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 {SOLKX, SOLCX, NUM_SOL_TYPES} SolutionType;
23: const char *solTypes[NUM_SOL_TYPES+1] = {"solkx", "solcx", "unknown"};

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

34: typedef struct {
35:   SolutionType solType; /* The type of exact solution */
36:   PetscBag     bag;     /* Holds problem parameters */
37: } AppCtx;

39: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
40: {
41:   PetscInt c;
42:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
43:   return 0;
44: }
45: static PetscErrorCode one(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nc, PetscScalar *u, void *ctx)
46: {
47:   PetscInt c;
48:   for (c = 0; c < Nc; ++c) u[c] = 1.0;
49:   return 0;
50: }

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

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

69:   for (c = 0; c < dim; ++c) {
70:     for (d = 0; d < dim; ++d) {
71:       f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
72:     }
73:     f1[c*dim+c] -= u[dim];
74:   }
75: }

77: static void stokes_momentum_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
78:                                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
79:                                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
80:                                PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
81: {
82:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
83:   PetscInt        c, d;

85:   for (c = 0; c < dim; ++c) {
86:     for (d = 0; d < dim; ++d) {
87:       f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]);
88:     }
89:     f1[c*dim+c] -= u[dim];
90:   }
91: }

93: static void stokes_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux,
94:                         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
95:                         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
96:                         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
97: {
98:   PetscInt d;
99:   f0[0] = 0.0;
100:   for (d = 0; d < dim; ++d) f0[0] -= u_x[d*dim+d];
101: }

103: static void f1_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux,
104:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
105:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
106:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
107: {
108:   PetscInt d;
109:   for (d = 0; d < dim*dim; ++d) f1[d] = 0.0;
110: }

112: /* < q, \nabla\cdot u >, J_{pu} */
113: static void stokes_mass_J(PetscInt dim, PetscInt Nf, PetscInt NfAux,
114:                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
115:                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
116:                           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
117: {
118:   PetscInt d;
119:   for (d = 0; d < dim; ++d) g1[d*dim+d] = -1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
120: }

122: /* -< \nabla\cdot v, p >, J_{up} */
123: static void stokes_momentum_pres_J(PetscInt dim, PetscInt Nf, PetscInt NfAux,
124:                                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
125:                                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
126:                                    PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
127: {
128:   PetscInt d;
129:   for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
130: }

132: /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu}
133:    This just gives \nabla u, give the perdiagonal for the transpose */
134: static void stokes_momentum_vel_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
135:                                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
136:                                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
137:                                      PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
138: {
139:   const PetscReal mu  = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]);
140:   PetscInt        cI, d;

142:   for (cI = 0; cI < dim; ++cI) {
143:     for (d = 0; d < dim; ++d) {
144:       g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/
145:       g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/
146:     }
147:   }
148: }
149: static void stokes_momentum_vel_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
150:                                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
151:                                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
152:                                      PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
153: {
154:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
155:   PetscInt        cI, d;

157:   for (cI = 0; cI < dim; ++cI) {
158:     for (d = 0; d < dim; ++d) {
159:       g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/
160:       g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/
161:     }
162:   }
163: }

165: /* 1/mu < q, I q >, Jp_{pp} */
166: static void stokes_identity_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
167:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
168:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
169:                                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
170: {
171:   const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]);
172:   g0[0] = 1.0/mu;
173: }

175: static void stokes_identity_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux,
176:                                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
177:                                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
178:                                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
179: {
180:   const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]);
181:   g0[0] = 1.0/mu;
182: }

184: /*
185:   SolKxSolution - Exact Stokes solutions for exponentially varying viscosity

187:  Input Parameters:
188: + pos   - The (x,z) coordinate at which to evaluate the solution
189: . n     - The constant defining the x-dependence of the forcing function
190: . m     - The constant defining the z-dependence of the forcing function
191: - B     - The viscosity coefficient

193:   Output Parameters:
194: + vel   - The (x,z)-velocity at (x,z), or NULL
195: . p     - The pressure at (x,z), or NULL
196: . s     - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL
197: . gamma - The strain rate, or NULL
198: - mu    - The viscosity at (x,z), or NULL

