e1 * t40 * t41 * xc * t36 - t123 * t82 * t128 - 0.6e1 * t58 * t233 + 0.2e1 * t58 * t891;
2282: t903 = t179 * t19;
2283: t920 = t56 * t1 * t160;
2284: t925 = -0.2e1 * t174 * t175 * t66 - 0.4e1 * t493 * t714 + 0.4e1 * t649 * t903 - 0.4e1 * t81 * t43 + t123 * t82 * t207 + 0.4e1 * t206 * t891 - 0.16e2 * t273 * t759 - 0.8e1 * t27 * t203 + 0.32e2 * t221 * ZB * t51 - 0.16e2 * t920 * t759 - 0.8e1 * t9 * t453;
2285: t932 = t87 * t29;
2286: t945 = t82 * t21;
2287: t953 = -0.16e2 * t920 * t276 - 0.8e1 * t169 * t30 - 0.8e1 * t633 * t77 - 0.2e1 * t27 * t932 - 0.4e1 * t174 * t49 * t162 + 0.8e1 * t206 * t87 * t124 - 0.2e1 * t147 * t768 + 0.4e1 * t169 * t522 - 0.12e2 * t81 * t945 + 0.4e1 * t33 * t28 * t115 + 0.4e1 * t525 * t819;
2288: t971 = t282 * t127;
2289: t978 = -0.6e1 * t98 * t102 + 0.2e1 * t169 * t515 - 0.2e1 * t310 * t377 + 0.2e1 * t147 * t830 + 0.8e1 * t368 * t22 - 0.2e1 * t169 * t617 + 0.16e2 * t662 * t276 - 0.8e1 * t355 * t854 + 0.4e1 * t493 * t971 - 0.16e2 * t9 * t533 - 0.2e1 * t169 * t279;
2290: t997 = xc * t127;
2291: t998 = t997 * t59;
2292: t1003 = 0.4e1 * t40 * t579 + 0.2e1 * t169 * t845 + 0.16e2 * t9 * t515 + 0.8e1 * t206 * t551 + t123 * t41 * t128 + 0.16e2 * t98 * t60 * t162 + 0.2e1 * t169 * t364 - 0.2e1 * t169 * t932 + t139 * t778 + 0.4e1 * t648 * t998 + 0.2e1 * t147 * t412;
2293: t1006 = t2 * t59;
2294: t1017 = xc * t35;
2295: t1033 = 0.4e1 * t1006 * t335 + 0.4e1 * t81 * t806 - 0.2e1 * t33 * t34 * t115 + 0.8e1 * t498 * t374 - 0.16e2 * t261 * t7 * t1017 * t15 + 0.8e1 * t206 * t101 * t124 - t123 * t448 + 0.2e1 * t147 * t735 + 0.6e1 * t98 * t208 + 0.6e1 * t98 * t88 - 0.4e1 * t33 * t755;
2296: t1055 = -0.4e1 * t173 * t971 + 0.2e1 * t98 * t891 + 0.8e1 * t9 * t880 + 0.4e1 * t169 * t835 - t304 * t184 + t344 * t184 - t123 * t41 * t62 - 0.2e1 * t98 * t598 + 0.2e1 * t58 * t859 + 0.32e2 * t47 * t351 * t224 + 0.2e1 * t98 * t389;
2297: t1070 = t15 * t19;
2298: t1089 = -0.16e2 * t368 * t352 - 0.8e1 * t9 * t719 + 0.4e1 * t96 * t2 * xc * t134 - 0.2e1 * t91 * t236 * t115 + 0.4e1 * t27 * t573 + 0.4e1 * t493 * t282 * t1070 + 0.2e1 * t33 * t59 * t18 * t15 + 0.12e2 * t40 * t945 - 0.4e1 * t492 * xc * t82 * t1070 - 0.2e1 * t91 * t528 * t20 + 0.8e1 * t324 * t608;
2299: t1113 = t123 * t82 * t124 + 0.8e1 * t421 * t428 - t139 * t417 + 0.4e1 * t40 * t645 + 0.16e2 * t393 * t759 - 0.2e1 * t33 * t179 * t115 - 0.4e1 * t525 * t335 + 0.4e1 * t33 * t28 * t36 - 0.4e1 * t1006 * t714 + 0.6e1 * t206 * t166 - 0.8e1 * t421 * t450;
2300: t1119 = t321 * t46;
2301: t1122 = t157 * t11;
2302: t1123 = t1122 * t2;
2303: t1124 = t184 * t46;
2304: t1128 = t108 * nz;
2305: t1132 = t7 * t7;
2306: t1133 = t1132 * t11;
2307: t1134 = t1133 * t108;
2308: t1135 = t15 * t46;
2309: t1139 = t7 * ZA;
2310: t1140 = t1139 * ZB;
2311: t1141 = t1 * t35;
2312: t1145 = t629 * t2;
2313: t1146 = t1135 * t730;
2314: t1149 = t157 * t1128;
2315: t1150 = t1149 * xc;
2316: t1153 = t46 * xc;
2317: t1154 = t1153 * t127;
2318: t1158 = t184 * t1 * t46;
2319: t1161 = t46 * t46;
2320: t1162 = t35 * t1161;
2321: t1166 = t7 * t1;
2322: t1170 = -0.4e1 * t133 * t1119 + 0.16e2 * t1123 * t1124 * t730 - 0.8e1 * t1122 * t1128 * t196 - 0.64e2 * t1134 * t1135 * t1017 - 0.32e2 * t1140 * t1141 * t1135 + 0.16e2 * t1145 * t1146 - 0.8e1 * t1150 * t650 - 0.16e2 * t1123 * t1154 - 0.4e1 * t133 * t1158 - 0.16e2 * t1140 * t1162 * t15 + 0.8e1 * t1166 * t35 * t312;
2323: t1171 = t1161 * t184;
2324: t1175 = t1122 * nz;
2325: t1176 = t15 * t1161;
2326: t1180 = t1132 * ZA;
2327: t1181 = t1180 * t355;
2328: t1182 = t1176 * t1017;
2329: t1185 = t1161 * xc;
2330: t1189 = t1133 * t1;
2331: t1192 = t108 * t1;
2332: t1193 = t1132 * t1192;
2333: t1195 = t10 * t35;
2334: t1199 = t157 * t15;
2335: t1203 = t1141 * t46;
2336: t1211 = t184 * t108;
2337: t1218 = 0.2e1 * t133 * t1171 * t35 + 0.8e1 * t1175 * t1176 * t997 + 0.64e2 * t1181 * t1182 - 0.8e1 * t1175 * t1185 * t127 - 0.32e2 * t1189 * t1182 - 0.64e2 * t1193 * ZA * t1195 * t228 + 0.8e1 * t1199 * t416 * t1128 + 0.8e1 * t1140 * t1203 - 0.4e1 * t75 * t1158 - 0.8e1 * t1199 * t560 * t1128 - 0.2e1 * t133 * t1211 - 0.8e1 * t1199 * t127 * t11 * t1128;
2338: t1221 = t256 * t1161;
2339: t1224 = t35 * t108;
2340: t1233 = t7 * t256;
2341: t1236 = -t75 * t1211 - t75 * t1221 - t133 * t1221 + t75 * t1224 - t75 * t1171 - t133 * t1171 + t133 * t1224 + t75 * t1162 - t75 * t108 * t256 + t133 * t1162 - t1233 * t59 * t108;
2342: t1240 = t1135 * t1195;
2343: t1252 = t629 * t127;
2344: t1263 = t1171 * ZA;
2345: t1280 = -0.128e3 * t1180 * ZB * t108 * t1240 + 0.32e2 * t1193 * t10 * t112 + 0.4e1 * t133 * t1203 + 0.4e1 * t109 * t256 * ZA * ZB - 0.8e1 * t1252 * nz * t15 * t1185 + 0.8e1 * t1175 * t1171 * t730 - 0.8e1 * t1175 * t1176 * t127 + 0.4e1 * t223 * t1263 - 0.8e1 * t1175 * t1176 * t730 + 0.8e1 * t1166 * ZA * t341 * ZB + 0.64e2 * t1134 * t1240 + 0.8e1 * t1122 * xc * t1128 * t127 * t15;
2346: t1283 = t1199 * t19;
2347: t1287 = t1199 * t127;
2348: t1289 = t59 * nz * t1161;
2349: t1293 = t157 * nz * xc;
2350: t1304 = t1132 * t108;
2351: t1310 = t263 * ZB;
2352: t1316 = t2 * t15;
2353: t1323 = -0.16e2 * t1283 * t1006 * t46 + 0.8e1 * t1287 * t1289 + 0.8e1 * t1293 * t127 * t1161 * t59 + 0.16e2 * t1123 * t1135 * t19 + 0.8e1 * t1293 * t560 * t1176 + 0.64e2 * t1304 * t59 * t1240 + 0.4e1 * t75 * t1203 + 0.4e1 * t1310 * t1263 + 0.4e1 * t223 * t338 * t108 - 0.16e2 * t1252 * t1316 * t1153 - 0.16e2 * t1310 * t221 * t15;
2354: t1330 = t1132 * t15;
2355: t1336 = t1132 * t1;
2356: t1338 = t1162 * t179;
2357: t1370 = 0.8e1 * t1175 * t1176 * t19 + 0.4e1 * t1139 * t318 * t1161 + 0.128e3 * t1330 * t318 * t108 * t46 * t227 - 0.32e2 * t1336 * xc * t1338 + 0.4e1 * t1233 * ZA * t1161 * ZB - 0.8e1 * t1287 * t59 * t1128 * xc + 0.2e1 * t75 * t305 * t108 + 0.8e1 * t1199 * t127 * t59 * t1128 - 0.8e1 * t1283 * t1289 - 0.8e1 * t1293 * t560 * t1171 + 0.4e1 * t133 * t35 * t1158 + 0.8e1 * t157 * t184 * t19 * t11 * t1128 * xc;
2358: t1376 = t7 * t184;
2359: t1380 = t1176 * t1195;
2360: t1393 = t1330 * t35;
2361: t1411 = 0.16e2 * t1145 * t1154 + 0.8e1 * t1149 * t998 + 0.4e1 * t1376 * t35 * t48 + 0.32e2 * t1189 * t1380 + 0.32e2 * t1193 * t11 * t1195 * t15 - 0.64e2 * t1304 * xc * t111 * t1135 - 0.16e2 * t1123 * t1146 + 0.64e2 * t1393 * t28 * t1192 * xc - 0.16e2 * t1123 * t1135 * t127 - 0.8e1 * t1122 * xc * t1128 * t127 - 0.32e2 * t1193 * xc * t112 + 0.16e2 * t1252 * t1316 * t46;
2362: t1450 = 0.2e1 * t1376 * t767 * t1161 + 0.2e1 * t1376 * t111 * t108 + 0.4e1 * t223 * t311 * t108 + 0.4e1 * t109 * t35 * t520 * ZA + 0.16e2 * t1123 * t1135 * t997 - 0.64e2 * t1181 * t1380 + 0.8e1 * t1150 * t903 - 0.32e2 * t1393 * t11 * t1192 * xc - 0.16e2 * t157 * t2 * xc * t560 * t1124 + 0.8e1 * t223 * t184 * t317 * t46 + 0.32e2 * t1336 * t10 * t1338 - 0.4e1 * t75 * t1119;