200:   Note:
201: $The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary 202:$  conditions everywhere. The forcing term f is given by
203: $204:$    fx = 0
205: $fz = sigma*sin(km*z)*cos(kn*x) 206:$
207: $where 208:$
209: $km = m*Pi (m may be non-integral) 210:$    kn = n*Pi
211: $212:$  meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1.
213: $The viscosity eta is exp(2*B*x). 214: */ 215: static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B, 216: PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu) 217: { 218: PetscReal sigma = 1.0; 219: PetscReal Z; 220: PetscReal u1,u2,u3,u4,u5,u6; 221: PetscReal sum1,sum2,sum3,sum4,sum5,sum6; 222: PetscReal kn,km,x,z; 223: PetscReal _PC1,_PC2,_PC3,_PC4; 224: PetscReal Rp, UU, VV; 225: PetscReal a,b,r,_aa,_bb,AA,BB,Rm; 226: PetscReal num1,num2,num3,num4,den1; 228: PetscReal t1,t2,t3,t4,t5,t6,t7,t8,t9,t10; 229: PetscReal t11,t12,t13,t14,t15,t16,t17,t18,t19,t20; 230: PetscReal t21,t22,t23,t24,t25,t26,t27,t28,t29,t30; 231: PetscReal t31,t32,t33,t34,t35,t36,t37,t38,t39,t40; 232: PetscReal t41,t42,t43,t44,t45,t46,t47,t49,t51,t53; 233: PetscReal t56,t58,t61,t62,t63,t64,t65,t66,t67,t68; 234: PetscReal t69,t70,t71,t72,t73,t74,t75,t76,t77,t78; 235: PetscReal t79,t80,t81,t82,t83,t84,t85,t86,t87,t88; 236: PetscReal t89,t90,t91,t92,t93,t94,t95,t96,t97,t99; 237: PetscReal t100,t101,t103,t104,t105,t106,t107,t108,t109,t110; 238: PetscReal t111,t112,t113,t114,t115,t116,t117,t118,t119,t120; 239: PetscReal t121,t124,t125,t126,t127,t129,t130,t132,t133,t135; 240: PetscReal t136,t138,t140,t141,t142,t143,t152,t160,t162; 242: /*************************************************************************/ 243: /*************************************************************************/ 244: /* rho = -sin(km*z)*cos(kn*x) */ 245: x = pos[0]; 246: z = pos[1]; 247: Z = PetscExpReal( 2.0 * B * x); 248: km = m*PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */ 249: kn = (PetscReal) n*PETSC_PI; 250: /*************************************************************************/ 251: /*************************************************************************/ 252: a = B*B + km*km; 253: b = 2.0*km*B; 254: r = PetscSqrtReal(a*a + b*b); 255: Rp = PetscSqrtReal( (r+a)/2.0); 256: Rm = PetscSqrtReal( (r-a)/2.0); 257: UU = Rp - B; 258: VV = Rp + B; 260: sum1=0.0; 261: sum2=0.0; 262: sum3=0.0; 263: sum4=0.0; 264: sum5=0.0; 265: sum6=0.0; 266: /*sum7=0.0;*/ 268: /*******************************************/ 269: /* calculate the constants */ 270: /*******************************************/ 272: t1 = kn * kn; 273: t4 = km * km; 274: t5 = t4 + t1; 275: t6 = t5 * t5; 276: t8 = pow(km + kn, 0.2e1); 277: t9 = B * B; 278: t16 = pow(km - kn, 0.2e1); 279: _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9); 281: t2 = km * km; 282: t3 = kn * kn; 283: t5 = pow(t2 + t3, 0.2e1); 284: t6 = km - kn; 285: t7 = km + kn; 286: t9 = B * B; 287: t13 = t7 * t7; 288: t19 = t6 * t6; 289: _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9); 291: AA = _aa; 