2363: _PC3B = (t606 + t722 + t1089 + t781 + 0.16e2 * t48 * t51 + t978 + t868 + t507 - t304 * t256 + 0.8e1 * t9 * t22 + t752 + 0.4e1 * t174 * t144 - 0.2e1 * t81 * t469 + 0.6e1 * t139 * t166 + t362 + 0.2e1 * t98 * t211 + t925 + t137 - t290 * t184 + 0.12e2 * t81 * t83 + t842 + 0.8e1 * t74 * t77 + 0.16e2 * t98 * t12 * t162 - 0.4e1 * t33 * t28 * t443 - 0.8e1 * t27 * t70 - 0.2e1 * t33 * t34 * t36 - 0.8e1 * t27 * t30 + 0.2e1 * t58 * t67 - 0.4e1 * t40 * t43 + 0.2e1 * t58 * t63 + t1033 - t290 * t256 + t290 * t35 + t193 + t1113 + t578 + t442 + t474 + t544 + t329 + t679 + t401 + t953 + t811 + t644 + t894 + t289 + t240 + t1055 + t1003) / (t1170 + t1218 + 0.2e1 * t1236 + t1280 + t1323 + t1370 + t1411 + t1450);
2364: /****************************************************************************************/
2365: t1 = nz * nz;
2366: t2 = t1 * xc;
2367: t3 = ZB * ZB;
2368: t5 = t2 * 0.3141592654e1 * t3;
2369: t6 = nx * 0.3141592654e1;
2370: t7 = t6 * xc;
2371: t8 = PetscCosReal(t7);
2372: t9 = nx * nx;
2373: t10 = t8 * t9;
2374: t11 = nz * 0.3141592654e1;
2375: t12 = PetscExpReal(t11);
2376: t13 = t12 * t12;
2377: t16 = PetscExpReal(xc * nz * 0.3141592654e1);
2378: t17 = t16 * t16;
2379: t18 = t17 * t16;
2380: t19 = t17 * t17;
2381: t20 = t19 * t18;
2382: t21 = t13 * t20;
2383: t22 = t10 * t21;
2384: t25 = ZA * ZA;
2385: t26 = t1 * t25;
2386: t27 = xc * 0.3141592654e1;
2387: t28 = t26 * t27;
2388: t29 = t19 * t16;
2389: t30 = t13 * t13;
2390: t31 = t29 * t30;
2391: t35 = t9 * nx;
2392: t36 = t3 * t35;
2393: t37 = PetscSinReal(t6);
2394: t38 = t13 * t12;
2395: t39 = t37 * t38;
2396: t40 = t39 * t19;
2397: t42 = t1 * t1;
2398: t43 = nx * t42;
2399: t44 = xc * xc;
2400: t45 = t25 * t44;
2401: t46 = t43 * t45;
2402: t47 = 0.3141592654e1 * 0.3141592654e1;
2403: t48 = t47 * t37;
2404: t49 = t17 * t38;
2405: t54 = 0.3141592654e1 * t35;
2406: t55 = ZA * nz * t54;
2407: t56 = t37 * ZB;
2408: t57 = t19 * t12;
2409: t61 = t25 * t8;
2410: t62 = t61 * t9;
2411: t63 = nz * t30;
2412: t64 = t63 * t16;
2413: t67 = t1 * nz;
2414: t69 = t47 * ZB;
2415: t70 = t67 * t44 * t69;
2416: t75 = nx * t3;
2417: t76 = t75 * t37;
2418: t77 = t67 * 0.3141592654e1;
2419: t78 = t19 * t19;
2420: t79 = t78 * t12;
2421: t80 = t77 * t79;
2422: t82 = t3 * t38;
2423: t84 = t54 * t37;
2424: t87 = PetscSinReal(t7);
2425: t88 = t29 * t87;
2426: t89 = t47 * t44;
2427: t93 = nx * t25;
2428: t94 = t87 * t42;
2429: t95 = t93 * t94;
2430: t96 = t47 * xc;
2431: t97 = t13 * t29;
2432: t98 = t96 * t97;
2433: t101 = t87 * t67;
2434: t102 = t93 * t101;
2435: t103 = t13 * t18;
2436: t107 = t47 * t35;
2437: t108 = t26 * t107;
2438: t109 = t37 * t44;
2439: t110 = t19 * t17;
2440: t111 = t12 * t110;
2441: t116 = t37 * t19 * t12;
2442: t118 = t37 * xc;
2443: t119 = ZB * t19;
2444: t120 = t119 * t12;
2445: t121 = t118 * t120;
2446: t125 = xc * t3;
2447: t126 = t1 * t47 * t125;
2448: t127 = t35 * t37;
2449: t128 = t38 * t19;
2450: t129 = t127 * t128;
2451: t132 = t26 * 0.3141592654e1;
2452: t133 = t16 * t13;
2453: t134 = t10 * t133;
2454: t137 = 0.3141592654e1 * ZB;
2455: t138 = t2 * t137;
2456: t139 = ZA * t8;
2457: t140 = t9 * t13;
2458: t145 = t30 * t18;
2459: t146 = t10 * t145;
2460: t149 = t3 * t8;
2461: t150 = t149 * t9;
2462: t153 = 0.2e1 * t5 * t22 + 0.2e1 * t28 * t10 * t31 + t36 * t40 - 0.2e1 * t46 * t48 * t49 - 0.2e1 * t55 * t56 * t57 - 0.2e1 * t62 * t64 + 0.16e2 * t70 * t29 * ZA * t10 - t76 * t80 + t82 * nz * t84 + 0.8e1 * t43 * t3 * t88 * t89 + 0.16e2 * t95 * t98 + 0.2e1 * t102 * t27 * t103 - 0.2e1 * t108 * t109 * t111 + t36 * t116 + 0.8e1 * t55 * t121 - 0.4e1 * t126 * t129 - 0.4e1 * t132 * t134 - 0.4e1 * t138 * t139 * t140 * t20 + 0.8e1 * t28 * t146 - 0.2e1 * t150 * t64;
2463: t154 = t42 * nz;
2464: t155 = nx * t154;
2465: t156 = t44 * xc;
2466: t157 = t47 * 0.3141592654e1;
2467: t158 = t156 * t157;
2468: t159 = t155 * t158;
2469: t162 = t56 * ZA * t19 * t12;
2470: t165 = t77 * t49;
2471: t167 = t1 * t3;
2472: t168 = t167 * t89;
2473: t169 = t127 * t49;
2474: t172 = t37 * t67;
2475: t173 = t75 * t172;
2476: t174 = t38 * t110;
2477: t175 = t27 * t174;
2478: t179 = t47 * t25;
2479: t181 = t10 * t97;
2480: t184 = t27 * t31;
2481: t187 = t67 * t47;
2482: t188 = t44 * t3;
2483: t189 = t187 * t188;
2484: t192 = t25 * t35;
2485: t193 = t37 * t17;
2486: t194 = t193 * t12;
2487: t196 = nx * ZA;
2488: t197 = t196 * t172;
2489: t198 = ZB * t38;
2490: t199 = t198 * t19;
2491: t204 = t1 * t12 * t110;
2492: t207 = nx * ZB;
2493: t209 = t1 * ZA;
2494: t215 = t67 * t3;
2495: t216 = t47 * t8;
2496: t217 = t215 * t216;
2497: t218 = t9 * xc;
2498: t222 = nx * t67;
2499: t223 = t222 * t27;
2500: t224 = t3 * t87;
2501: t228 = t167 * t107;
2502: t232 = t26 * t96;
2503: t235 = t207 * t94;
2504: t236 = t47 * ZA;
2505: t243 = xc * t13;
2506: t244 = t243 * t29;
2507: t248 = t25 * nz;
2508: t249 = t248 * 0.3141592654e1;
2509: t253 = ZB * ZA;
2510: t254 = t253 * t8;
2511: t255 = t9 * nz;
2512: t256 = t30 * t16;
2513: t260 = 0.2e1 * t207 * t37 * t209 * t128 + 0.2e1 * t5 * t134 - 0.16e2 * t217 * t218 * t97 - 0.2e1 * t223 * t224 * t31 - 0.2e1 * t228 * t109 * t174 - 0.2e1 * t232 * t169 - 0.16e2 * t235 * t236 * t44 * t30 * t18 - 0.4e1 * t196 * t101 * t137 * t244 + t249 * t169 + 0.8e1 * t168 * t129 + 0.4e1 * t254 * t255 * t256;
2514: t263 = t43 * t179;
2515: t267 = t3 * nz;
2516: t268 = t267 * t54;
2517: t269 = t118 * t57;
2518: t272 = t39 * t1;
2519: t274 = t67 * t25;
2520: t275 = t274 * t158;
2521: t278 = t75 * t87;
2522: t279 = t77 * t103;
2523: t282 = t25 * t38;
2524: t285 = ZA * t38;
2525: t290 = t267 * 0.3141592654e1;
2526: t296 = t77 * t111;
2527: t298 = t196 * t37;
2528: t299 = t1 * ZB;
2529: t303 = t37 * t42;
2530: t304 = t196 * t303;
2531: t308 = t77 * t57;
2532: t310 = t26 * t89;
2533: t313 = t77 * t128;
2534: t316 = t101 * t27;
2535: t319 = t93 * t87;
2536: t320 = t77 * t97;
2537: t323 = t127 * t57;
2538: t326 = t10 * nz;
2539: t329 = t118 * t174;
2540: t332 = -0.8e1 * t263 * t109 * t57 - 0.4e1 * t268 * t269 + t93 * t272 + 0.8e1 * t275 * t129 - 0.4e1 * t278 * t279 + t282 * nz * t84 - 0.2e1 * t285 * nz * t54 * t56 - t290 * t169 - 0.2e1 * t196 * t38 * t172 * t137 + t76 * t296 - 0.2e1 * t298 * t299 * t79 + 0.8e1 * t304 * t96 * t120 + t76 * t308 - 0.2e1 * t310 * t169 - t76 * t313 + 0.2e1 * t75 * t18 * t316 + 0.4e1 * t319 * t320 + t249 * t323 - 0.2e1 * t25 * t18 * t326 + 0.2e1 * t228 * t329;
2541: t335 = t75 * t101;
2542: t336 = t27 * t21;
2543: t342 = t77 * t133;
2544: t347 = t209 * t137;
2545: t350 = t9 * t1;
2546: t351 = t149 * t350;
2547: t355 = t37 * t78 * t12;
2548: t359 = t93 * t303;
2549: t367 = t172 * 0.3141592654e1;
2550: t369 = t96 * t103;
2551: t376 = t209 * t107;
2552: t379 = t10 * t103;
2553: t383 = t207 * t101;
2554: t389 = 0.3141592654e1 * ZA;
2555: t390 = t222 * t389;
2556: t391 = t87 * ZB;
2557: t398 = -0.2e1 * t102 * t336 + t93 * t38 * t367 + 0.16e2 * t95 * t369 - t82 * t127 - 0.8e1 * t197 * t27 * t120 + 0.8e1 * t376 * t121 - 0.8e1 * t189 * t379 - t249 * t129 - 0.4e1 * t383 * t27 * ZA * t16 * t13 - 0.8e1 * t390 * t391 * t21 - 0.2e1 * t197 * t137 * t57;
2558: t402 = t39 * t110;
2559: t404 = t193 * t38;
2560: t406 = t127 * t174;
2561: t408 = t167 * 0.3141592654e1;
2562: t411 = t44 * t157;
2563: t412 = t155 * t411;
2564: t413 = t285 * t19;
2565: t414 = t56 * t413;
2566: t417 = ZA * t30;
2567: t424 = t93 * t37;
2568: t426 = t248 * t54;
2569: t427 = t17 * t12;
2570: t428 = t118 * t427;
2571: t431 = t77 * t21;
2572: t438 = ZA * t13;
2573: t443 = t93 * t172;
2574: t444 = t27 * t427;
2575: t448 = t1 * t78 * t12;
2576: t455 = t274 * t89;
2577: t461 = t118 * t111;
2578: t464 = -t36 * t402 + t36 * t404 - t249 * t406 - 0.4e1 * t408 * t134 + 0.16e2 * t412 * t414 - 0.4e1 * t383 * t27 * t417 * t18 + 0.2e1 * t28 * t22 - t424 * t80 - 0.2e1 * t426 * t428 + 0.4e1 * t278 * t431 + 0.4e1 * t254 * t255 * t103 + t290 * t323 + 0.4e1 * t383 * t27 * t438 * t20 + 0.2e1 * t443 * t444 + t424 * t448 - t36 * t194 - 0.32e2 * t235 * t236 * t243 * t18 + 0.8e1 * t455 * t181 - 0.4e1 * t359 * t96 * t128 - 0.2e1 * t426 * t461;
2579: t469 = nz * t16 * t13;
2580: t474 = t1 * t38;
2581: t475 = t474 * t19;
2582: t480 = t89 * t103;
2583: t483 = t67 * ZA;
2584: t484 = t483 * t411;
2585: t485 = t127 * t120;
2586: t488 = t127 * t111;
2587: t497 = t77 * t427;
2588: t502 = t27 * t97;
2589: t508 = t1 * t19 * t12;
2590: t511 = t155 * t25 * t156;
2591: t512 = t157 * t37;
2592: t513 = t512 * t128;
2593: t527 = t1 * t17;
2594: t528 = t527 * t38;
2595: t530 = -t76 * t497 - 0.4e1 * t254 * t255 * t97 - 0.2e1 * t102 * t502 - 0.4e1 * t108 * t269 - t76 * t508 + 0.8e1 * t511 * t513 + 0.4e1 * t150 * t63 * t18 + 0.4e1 * t383 * t27 * t438 * t18 + 0.4e1 * t132 * t379 + 0.2e1 * t168 * t488 - t76 * t528;
2596: t535 = t44 * t13;
2597: t542 = t527 * t12;
2598: t544 = nz * t13;
2599: t545 = t544 * t20;
2600: t548 = t75 * t303;
2601: t549 = t96 * t111;
2602: t552 = ZA * t35;
2603: t553 = t552 * t37;
2604: t562 = t43 * t96;
2605: t563 = t3 * t37;
2606: t564 = t563 * t128;
2607: t579 = t474 * t110;
2608: t590 = t9 * t30;
2609: t591 = t590 * t18;
2610: t595 = t127 * t427;
2611: t598 = t77 * t174;
2612: t600 = 0.4e1 * t5 * t146 + 0.16e2 * t235 * t236 * t535 * t18 + 0.8e1 * t455 * t146 + t76 * t542 - 0.2e1 * t150 * t545 + 0.2e1 * t548 * t549 - 0.2e1 * t553 * t120 + t290 * t488 - 0.8e1 * t274 * t47 * t44 * t29 * t10 - 0.4e1 * t562 * t564 - 0.2e1 * t132 * xc * t20 * t10 - 0.32e2 * t562 * ZA * t87 * ZB * t13 * t29 - 0.8e1 * t347 * t379 + t76 * t579 - 0.4e1 * t359 * t96 * t57 + 0.4e1 * t408 * t181 - 0.4e1 * t223 * t564 - 0.12e2 * t209 * t27 * ZB * t8 * t591 + 0.2e1 * t310 * t595 + t76 * t598;
2613: t601 = t27 * t49;
2614: t604 = t127 * t79;
2615: t606 = ZB * t29;
2616: t616 = t139 * t140 * t18;
2617: t638 = t10 * t256;
2618: t643 = t118 * t199;
2619: t653 = t544 * t29;
2620: t658 = t3 * t29;
2621: t660 = t350 * t27;
2622: t663 = -0.4e1 * t254 * t255 * t145 + 0.2e1 * t267 * t20 * t8 * t9 - 0.4e1 * t138 * t139 * t9 * t16 * t13 - 0.2e1 * t5 * t638 + 0.2e1 * t126 * t169 + 0.8e1 * t376 * t643 + 0.4e1 * t335 * t27 * t145 + 0.16e2 * t235 * t236 * t535 * t29 + 0.6e1 * t150 * t653 - 0.4e1 * t426 * t269 + 0.4e1 * t658 * t8 * t660;
2623: t670 = t274 * t411;
2624: t673 = t118 * t49;
2625: t694 = t155 * t45;
2626: t713 = nz * t29 * t30;
2627: t717 = t20 * t87;
2628: t723 = t512 * t57;
2629: t728 = -0.2e1 * t443 * t175 - 0.8e1 * t670 * t129 + 0.2e1 * t426 * t673 - 0.16e2 * t207 * t88 * t42 * t47 * ZA * t44 + 0.4e1 * t254 * t255 * t21 + t249 * t595 + 0.8e1 * t25 * t29 * t8 * t660 + 0.2e1 * t268 * t461 + 0.8e1 * t189 * t181 - 0.8e1 * t694 * t513 + 0.2e1 * t198 * t553 - 0.12e2 * t606 * t139 * t660 - 0.2e1 * t359 * t549 + 0.4e1 * t138 * t139 * t590 * t16 + 0.8e1 * t93 * t29 * t94 * t89 - 0.2e1 * t150 * t713 + 0.2e1 * t222 * t3 * t717 * t27 + 0.8e1 * t670 * t323 + 0.8e1 * t694 * t723 - 0.2e1 * t62 * t653;
2630: t734 = t43 * t89;
2631: t735 = t563 * t427;
2632: t740 = t75 * t94;
2633: t744 = ZB * xc;
2634: t750 = t563 * t57;
2635: t754 = t218 * t103;
2636: t771 = t127 * t199;
2637: t776 = t89 * t174;
2638: t791 = -0.4e1 * t207 * t717 * t77 * xc * ZA + 0.4e1 * t443 * t27 * t57 + t192 * t40 - 0.8e1 * t55 * t643 - 0.16e2 * t209 * t89 * t771 - 0.8e1 * t275 * t323 + 0.2e1 * t359 * t776 + 0.16e2 * t304 * t89 * t199 + 0.4e1 * t278 * t320 + 0.2e1 * t207 * t172 * t389 * t79 - 0.8e1 * t390 * t391 * t97;
2639: t794 = t483 * t158;
2640: t801 = t2 * 0.3141592654e1;
2641: t818 = t215 * t411;
2642: t827 = t96 * t174;
2643: t837 = t37 * t12 * t110;
2644: t845 = 0.16e2 * t794 * t485 + 0.8e1 * t159 * t564 - 0.8e1 * t455 * t379 - 0.2e1 * t801 * t3 * t20 * t10 - 0.4e1 * t132 * t22 - 0.8e1 * t734 * t564 - 0.8e1 * t187 * t44 * t658 * t10 - 0.8e1 * t412 * t564 + 0.4e1 * t132 * t181 - 0.8e1 * t818 * t129 + 0.2e1 * t46 * t48 * t427 - 0.4e1 * t75 * t29 * t316 - 0.2e1 * t359 * t827 - t290 * t595 + 0.16e2 * t217 * t754 - t424 * t542 - 0.8e1 * t734 * t750 - t192 * t837 - 0.4e1 * t254 * t255 * t133 + 0.8e1 * t304 * t96 * t199;
2645: t864 = t544 * t18;
2646: t867 = t3 * t18;
2647: t884 = t27 * t256;
2648: t891 = t187 * t744;
2649: t894 = t563 * t49;
2650: t900 = -0.2e1 * t263 * t428 + 0.2e1 * t228 * t428 - 0.6e1 * t223 * t224 * t103 - t192 * t404 + 0.2e1 * t268 * t428 - 0.2e1 * t335 * t884 - t424 * t296 + 0.2e1 * t93 * t20 * t316 - 0.32e2 * t891 * t616 + 0.2e1 * t562 * t894 - 0.2e1 * t801 * t867 * t10;
2651: t904 = t27 * t111;
2652: t907 = t118 * t128;
2653: t915 = t89 * t145;
2654: t947 = t139 * t140 * t29;
2655: t952 = -0.2e1 * t173 * t904 + 0.4e1 * t426 * t907 + 0.12e2 * t253 * t10 * t1 * 0.3141592654e1 * t244 + 0.8e1 * t95 * t915 - t36 * t355 - 0.16e2 * t794 * t771 - 0.8e1 * t511 * t723 + 0.16e2 * t734 * t162 + t36 * t837 + 0.2e1 * t298 * t299 * t57 - 0.2e1 * t28 * t638 - 0.2e1 * t62 * t545 + 0.2e1 * t310 * t406 + 0.12e2 * t138 * t616 + 0.4e1 * t223 * t750 + t424 * t497 + 0.2e1 * t734 * t894 + 0.2e1 * t132 * xc * t18 * t10 - 0.16e2 * t70 * t947 + 0.32e2 * t891 * t947;
2656: t969 = t67 * t157 * t156 * t3;
2657: t974 = t27 * t133;
2658: t1001 = -0.8e1 * t159 * t750 - 0.16e2 * t412 * t162 - t290 * t129 + 0.8e1 * t310 * t323 - 0.4e1 * t319 * t342 + t75 * t272 + t192 * t402 - 0.8e1 * t359 * t89 * t128 - 0.10e2 * t61 * t350 * t502 + 0.8e1 * t818 * t323 - 0.4e1 * t108 * t907;
2659: t1042 = t89 * t97;
2660: t1055 = -0.2e1 * t168 * t595 + 0.16e2 * t484 * t771 + 0.4e1 * t11 * t125 * t129 - 0.2e1 * t173 * t444 + 0.2e1 * ZB * nz * t54 * t37 * ZA * t79 - t424 * t475 + 0.2e1 * t562 * t735 - 0.2e1 * t548 * t776 + t424 * t204 + 0.2e1 * t25 * t20 * t326 + 0.8e1 * t383 * t389 * t133 + t75 * t38 * t367 + 0.2e1 * t62 * t469 + 0.2e1 * t197 * t137 * t128 - 0.2e1 * t102 * t884 - 0.2e1 * t5 * t379 - 0.8e1 * t740 * t1042 - 0.16e2 * t159 * t414 - 0.2e1 * ZB * t35 * t37 * t413 + 0.2e1 * t553 * ZB * t78 * t12;