292: BB = _bb; 294: /*******************************************/ 295: /* calculate the velocities etc */ 296: /*******************************************/ 297: t1 = Rm * Rm; 298: t2 = B - Rp; 299: t4 = Rp + B; 300: t6 = UU * x; 301: t9 = PetscExpReal(t6 - 0.4e1 * Rp); 302: t13 = B * B; 303: t16 = Rp * t1; 304: t18 = Rp * Rp; 305: t19 = B * t18; 306: t20 = t13 * Rp; 307: t22 = kn * kn; 308: t24 = B * t1; 309: t32 = 0.8e1 * t13 * BB * kn * Rp; 310: t34 = 0.2e1 * Rm; 311: t35 = PetscCosReal(t34); 312: t37 = Rp * Rm; 313: t49 = PetscSinReal(t34); 314: t63 = PetscExpReal(t6 - 0.2e1 * Rp); 315: t65 = Rm * t2; 316: t67 = 0.2e1 * B * kn; 317: t68 = B * Rm; 318: t69 = t67 + t68 + t37; 319: t73 = 0.3e1 * t13; 320: t75 = 0.2e1 * B * Rp; 321: t76 = t73 - t75 + t1 - t22 - t18; 322: t78 = t65 * t76 * BB; 323: t80 = Rm - kn; 324: t81 = PetscCosReal(t80); 325: t83 = -t67 + t68 + t37; 326: t88 = Rm + kn; 327: t89 = PetscCosReal(t88); 328: t92 = t65 * t76 * AA; 329: t97 = PetscSinReal(t80); 330: t103 = PetscSinReal(t88); 331: t108 = PetscExpReal(t6 - 0.3e1 * Rp - B); 332: t110 = Rm * t4; 333: t111 = t67 + t68 - t37; 334: t115 = t73 + t75 + t1 - t22 - t18; 335: t117 = t110 * t115 * BB; 336: t120 = -t67 + t68 - t37; 337: t127 = t110 * t115 * AA; 338: t140 = PetscExpReal(t6 - Rp - B); 339: 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; 341: t1 = Rp + B; 342: t2 = Rm * t1; 343: t3 = B * B; 344: t4 = 0.3e1 * t3; 345: t5 = B * Rp; 346: t7 = Rm * Rm; 347: t8 = kn * kn; 348: t9 = Rp * Rp; 349: t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9; 350: t12 = t2 * t10 * AA; 351: t14 = B * Rm; 352: t20 = UU * x; 353: t23 = PetscExpReal(t20 - 0.4e1 * Rp); 354: t25 = Rp * Rm; 355: t32 = Rm * kn; 356: t37 = 0.2e1 * Rm; 357: t38 = PetscCosReal(t37); 358: t40 = t3 * B; 359: t44 = B * t9; 360: t45 = t3 * Rp; 361: t53 = t3 * BB; 362: t58 = PetscSinReal(t37); 363: t69 = PetscExpReal(t20 - 0.2e1 * Rp); 364: t72 = 0.3e1 * t40 * Rm; 365: t73 = t9 * Rp; 366: t74 = t73 * Rm; 367: t75 = t7 * Rm; 368: t76 = B * t75; 369: t77 = t14 * t8; 370: t78 = Rp * t75; 371: t80 = 0.8e1 * t45 * kn; 372: t81 = t25 * t8; 373: t83 = 0.5e1 * t45 * Rm; 374: t84 = t44 * Rm; 375: t85 = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84; 376: t88 = 0.2e1 * t9 * t3; 377: t90 = 0.3e1 * t40 * Rp; 378: t91 = t7 * t3; 379: t93 = 0.2e1 * t5 * t32; 380: t94 = t5 * t7; 381: t95 = t5 * t8; 382: t96 = B * t73; 383: t97 = t7 * t9; 384: t100 = 0.2e1 * t3 * Rm * kn; 385: t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100; 386: t105 = Rm - kn; 387: t106 = PetscCosReal(t105); 388: t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77; 389: t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94; 390: t114 = Rm + kn; 391: t115 = PetscCosReal(t114); 392: t121 = PetscSinReal(t105); 393: t127 = PetscSinReal(t114); 394: t132 = PetscExpReal(t20 - 0.3e1 * Rp - B); 395: t135 = 0.2e1 * B * kn; 396: t136 = t135 + t14 - t25; 397: t142 = -t135 + t14 - t25; 398: t152 = t2 * t10 * BB; 399: t162 = PetscExpReal(t20 - Rp - B); 400: 