2661: t1096 = 0.2e1 * t443 * t904 - 0.2e1 * t268 * t329 - 0.2e1 * t443 * t601 + 0.2e1 * t102 * t974 - 0.2e1 * t263 * t673 + t424 * t165 + 0.2e1 * t62 * t713 + t424 * t308 - t424 * t313 + 0.8e1 * t347 * t22 - t424 * t598;
2662: t1103 = t42 * t1 * t157;
2663: t1104 = t1103 * t25;
2664: t1108 = t3 * t19;
2665: t1112 = nz * t47;
2666: t1113 = t9 * t9;
2667: t1118 = t42 * t157;
2668: t1119 = t1118 * t9;
2669: t1120 = t25 * xc;
2670: t1121 = t13 * t110;
2671: t1122 = t1120 * t1121;
2672: t1125 = t47 * t47;
2673: t1126 = t67 * t1125;
2674: t1127 = t1113 * ZA;
2675: t1128 = t1126 * t1127;
2676: t1129 = t19 * t13;
2677: t1130 = t744 * t1129;
2678: t1133 = t154 * t1125;
2679: t1134 = t1133 * t9;
2680: t1135 = t45 * t1129;
2681: t1138 = t154 * t47;
2682: t1139 = t25 * t30;
2683: t1142 = t1126 * t1113;
2684: t1145 = t125 * t1129;
2685: t1148 = t1103 * xc;
2686: t1149 = t3 * t13;
2687: t1150 = t1149 * t17;
2688: t1153 = t25 * t78;
2689: t1156 = -0.8e1 * t1104 * t243 * t17 + 0.4e1 * t187 * t1108 * t9 - 0.2e1 * t1112 * t3 * t1113 * t30 + 0.16e2 * t1119 * t1122 + 0.64e2 * t1128 * t1130 + 0.64e2 * t1134 * t1135 - 0.2e1 * t1138 * t1139 + 0.32e2 * t1142 * t1135 - 0.32e2 * t1142 * t1145 + 0.8e1 * t1148 * t1150 - 0.2e1 * t1138 * t1153;
2690: t1157 = t25 * t13;
2691: t1158 = t1157 * t17;
2692: t1161 = t13 * t17;
2693: t1162 = t1120 * t1161;
2694: t1165 = t3 * t78;
2695: t1170 = t42 * t67 * t1125;
2696: t1172 = t1108 * t13;
2697: t1175 = t1 * t157;
2698: t1176 = t1175 * t1113;
2699: t1182 = t1120 * t1129;
2700: t1189 = t110 * t9 * xc;
2701: t1192 = t1149 * t110;
2702: t1201 = 0.8e1 * t1103 * t1158 - 0.16e2 * t1119 * t1162 - 0.2e1 * t1112 * t1165 * t1113 + 0.32e2 * t1170 * t44 * t1172 - 0.8e1 * t1176 * t1162 + 0.8e1 * t1104 * t243 * t110 - 0.64e2 * t1134 * t1182 - 0.64e2 * t1134 * t1145 + 0.16e2 * t1118 * t3 * t1189 + 0.16e2 * t1119 * t1192 - 0.4e1 * t187 * t1165 * t9 - 0.4e1 * t187 * t1139 * t9;
2703: t1209 = t17 * t30;
2704: t1210 = t125 * t1209;
2705: t1213 = t1138 * ZA;
2706: t1214 = ZB * t30;
2707: t1218 = t1157 * t110;
2708: t1226 = t3 * t30;
2709: t1237 = t1170 * t25;
2710: t1242 = 0.4e1 * t1112 * ZA * t119 * t1113 - 0.16e2 * t1119 * t1150 - 0.8e1 * t1176 * t1210 + 0.4e1 * t1213 * t1214 * t19 - 0.16e2 * t1119 * t1218 - 0.32e2 * t1142 * t1182 - 0.8e1 * t1103 * t1120 * t110 - 0.4e1 * t187 * t1226 * t9 + 0.8e1 * t1103 * t1192 + 0.4e1 * t1112 * ZB * t1113 * t30 * ZA - 0.32e2 * t1237 * xc * t19 * t13;
2711: t1251 = t125 * t1121;
2712: t1260 = t1120 * t1209;
2713: t1263 = t1139 * t19;
2714: t1282 = 0.8e1 * t1103 * t110 * t3 * xc + 0.8e1 * t1104 * xc * t17 * t30 - 0.8e1 * t1176 * t1251 + 0.16e2 * t1119 * t1158 + 0.4e1 * t1112 * t78 * t1127 * ZB + 0.16e2 * t1119 * t1260 + 0.2e1 * t1138 * t1263 - 0.32e2 * t1170 * xc * t1172 - 0.16e2 * t1213 * t119 * t13 + 0.4e1 * t1138 * t1214 * ZA + 0.32e2 * t1237 * t44 * t19 * t13 - 0.16e2 * t1118 * t25 * t1189;
2715: t1287 = t188 * t1129;
2716: t1292 = t25 * t19;
2717: t1296 = t187 * t9;
2718: t1297 = t1226 * t19;
2719: t1311 = t1112 * t1113;
2720: t1317 = -0.8e1 * t1176 * t1150 + 0.32e2 * t1142 * t1287 - 0.8e1 * t1103 * t1150 + 0.2e1 * t1112 * t1292 * t1113 + 0.4e1 * t1296 * t1297 + 0.8e1 * t1176 * t1192 + 0.4e1 * t1296 * t1263 + 0.8e1 * t1176 * t1158 - 0.8e1 * t1175 * t25 * t1113 * xc * t110 + 0.2e1 * t1311 * t1297 + 0.2e1 * t1112 * t1108 * t1113;
2721: t1320 = t253 * t1129;
2722: t1328 = t253 * t30 * t19;
2723: t1333 = t125 * t1161;
2724: t1343 = ZB * t44 * t1129;
2725: t1350 = -0.8e1 * t1176 * t1218 - 0.16e2 * t1311 * t1320 + 0.8e1 * t1176 * t1260 - 0.16e2 * t1119 * t1210 + 0.4e1 * t1311 * t1328 + 0.2e1 * t1311 * t1263 + 0.8e1 * t1176 * t1333 + 0.8e1 * t187 * ZB * t417 * t9 - 0.2e1 * t1138 * t1165 - 0.64e2 * t1128 * t1343 + 0.64e2 * t1134 * t1287 + 0.2e1 * t1138 * t1108;
2726: t1369 = t1133 * t9 * ZA;
2727: t1378 = t187 * ZA;
2728: t1383 = t1170 * ZA;
2729: t1388 = 0.2e1 * t1138 * t1297 - 0.8e1 * t1148 * t1192 + 0.2e1 * t1138 * t1292 - 0.16e2 * t1119 * t1251 + 0.8e1 * t1175 * xc * t110 * t1113 * t3 - 0.2e1 * t1112 * t1153 * t1113 + 0.128e3 * t1369 * t1130 + 0.16e2 * t1119 * t1333 + 0.4e1 * t1138 * t78 * ZA * ZB + 0.8e1 * t1378 * t78 * t9 * ZB - 0.64e2 * t1383 * t1343 + 0.64e2 * t1383 * t1130;
2730: t1420 = 0.4e1 * t1138 * t119 * ZA - 0.128e3 * t1369 * t1343 - 0.4e1 * t187 * t1153 * t9 - 0.2e1 * t1138 * t1226 + 0.8e1 * t1296 * t1328 - 0.2e1 * t1112 * t1139 * t1113 - 0.8e1 * t1148 * t3 * t17 * t30 - 0.32e2 * t1296 * t1320 + 0.8e1 * t1176 * t1122 + 0.4e1 * t187 * t1292 * t9 + 0.8e1 * t1378 * t119 * t9 - 0.8e1 * t1103 * t1218;
2732: _PC4B = (-t424 * t508 + 0.8e1 * t412 * t750 - 0.2e1 * t232 * t595 - 0.4e1 * t126 * t323 + t1096 - t76 * t204 + t728 + 0.2e1 * t548 * t827 + 0.2e1 * t150 * t469 + t398 + 0.8e1 * t189 * t146 + t260 - 0.2e1 * t351 * t184 - 0.2e1 * t268 * t673 - 0.4e1 * t319 * t279 + t464 - 0.2e1 * t108 * t461 + 0.16e2 * t740 * t369 + 0.16e2 * t274 * t216 * t754 - 0.16e2 * t70 * t139 * t591 + 0.2e1 * t55 * t56 * t128 - 0.2e1 * t359 * t89 * t111 + 0.2e1 * t734 * t563 * t111 + 0.6e1 * t223 * t224 * t97 + 0.8e1 * t383 * t389 * t103 + 0.4e1 * t606 * ZA * t326 - 0.2e1 * t93 * t18 * t316 - 0.4e1 * t443 * t27 * t128 + 0.8e1 * t197 * t27 * t199 + 0.8e1 * t108 * t109 * t128 - t249 * t604 + 0.16e2 * t70 * t616 - 0.8e1 * t969 * t323 + t845 - t424 * t579 + 0.16e2 * t159 * t162 + t290 * t406 - 0.6e1 * t150 * t864 + t192 * t116 + 0.2e1 * t867 * t326 - 0.4e1 * t658 * t326 - 0.2e1 * t351 * t502 - t76 * t165 + t900 + 0.8e1 * t168 * t323 + t791 + 0.8e1 * t740 * t915 - 0.4e1 * t562 * t750 - 0.4e1 * t278 * t342 + 0.4e1 * t319 * t431 + 0.2e1 * t173 * t175 + t424 * t528 + 0.8e1 * t969 * t129 - 0.8e1 * t347 * t181 + t332 + t530 - 0.2e1 * t108 * t329 - 0.2e1 * t207 * t38 * t37 * t1 * ZA + t1001 + 0.4e1 * t408 * t379 + t76 * t448 + 0.2e1 * t102 * t184 + 0.2e1 * t426 * t329 + 0.16e2 * t740 * t98 - t282 * t127 - 0.16e2 * t1 * t44 * t69 * t552 * t116 + 0.2e1 * t168 * t169 + 0.2e1 * t28 * t134 - t290 * t604 - 0.16e2 * t484 * t485 - 0.8e1 * t740 * t480 + 0.2e1 * t173 * t601 - 0.2e1 * t335 * t336 + t600 + 0.2e1 * t62 * t864 + t952 + 0.8e1 * t347 * t134 - t192 * t355 + t192 * t194 + 0.2e1 * t228 * t461 + t663 + 0.4e1 * t383 * t27 * t417 * t16 + 0.4e1 * t138 * t20 * ZA * t10 - 0.4e1 * t20 * ZB * ZA * t326 + 0.4e1 * t196 * t88 * t77 * t744 - 0.16e2 * t67 * xc * t179 * t181 - 0.8e1 * t95 * t480 - t249 * t488 - t76 * t475 + t1055 - 0.4e1 * t408 * t22 - 0.10e2 * t28 * t379 + 0.2e1 * t335 * t974 + t153 - 0.8e1 * t95 * t1042 - 0.2e1 * t734 * t735) / (t1156 + t1201 + t1242 + t1282 + t1317 + t1350 + t1388 + t1420);
2733: /****************************************************************************************/
2734: /****************************************************************************************/
2736: if (x > xc) {
2737: _PC1 = _PC1B;
2738: _PC2 = _PC2B;
2739: _PC3 = _PC3B;
2740: _PC4 = _PC4B;
2741: Z = ZB;
2742: } else {
2743: _PC1 = _PC1A;
2744: _PC2 = _PC2A;
2745: _PC3 = _PC3A;
2746: _PC4 = _PC4A;
2747: Z = ZA;
2748: }
2749: /****************************************************************************************/
2750: /****************************************************************************************/
2751: t1 = nz * nz;
2752: t2 = t1 * t1;
2753: t3 = t2 * nz;
2754: t4 = x * t3;
2755: t5 = 0.3141592654e1 * 0.3141592654e1;
2756: t6 = t5 * 0.3141592654e1;
2757: t11 = _PC3 * t6;
2758: t12 = x * nz;
2759: t13 = nx * nx;
2760: t14 = t13 * t13;
2761: t15 = t12 * t14;
2762: t19 = PetscExpReal(t12 * 0.3141592654e1);
2763: t20 = t19 * t19;
2764: t21 = t4 * t20;
2765: t24 = _PC1 * t5;
2766: t25 = Z * t20;
2767: t29 = _PC1 * t6;
2768: t30 = t29 * Z;
2769: t31 = t1 * nz;
2770: t32 = x * t31;
2771: t33 = t32 * t13;
2772: t36 = t11 * x;
2773: t41 = nz * t20;
2774: t45 = t6 * _PC4;
2775: t49 = t20 * t1;
2776: t51 = _PC2 * Z;
2777: t55 = -0.2e1 * t4 * t6 * _PC2 * Z - 0.2e1 * t11 * t15 - 0.2e1 * t11 * t21 + 0.2e1 * t24 * t25 * t14 - t13 + 0.4e1 * t30 * t33 - 0.4e1 * t36 * t31 * t20 * t13 - 0.2e1 * t36 * t41 * t14 - 0.2e1 * t4 * t45 * t20 - t49 - 0.2e1 * t4 * t6 * t51 * t20;
2778: t58 = t32 * t6;
2779: t59 = _PC4 * t20;
2780: t63 = t20 * t13;
2781: t67 = t12 * t6;
2782: t68 = t20 * t14;
2783: t87 = t49 * t13;
2784: t90 = -0.4e1 * t11 * t33 - 0.4e1 * t58 * t59 * t13 - 0.4e1 * t58 * t51 * t63 - 0.2e1 * t67 * t51 * t68 + 0.4e1 * t32 * t45 * t13 - 0.2e1 * t67 * t59 * t14 - 0.2e1 * t30 * t21 + t1 + 0.2e1 * t24 * t25 * t2 + 0.2e1 * t12 * t45 * t14 + 0.4e1 * t24 * Z * t87;
2785: t106 = _PC3 * t5;
2786: t120 = -0.4e1 * t30 * t32 * t63 + t63 + 0.4e1 * t24 * Z * t1 * t13 + 0.2e1 * t29 * Z * x * t3 - 0.4e1 * t58 * t51 * t13 - 0.2e1 * t106 * t2 + t32 * 0.3141592654e1 - 0.2e1 * t106 * t14 - 0.2e1 * t30 * t12 * t68 - 0.2e1 * t67 * t51 * t14 + 0.4e1 * t106 * t87;
2787: t129 = PetscSinReal(nx * 0.3141592654e1 * x);
2788: t155 = 0.2e1 * t30 * t15 + x * 0.3141592654e1 * t41 * t13 - 0.4e1 * t19 * nx * t129 * nz + t32 * 0.3141592654e1 * t20 + 0.2e1 * t106 * t68 + 0.2e1 * t106 * t20 * t2 - 0.4e1 * t106 * t1 * t13 - 0.2e1 * t11 * t4 + 0.2e1 * t4 * t45 + 0.2e1 * t24 * Z * t2 + 0.2e1 * t24 * Z * t14 + t12 * 0.3141592654e1 * t13;
2789: t158 = t5 * Z;
2791: u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14);
2792: /****************************************************************************************/
2793: /****************************************************************************************/
2794: t1 = nz * nz;
2795: t2 = t1 * nz;
2796: t3 = x * t2;
2797: t4 = 0.3141592654e1 * 0.3141592654e1;
2798: t5 = t4 * 0.3141592654e1;
2799: t6 = t3 * t5;
2800: t7 = _PC2 * Z;
2801: t8 = nx * nx;
2802: t12 = t1 * t1;
2803: t13 = t12 * nz;
2804: t14 = x * t13;
2805: t15 = t5 * _PC4;
2806: t16 = x * nz;
2807: t18 = PetscExpReal(t16 * 0.3141592654e1);
2808: t19 = t18 * t18;
2809: t23 = t16 * t5;
2810: t24 = t8 * t8;
2811: t28 = _PC3 * t5;
2812: t29 = t14 * t19;
2813: t32 = _PC1 * t5;
2814: t33 = t32 * Z;
2815: t34 = t16 * t24;
2816: t37 = _PC4 * t19;
2817: t45 = _PC2 * t4;
2818: t53 = t19 * t8;
2819: t58 = _PC4 * t4;
2820: t60 = t1 * t19 * t8;
2821: t63 = t19 * t24;
2822: t67 = t3 * t8;
2823: t73 = nz * t19;
2824: t86 = t28 * x;
2825: t91 = 0.4e1 * t58 * t60 + 0.2e1 * t33 * t16 * t63 + 0.4e1 * t33 * t67 + 0.2e1 * t33 * t29 - x * 0.3141592654e1 * t73 * t8 - 0.2e1 * t53 + 0.2e1 * t32 * Z * x * t13 - 0.2e1 * t58 * t12 - 0.2e1 * t58 * t24 + t3 * 0.3141592654e1 + 0.4e1 * t86 * t2 * t19 * t8;
2826: t94 = Z * t12;
2827: t121 = -0.2e1 * t8 + 0.2e1 * t45 * t94 * t19 + 0.2e1 * t14 * t5 * t7 * t19 + 0.4e1 * t6 * t7 * t53 + 0.2e1 * t23 * t7 * t63 - 0.4e1 * t28 * t67 + 0.2e1 * t45 * t94 + 0.2e1 * t58 * t12 * t19 + t16 * 0.3141592654e1 * t8 + 0.2e1 * t14 * t15 - 0.2e1 * t28 * t14;
2828: t146 = PetscCosReal(nx * 0.3141592654e1 * x);
2829: t156 = -t3 * 0.3141592654e1 * t19 + 0.2e1 * t58 * t63 - 0.4e1 * t58 * t1 * t8 + 0.4e1 * t45 * Z * t1 * t8 - 0.2e1 * t28 * t34 + 0.2e1 * t86 * t73 * t24 + 0.4e1 * t3 * t15 * t8 + 0.4e1 * t45 * Z * t60 + 0.4e1 * t18 * t146 * t8 + 0.2e1 * t45 * Z * t24 + 0.2e1 * t16 * t15 * t24;
2830: t159 = t4 * Z;
2832: u2 = (-0.4e1 * t6 * t7 * t8 + 0.2e1 * t14 * t15 * t19 - 0.2e1 * t23 * t7 * t24 + 0.2e1 * t28 * t29 + 0.2e1 * t33 * t34 + 0.4e1 * t6 * t37 * t8 - 0.2e1 * t14 * t5 * _PC2 * Z + 0.2e1 * t45 * Z * t19 * t24 + 0.2e1 * t23 * t37 * t24 + 0.4e1 * t33 * t3 * t53 + t91 + t121 + t156) / (0.4e1 * t159 * t18 * t12 + 0.8e1 * t159 * t18 * t1 * t8 + 0.4e1 * t159 * t18 * t24);
2833: /****************************************************************************************/
2834: /****************************************************************************************/
2835: t1 = 0.3141592654e1 * 0.3141592654e1;
2836: t2 = t1 * 0.3141592654e1;
2837: t3 = _PC1 * t2;
2838: t4 = t3 * Z;
2839: t5 = nz * nz;
2840: t6 = t5 * t5;
2841: t7 = t6 * nz;
2842: t8 = x * t7;
2843: t9 = x * nz;
2844: t11 = PetscExpReal(t9 * 0.3141592654e1);
2845: t12 = t11 * t11;
2846: t13 = t8 * t12;
2847: t16 = t5 * nz;
2848: t17 = x * t16;
2849: t18 = t17 * t2;
2850: t19 = _PC4 * t12;
2851: t20 = nx * nx;
2852: t24 = t2 * _PC4;
2853: t28 = _PC3 * t2;
2854: t29 = t28 * x;
2855: t30 = t12 * nz;
2856: t31 = t20 * t20;
2857: t40 = _PC2 * Z;
2858: t44 = t9 * t2;
2859: t48 = t12 * t20;
2860: t52 = t17 * t20;
2861: t57 = -0.2e1 * t4 * t13 - 0.4e1 * t18 * t19 * t20 - 0.2e1 * t8 * t24 * t12 - 0.2e1 * t29 * t30 * t31 + 0.2e1 * t8 * t2 * _PC2 * Z - 0.2e1 * t8 * t2 * t40 * t12 - 0.2e1 * t44 * t19 * t31 - 0.4e1 * t18 * t40 * t48 + t20 + 0.4e1 * t28 * t52 + t17 * 0.3141592654e1 * t12;
2862: t58 = t9 * t31;
2863: t61 = _PC3 * t1;
2864: t62 = t12 * t31;
2865: t73 = t5 * t20;
2866: t78 = _PC1 * t1;
2867: t90 = Z * t12;
2868: t94 = 0.2e1 * t28 * t58 + 0.2e1 * t61 * t62 + 0.2e1 * t61 * t12 * t6 - 0.4e1 * t4 * t17 * t48 + 0.2e1 * t28 * t8 + 0.4e1 * t61 * t73 - 0.2e1 * t8 * t24 - 0.2e1 * t78 * Z * t6 - 0.2e1 * t44 * t40 * t62 - 0.2e1 * t78 * Z * t31 - t9 * 0.3141592654e1 * t20 + 0.2e1 * t78 * t90 * t6;
2869: t101 = PetscCosReal(nx * 0.3141592654e1 * x);
2870: t102 = t11 * t101;
2871: t109 = t12 * t5;
2872: t110 = t109 * t20;
2873: t128 = 0.2e1 * t61 * t6 - t17 * 0.3141592654e1 + 0.2e1 * t102 * t5 - 0.4e1 * t17 * t24 * t20 + 0.4e1 * t78 * Z * t110 - 0.2e1 * t9 * t24 * t31 - 0.4e1 * t4 * t52 - 0.2e1 * t4 * t9 * t62 + x * 0.3141592654e1 * t30 * t20 - t5 - 0.4e1 * t78 * Z * t5 * t20;
2874: t156 = 0.2e1 * t78 * t90 * t31 - 0.2e1 * t3 * Z * x * t7 + t48 + 0.4e1 * t61 * t110 + 0.4e1 * t18 * t40 * t20 - 0.2e1 * t102 * t20 + 0.2e1 * t61 * t31 + 0.2e1 * t44 * t40 * t31 - t109 - 0.2e1 * t4 * t58 - 0.2e1 * t28 * t13 - 0.4e1 * t29 * t16 * t12 * t20;
2875: t159 = t1 * t11;
2877: u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31);
2878: /****************************************************************************************/
2879: /****************************************************************************************/
2880: t1 = _PC2 * Z;
2881: t2 = 0.3141592654e1 * 0.3141592654e1;
2882: t3 = t2 * 0.3141592654e1;
2883: t4 = nz * nz;
2884: t5 = t4 * t4;
2885: t6 = t5 * t4;
2886: t8 = t3 * t6 * x;
2887: t11 = x * t4;
2888: t12 = t11 * t3;
2889: t15 = PetscExpReal(x * nz * 0.3141592654e1);
2890: t16 = t15 * t15;
2891: t17 = _PC3 * t16;
2892: t18 = nx * nx;
2893: t19 = t18 * t18;
2894: t23 = t5 * nz;
2895: t24 = t2 * t23;
2896: t28 = t1 * t3;
2897: t29 = t6 * x;
2898: t30 = t29 * t16;
2899: t33 = _PC4 * t3;
2900: t34 = t5 * x;
2901: t35 = t34 * t18;
2902: t41 = PetscSinReal(nx * 0.3141592654e1 * x);
2903: t47 = t11 * t19;
2904: t54 = t3 * _PC3;
2905: t57 = 0.2e1 * t1 * t8 + 0.2e1 * t12 * t17 * t19 + 0.2e1 * t1 * t24 * t16 + 0.2e1 * t28 * t30 - 0.4e1 * t33 * t35 + 0.2e1 * t15 * nx * t41 * t4 + 0.4e1 * t28 * t35 - 0.2e1 * t33 * t47 - 0.2e1 * t1 * t24 - 0.2e1 * t33 * t29 + 0.2e1 * t29 * t54;
2906: t58 = 0.3141592654e1 * t16;
2907: t60 = t2 * _PC4;
2908: t69 = t4 * nz;
2909: t73 = t1 * t2;
2910: t75 = t69 * t16 * t18;
2911: t79 = x * t16;
2912: t83 = nz * t16;
2913: t84 = t83 * t19;
2914: t95 = -t34 * t58 + 0.2e1 * t60 * t23 * t16 + 0.2e1 * t60 * nz * t19 - t11 * 0.3141592654e1 * t18 + 0.4e1 * t60 * t69 * t18 + 0.4e1 * t73 * t75 + 0.4e1 * t33 * t5 * t79 * t18 + 0.2e1 * t73 * t84 + 0.2e1 * t60 * t84 + 0.2e1 * t33 * t4 * t79 * t19 + 0.4e1 * t60 * t75;
2915: t97 = t34 * t3;
2916: t101 = Z * _PC1;
2917: t102 = t16 * t19;
2918: t106 = t16 * t18;
2919: t127 = t2 * t69;
2920: t131 = t2 * nz;
2921: t135 = 0.4e1 * t97 * t17 * t18 + 0.2e1 * t12 * t101 * t102 + 0.4e1 * t28 * t34 * t106 + 0.2e1 * t28 * t11 * t102 - 0.2e1 * t29 * t3 * Z * _PC1 - 0.4e1 * t97 * t101 * t18 - 0.2e1 * t12 * t101 * t19 + 0.2e1 * t60 * t23 - 0.2e1 * t83 * t18 - 0.4e1 * t1 * t127 * t18 - 0.2e1 * t1 * t131 * t19;
2922: t164 = 0.2e1 * t28 * t47 + 0.2e1 * t11 * t54 * t19 + 0.2e1 * t8 * t101 * t16 + 0.2e1 * t33 * t30 - t11 * t58 * t18 + 0.2e1 * t29 * t54 * t16 + 0.4e1 * t34 * t54 * t18 + 0.4e1 * t97 * t101 * t106 - 0.2e1 * t15 * t18 * nx * t41 - t34 * 0.3141592654e1 + 0.2e1 * nz * t18;
2924: u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19);
2926: /****************************************************************************************/
2927: /****************************************************************************************/
2929: u5 = (-2 * Z * nz * PETSC_PI * u2 - u3 * 2 * nz * PETSC_PI) * PetscCosReal(nz * PETSC_PI * z); /* pressure */
2931: u6 = (u3 * 2 * nz * PETSC_PI + 4 * Z * nz * PETSC_PI * u2) * PetscCosReal(nz * PETSC_PI * z); /* zz stress */
2932: sum5 += u5;
2933: sum6 += u6;
2935: u1 *= PetscCosReal(nz * PETSC_PI * z); /* x velocity */
2936: sum1 += u1;
2937: u2 *= PetscSinReal(nz * PETSC_PI * z); /* z velocity */
2938: sum2 += u2;
2939: u3 *= 2 * nz * PETSC_PI * PetscCosReal(nz * PETSC_PI * z); /* xx stress */
2940: sum3 += u3;
2941: u4 *= 2 * nz * PETSC_PI * PetscSinReal(nz * PETSC_PI * z); /* zx stress */
2942: sum4 += u4;
2944: /* Output */
2945: if (mu) *mu = Z;
2946: if (vel) {
2947: vel[0] = sum1;
2948: vel[1] = sum2;
2949: }
2950: if (p) (*p) = sum5;
2951: if (s) {
2952: s[0] = sum3;
2953: s[1] = sum4;
2954: s[2] = sum6;
2955: }
2956: if (gamma) {
2957: /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
2958: gamma[0] = (sum3 + sum5) / (2.0 * Z);
2959: gamma[1] = (sum4) / (2.0 * Z);
2960: gamma[2] = (sum6 + sum5) / (2.0 * Z);
2961: }
2962: PetscFunctionReturn(PETSC_SUCCESS);
2963: }
2965: static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
2966: {
2967: Parameter *s = (Parameter *)ctx;
2969: PetscFunctionBegin;
2970: PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL));
2971: PetscFunctionReturn(PETSC_SUCCESS);
2972: }
2974: static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
2975: {
2976: Parameter *s = (Parameter *)ctx;
2978: PetscFunctionBegin;
2979: PetscCall(SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL));
2980: PetscFunctionReturn(PETSC_SUCCESS);
2981: }
2983: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
2984: {
2985: PetscInt sol;
2987: PetscFunctionBeginUser;
2988: options->solType = SOLKX;
2989: PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");
2990: sol = options->solType;
2991: PetscCall(PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL));
2992: options->solType = (SolutionType)sol;
2993: PetscOptionsEnd();
2994: PetscFunctionReturn(PETSC_SUCCESS);
2995: }
2997: static PetscErrorCode SetUpParameters(AppCtx *user)
2998: {
2999: PetscBag bag;
3000: Parameter *p;
3002: PetscFunctionBeginUser;
3003: /* setup PETSc parameter bag */
3004: PetscCall(PetscBagGetData(user->bag, (void **)&p));
3005: PetscCall(PetscBagSetName(user->bag, "par", "Problem parameters"));
3006: bag = user->bag;
3007: switch (user->solType) {
3008: case SOLKX:
3009: PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3010: PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3011: PetscCall(PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation"));
3012: break;
3013: case SOLCX:
3014: PetscCall(PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation"));
3015: PetscCall(PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation"));
3016: PetscCall(PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc"));
3017: PetscCall(PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc"));
3018: PetscCall(PetscBagRegisterReal(bag, &p->xc, 0.5, "xc", "x-coordinate of the viscosity jump"));
3019: break;
3020: default:
3021: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3022: }
3023: PetscCall(PetscBagSetFromOptions(bag));
3024: PetscCall(PetscBagViewFromOptions(bag, NULL, "-param_view"));
3025: PetscFunctionReturn(PETSC_SUCCESS);
3026: }
3028: /* Make split labels so that we can have corners in multiple labels */
3029: static PetscErrorCode CreateSplitLabels(DM dm)
3030: {
3031: const char *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"};
3032: PetscInt ids[4] = {1, 2, 3, 4};
3033: DMLabel label;
3034: IS is;
3035: PetscInt f;
3037: PetscFunctionBeginUser;
3038: for (f = 0; f < 4; ++f) {
3039: PetscCall(DMCreateLabel(dm, names[f]));
3040: PetscCall(DMGetStratumIS(dm, "marker", ids[f], &is));
3041: if (!is) continue;
3042: PetscCall(DMGetLabel(dm, names[f], &label));
3043: PetscCall(DMLabelInsertIS(label, is, 1));
3044: PetscCall(ISDestroy(&is));
3045: }
3046: PetscFunctionReturn(PETSC_SUCCESS);
3047: }
3049: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
3050: {
3051: DM cdm;
3053: PetscFunctionBeginUser;
3054: PetscCall(DMCreate(comm, dm));
3055: PetscCall(DMSetType(*dm, DMPLEX));
3056: PetscCall(DMSetFromOptions(*dm));
3057: cdm = *dm;
3058: while (cdm) {
3059: PetscCall(CreateSplitLabels(cdm));
3060: PetscCall(DMGetCoarseDM(cdm, &cdm));
3061: }
3062: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
3063: PetscFunctionReturn(PETSC_SUCCESS);
3064: }
3066: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
3067: {
3068: PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3069: PetscDS prob;
3070: DMLabel label;
3071: const PetscInt id = 1;
3072: PetscInt dim, comp;
3073: Parameter *ctx;
3074: void *data;
3076: PetscFunctionBeginUser;
3077: PetscCall(DMGetDimension(dm, &dim));
3078: PetscCall(DMGetDS(dm, &prob));
3079: switch (user->solType) {
3080: case SOLKX:
3081: PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx));
3082: PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3083: PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3084: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3085: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3086: PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx));
3087: PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL));
3088: break;
3089: case SOLCX:
3090: PetscCall(PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx));
3091: PetscCall(PetscDSSetResidual(prob, 1, stokes_mass, f1_zero));
3092: PetscCall(PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3093: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL));
3094: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL));
3095: PetscCall(PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx));
3096: PetscCall(PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL));
3097: break;
3098: default:
3099: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3100: }
3101: PetscCall(PetscBagGetData(user->bag, &data));
3102: switch (dim) {
3103: case 2:
3104: switch (user->solType) {
3105: case SOLKX:
3106: PetscCall(PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data));
3107: PetscCall(PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data));
3108: break;
3109: case SOLCX:
3110: PetscCall(PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data));
3111: PetscCall(PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data));
3112: break;
3113: default:
3114: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3115: }
3116: break;
3117: default:
3118: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %" PetscInt_FMT, dim);
3119: }
3120: /* Setup constants */
3121: {
3122: Parameter *param;
3124: PetscCall(PetscBagGetData(user->bag, (void **)¶m));
3125: switch (user->solType) {
3126: case SOLKX: {
3127: PetscScalar constants[3];
3129: constants[0] = param->m;
3130: constants[1] = param->n;
3131: constants[2] = param->B;
3132: PetscCall(PetscDSSetConstants(prob, 3, constants));
3133: } break;
3134: case SOLCX: {
3135: PetscScalar constants[5];
3137: constants[0] = param->m;
3138: constants[1] = param->n;
3139: constants[2] = param->etaA;
3140: constants[3] = param->etaB;
3141: constants[4] = param->xc;
3142: PetscCall(PetscDSSetConstants(prob, 5, constants));
3143: } break;
3144: default:
3145: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType);
3146: }
3147: }
3148: /* Setup Boundary Conditions */
3149: PetscCall(PetscDSGetExactSolution(prob, 0, &exactFunc, (void **)&ctx));
3150: comp = 1;
3151: PetscCall(DMGetLabel(dm, "markerBottom", &label));
3152: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3153: comp = 0;
3154: PetscCall(DMGetLabel(dm, "markerRight", &label));
3155: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3156: comp = 1;
3157: PetscCall(DMGetLabel(dm, "markerTop", &label));
3158: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3159: comp = 0;
3160: PetscCall(DMGetLabel(dm, "markerLeft", &label));
3161: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", label, 1, &id, 0, 1, &comp, (void (*)(void))exactFunc, NULL, ctx, NULL));
3162: PetscFunctionReturn(PETSC_SUCCESS);
3163: }
3165: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
3166: {
3167: Vec vec;
3168: PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) = {zero, one};
3170: PetscFunctionBeginUser;
3171: PetscCheck(origField == 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Field %" PetscInt_FMT " should be 1 for pressure", origField);
3172: funcs[field] = one;
3173: {
3174: PetscDS ds;
3175: PetscCall(DMGetDS(dm, &ds));
3176: PetscCall(PetscObjectViewFromOptions((PetscObject)ds, NULL, "-ds_view"));
3177: }
3178: PetscCall(DMCreateGlobalVector(dm, &vec));
3179: PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec));
3180: PetscCall(VecNormalize(vec, NULL));
3181: PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace));
3182: PetscCall(VecDestroy(&vec));
3183: /* New style for field null spaces */
3184: {
3185: PetscObject pressure;
3186: MatNullSpace nullspacePres;
3188: PetscCall(DMGetField(dm, field, NULL, &pressure));
3189: PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres));
3190: PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullspacePres));
3191: PetscCall(MatNullSpaceDestroy(&nullspacePres));
3192: }
3193: PetscFunctionReturn(PETSC_SUCCESS);
3194: }
3196: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
3197: {
3198: DM cdm = dm;
3199: PetscFE fe[2];
3200: DMPolytopeType ct;
3201: PetscInt dim, cStart;
3202: PetscBool simplex;
3204: PetscFunctionBeginUser;
3205: PetscCall(DMGetDimension(dm, &dim));
3206: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
3207: PetscCall(DMPlexGetCellType(dm, cStart, &ct));
3208: simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
3209: /* Create discretization of solution fields */
3210: PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]));
3211: PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity"));
3212: PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]));
3213: PetscCall(PetscFECopyQuadrature(fe[0], fe[1]));
3214: PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure"));
3215: /* Set discretization and boundary conditions for each mesh */
3216: PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0]));
3217: PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1]));
3218: PetscCall(DMCreateDS(dm));
3219: PetscCall(SetupProblem(dm, user));
3220: while (cdm) {
3221: PetscCall(DMCopyDisc(dm, cdm));
3222: PetscCall(DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace));
3223: PetscCall(DMGetCoarseDM(cdm, &cdm));
3224: }
3225: PetscCall(PetscFEDestroy(&fe[0]));
3226: PetscCall(PetscFEDestroy(&fe[1]));
3227: {
3228: PetscObject pressure;
3229: MatNullSpace nullSpacePres;
3231: PetscCall(DMGetField(dm, 1, NULL, &pressure));
3232: PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres));
3233: PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullSpacePres));
3234: PetscCall(MatNullSpaceDestroy(&nullSpacePres));
3235: }
3236: PetscFunctionReturn(PETSC_SUCCESS);
3237: }
3239: /* Add a vector in the nullspace to make the continuum integral 0.
3241: If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0
3242: */
3243: static void pressure(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
3244: {
3245: p[0] = u[uOff[1]];
3246: }
3247: static PetscErrorCode CorrectDiscretePressure(DM dm, MatNullSpace nullspace, Vec u, AppCtx *user)
3248: {
3249: PetscDS ds;
3250: const Vec *nullvecs;
3251: PetscScalar pintd, intc[2], intn[2];
3252: MPI_Comm comm;
3254: PetscFunctionBeginUser;
3255: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
3256: PetscCall(DMGetDS(dm, &ds));
3257: PetscCall(PetscDSSetObjective(ds, 1, pressure));
3258: PetscCall(MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs));
3259: PetscCall(VecDot(nullvecs[0], u, &pintd));
3260: PetscCheck(PetscAbsScalar(pintd) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Discrete integral of pressure: %g", (double)PetscRealPart(pintd));
3261: PetscCall(DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, user));
3262: PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3263: PetscCall(VecAXPY(u, -intc[1] / intn[1], nullvecs[0]));
3264: PetscCall(DMPlexComputeIntegralFEM(dm, u, intc, user));
3265: PetscCheck(PetscAbsScalar(intc[1]) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Continuum integral of pressure after correction: %g", (double)PetscRealPart(intc[1]));
3266: PetscFunctionReturn(PETSC_SUCCESS);
3267: }
3269: static PetscErrorCode SNESConvergenceCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *user)
3270: {
3271: PetscFunctionBeginUser;
3272: PetscCall(SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, user));
3273: if (*reason > 0) {
3274: DM dm;
3275: Mat J;
3276: Vec u;
3277: MatNullSpace nullspace;
3279: PetscCall(SNESGetDM(snes, &dm));
3280: PetscCall(SNESGetSolution(snes, &u));
3281: PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
3282: PetscCall(MatGetNullSpace(J, &nullspace));
3283: PetscCheck(nullspace, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "SNES Jacobian has no attached null space");
3284: PetscCall(CorrectDiscretePressure(dm, nullspace, u, (AppCtx *)user));
3285: }
3286: PetscFunctionReturn(PETSC_SUCCESS);
3287: }
3289: int main(int argc, char **argv)
3290: {
3291: SNES snes; /* nonlinear solver */
3292: DM dm; /* problem definition */
3293: Vec u, r; /* solution, residual vectors */
3294: Mat J, M; /* Jacobian and preconditiong matrix */
3295: MatNullSpace nullSpace; /* May be necessary for pressure */
3296: AppCtx user; /* user-defined work context */
3297: PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) = {zero, zero};
3299: PetscFunctionBeginUser;
3300: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
3301: PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
3302: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
3303: PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
3304: PetscCall(SNESSetDM(snes, dm));
3305: PetscCall(DMSetApplicationContext(dm, &user));
3306: /* Setup problem parameters */
3307: PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag));
3308: PetscCall(SetUpParameters(&user));
3309: /* Setup problem */
3310: PetscCall(SetupDiscretization(dm, &user));
3311: PetscCall(DMPlexCreateClosureIndex(dm, NULL));
3313: PetscCall(DMCreateGlobalVector(dm, &u));
3314: PetscCall(VecDuplicate(u, &r));
3316: PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
3317: PetscCall(CreatePressureNullSpace(dm, 1, 1, &nullSpace));
3319: { /* set tolerances */
3320: KSP ksp;
3322: PetscCall(SNESGetKSP(snes, &ksp));
3323: PetscCall(KSPSetTolerances(ksp, 1.e-2 * PETSC_SMALL, PETSC_SMALL, PETSC_CURRENT, PETSC_CURRENT));
3324: }
3326: /* There should be a way to express this using the DM */
3327: PetscCall(SNESSetFromOptions(snes));
3328: PetscCall(SNESSetUp(snes));
3329: PetscCall(SNESGetJacobian(snes, &J, &M, NULL, NULL));
3330: PetscCall(MatSetNullSpace(J, nullSpace));
3331: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "prec_"));
3332: PetscCall(MatSetFromOptions(M));
3333: PetscCall(SNESSetConvergenceTest(snes, SNESConvergenceCorrectPressure, &user, NULL));
3335: PetscCall(DMSNESCheckFromOptions(snes, u));
3336: PetscCall(DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u));
3337: PetscCall(PetscObjectSetName((PetscObject)u, "Solution"));
3338: PetscCall(SNESSolve(snes, NULL, u));
3339: {
3340: PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3341: void *ectxs[2];
3342: PetscDS ds;
3343: Vec e;
3345: PetscCall(DMGetDS(dm, &ds));
3346: PetscCall(PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]));
3347: PetscCall(PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]));
3349: PetscCall(DMGetGlobalVector(dm, &e));
3350: PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", (PetscObject)dm));
3351: PetscCall(DMPlexComputeL2DiffVec(dm, 0.0, exacts, ectxs, u, e));
3352: PetscCall(PetscObjectSetName((PetscObject)e, "Solution Error"));
3353: PetscCall(VecViewFromOptions(e, NULL, "-error_vec_view"));
3354: PetscCall(PetscObjectCompose((PetscObject)e, "__Vec_bc_zero__", NULL));
3355: PetscCall(DMRestoreGlobalVector(dm, &e));
3356: }
3357: PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view"));
3359: PetscCall(MatNullSpaceDestroy(&nullSpace));
3360: PetscCall(VecDestroy(&u));
3361: PetscCall(VecDestroy(&r));
3362: PetscCall(SNESDestroy(&snes));
3363: PetscCall(DMDestroy(&dm));
3364: PetscCall(PetscBagDestroy(&user.bag));
3365: PetscCall(PetscFinalize());
3366: return 0;
3367: }
3369: /*TEST
3371: # 2D serial discretization tests
3372: test:
3373: suffix: p2p1
3374: requires: triangle
3375: args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3376: -snes_error_if_not_converged -dmsnes_check .001 \
3377: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3378: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3379: -fieldsplit_velocity_pc_type lu \
3380: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3381: test:
3382: suffix: p2p1_gmg
3383: TODO: broken (requires subDMs hooks)
3384: requires: triangle
3385: args: -dm_plex_separate_marker -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3386: -snes_error_if_not_converged -dmsnes_check .001 \
3387: -ksp_type fgmres -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3388: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3389: -fieldsplit_velocity_pc_type mg \
3390: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3391: test:
3392: suffix: p2p1_conv
3393: requires: triangle
3394: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.2]
3395: args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3396: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3397: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3398: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3399: -fieldsplit_velocity_pc_type lu \
3400: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3401: test:
3402: suffix: q2q1_conv
3403: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.1]
3404: args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3405: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3406: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3407: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3408: -fieldsplit_velocity_pc_type lu \
3409: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3410: test:
3411: suffix: q1p0_conv
3412: # -dm_refine 2 gives L_2 convergence rate: [2.0, 1.0]
3413: args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
3414: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3415: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3416: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3417: -fieldsplit_velocity_pc_type lu \
3418: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3419: test:
3420: suffix: q2p1_conv
3421: # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.0]
3422: args: -dm_plex_simplex 0 -dm_plex_separate_marker \
3423: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 \
3424: -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3425: -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3426: -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3427: -fieldsplit_velocity_pc_type lu \
3428: -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3430: # FETI-DP tests
3431: testset:
3432: output_file: output/ex69_q2p1fetidp.out
3433: suffix: q2p1fetidp
3434: requires: !single
3435: nsize: 5
3436: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3437: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3438: -snes_error_if_not_converged \
3439: -ksp_error_if_not_converged \
3440: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3441: -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd -fetidp_bddc_pc_bddc_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd
3442: test:
3443: suffix: aij
3444: args: -mat_is_localmat_type aij
3445: test:
3446: requires: viennacl !CUDA_VERSION_11PLUS
3447: TODO: broken
3448: suffix: aijviennacl
3449: args: -mat_is_localmat_type aijviennacl
3450: test:
3451: requires: cuda
3452: suffix: aijcusparse
3453: args: -mat_is_localmat_type aijcusparse
3455: testset:
3456: suffix: q2p1fetidp_deluxe
3457: output_file: output/ex69_q2p1fetidp_deluxe.out
3458: requires: mumps double
3459: nsize: 5
3460: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3461: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3462: -snes_error_if_not_converged \
3463: -ksp_error_if_not_converged \
3464: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3465: -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 \
3466: -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
3467: test:
3468: suffix: aij
3469: args: -mat_is_localmat_type aij
3470: test:
3471: suffix: aij_seqdense
3472: args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3473: test:
3474: requires: viennacl !CUDA_VERSION_11PLUS
3475: suffix: aijviennacl
3476: args: -mat_is_localmat_type aijviennacl
3477: test:
3478: requires: cuda
3479: suffix: aijcusparse
3480: args: -mat_is_localmat_type aijcusparse
3482: testset:
3483: suffix: q2p1fetidp_deluxe_adaptive
3484: output_file: output/ex69_q2p1fetidp_deluxe_adaptive.out
3485: requires: mumps double
3486: nsize: 5
3487: args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3488: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3489: -snes_error_if_not_converged \
3490: -ksp_error_if_not_converged \
3491: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3492: -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 \
3493: -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
3494: test:
3495: suffix: aij
3496: args: -mat_is_localmat_type aij
3497: test:
3498: suffix: aij_seqdense
3499: args: -mat_is_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3500: test:
3501: requires: viennacl !CUDA_VERSION_11PLUS
3502: suffix: aijviennacl
3503: args: -mat_is_localmat_type aijviennacl
3504: test:
3505: requires: cuda
3506: suffix: aijcusparse
3507: args: -mat_is_localmat_type aijcusparse
3509: test:
3510: suffix: p2p1fetidp
3511: requires: triangle
3512: nsize: 4
3513: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3514: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3515: -snes_error_if_not_converged \
3516: -ksp_error_if_not_converged \
3517: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3518: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3519: -fetidp_fieldsplit_lag_ksp_type preonly \
3520: -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
3522: test:
3523: suffix: p2p1fetidp_allp
3524: requires: triangle
3525: nsize: 4
3526: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3527: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3528: -snes_error_if_not_converged \
3529: -ksp_error_if_not_converged \
3530: -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 \
3531: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3532: -fetidp_fieldsplit_lag_ksp_type preonly \
3533: -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
3535: test:
3536: suffix: p2p1fetidp_discharm
3537: requires: triangle
3538: nsize: 4
3539: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3540: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3541: -snes_error_if_not_converged \
3542: -ksp_error_if_not_converged \
3543: -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 \
3544: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3545: -fetidp_fieldsplit_lag_ksp_type preonly \
3546: -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
3548: test:
3549: suffix: p2p1fetidp_lumped
3550: requires: triangle
3551: nsize: 4
3552: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3553: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3554: -snes_error_if_not_converged \
3555: -ksp_error_if_not_converged \
3556: -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 \
3557: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3558: -fetidp_fieldsplit_lag_ksp_type preonly \
3559: -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
3561: test:
3562: suffix: p2p1fetidp_deluxe
3563: requires: triangle mumps
3564: nsize: 4
3565: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3566: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3567: -snes_error_if_not_converged \
3568: -ksp_error_if_not_converged \
3569: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3570: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3571: -fetidp_fieldsplit_lag_ksp_type preonly \
3572: -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 \
3573: -fetidp_bddc_sub_schurs_mat_solver_type mumps -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0
3575: test:
3576: suffix: p2p1fetidp_deluxe_discharm
3577: requires: triangle mumps
3578: nsize: 4
3579: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3580: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3581: -snes_error_if_not_converged \
3582: -ksp_error_if_not_converged \
3583: -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3584: -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3585: -fetidp_fieldsplit_lag_ksp_type preonly \
3586: -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 \
3587: -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
3589: testset:
3590: nsize: 4
3591: requires: triangle
3592: output_file: output/ex69_p2p1fetidp_olof.out
3593: args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3594: -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3595: -snes_error_if_not_converged \
3596: -ksp_error_if_not_converged \
3597: -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 \
3598: -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none -fetidp_fieldsplit_p_ksp_type preonly \
3599: -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 \
3600: -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
3601: test:
3602: suffix: p2p1fetidp_olof_full
3603: args: -fetidp_pc_fieldsplit_schur_fact_type full
3604: test:
3605: suffix: p2p1fetidp_olof_diag
3606: args: -fetidp_pc_fieldsplit_schur_fact_type diag
3607: test:
3608: suffix: p2p1fetidp_olof_additive
3609: args: -fetidp_pc_fieldsplit_type additive
3611: #BDDC with benign trick
3612: testset:
3613: suffix: q2p1bddc
3614: output_file: output/ex69_q2p1fetidp_deluxe.out
3615: nsize: 5
3616: 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
3617: test:
3618: requires: double
3619: suffix: benign_card
3620: # no native support for saddle point factorizations from PETSc
3621: args: -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd
3622: test:
3623: requires: mumps double
3624: suffix: benign_deluxe_mumps
3625: args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3626: test:
3627: requires: mumps double
3628: suffix: benign_deluxe_adaptive_mumps
3629: 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
3630: test:
3631: TODO: broken (INDEFINITE PC)
3632: requires: mkl_pardiso double !complex
3633: suffix: benign_deluxe_mkl
3634: args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3635: test:
3636: TODO: broken (INDEFINITE PC)
3637: requires: mkl_pardiso double !complex
3638: suffix: benign_deluxe_adaptive_mkl
3639: 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
3641: TEST*/