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; 402: t1 = Rm * Rm; 403: t2 = B - Rp; 404: t4 = Rp + B; 405: t6 = VV * x; 406: t7 = PetscExpReal(-t6); 407: t11 = kn * kn; 408: t13 = B * t1; 409: t14 = Rp * Rp; 410: t15 = B * t14; 411: t16 = B * B; 412: t17 = t16 * Rp; 413: t21 = Rp * t1; 414: t30 = 0.8e1 * t16 * BB * kn * Rp; 415: t32 = 0.2e1 * Rm; 416: t33 = PetscCosReal(t32); 417: t35 = Rp * Rm; 418: t47 = PetscSinReal(t32); 419: t61 = PetscExpReal(-t6 - 0.2e1 * Rp); 420: t63 = Rm * t2; 421: t65 = 0.2e1 * B * kn; 422: t66 = B * Rm; 423: t67 = t65 + t66 + t35; 424: t71 = 0.3e1 * t16; 425: t73 = 0.2e1 * B * Rp; 426: t74 = t71 - t73 + t1 - t11 - t14; 427: t76 = t63 * t74 * BB; 428: t78 = Rm - kn; 429: t79 = PetscCosReal(t78); 430: t81 = -t65 + t66 + t35; 431: t86 = Rm + kn; 432: t87 = PetscCosReal(t86); 433: t90 = t63 * t74 * AA; 434: t95 = PetscSinReal(t78); 435: t101 = PetscSinReal(t86); 436: t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B); 437: t108 = Rm * t4; 438: t109 = t65 + t66 - t35; 439: t113 = t71 + t73 + t1 - t11 - t14; 440: t115 = t108 * t113 * BB; 441: t118 = -t65 + t66 - t35; 442: t125 = t108 * t113 * AA; 443: t138 = PetscExpReal(-t6 - Rp - B); 444: 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; 446: t1 = B - Rp; 447: t2 = Rm * t1; 448: t3 = B * B; 449: t4 = 0.3e1 * t3; 450: t5 = B * Rp; 451: t7 = Rm * Rm; 452: t8 = kn * kn; 453: t9 = Rp * Rp; 454: t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9; 455: t12 = t2 * t10 * AA; 456: t14 = B * Rm; 457: t20 = VV * x; 458: t21 = PetscExpReal(-t20); 459: t23 = Rp * Rm; 460: t30 = Rm * kn; 461: t35 = 0.2e1 * Rm; 462: t36 = PetscCosReal(t35); 463: t40 = B * t9; 464: t41 = t3 * Rp; 465: t43 = t3 * B; 466: t51 = t3 * BB; 467: t56 = PetscSinReal(t35); 468: t67 = PetscExpReal(-t20 - 0.2e1 * Rp); 469: t70 = 0.2e1 * B * kn; 470: t71 = t70 + t14 + t23; 471: t76 = Rm - kn; 472: t77 = PetscCosReal(t76); 473: t79 = -t70 + t14 + t23; 474: t84 = Rm + kn; 475: t85 = PetscCosReal(t84); 476: t91 = t2 * t10 * BB; 477: t93 = PetscSinReal(t76); 478: t99 = PetscSinReal(t84); 479: t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B); 480: t107 = 0.3e1 * t43 * Rm; 481: t108 = t9 * Rp; 482: t109 = t108 * Rm; 483: t110 = t7 * Rm; 484: t111 = B * t110; 485: t112 = t14 * t8; 486: t113 = Rp * t110; 487: t115 = 0.8e1 * t41 * kn; 488: t116 = t23 * t8; 489: t118 = 0.5e1 * t41 * Rm; 490: t119 = t40 * Rm; 491: t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119; 492: t124 = 0.2e1 * t3 * Rm * kn; 493: t125 = t5 * t8; 494: t126 = B * t108; 495: t127 = t7 * t9; 496: t129 = 0.2e1 * t9 * t3; 497: t130 = t5 * t7; 498: t132 = 0.3e1 * t43 * Rp; 499: t133 = t7 * t3; 500: t135 = 0.2e1 * t5 * t30; 501: t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135; 502: t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112; 503: t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135; 504: t160 = PetscExpReal(-t20 - Rp - B); 505: 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; 507: t1 = Rm * Rm; 508: t2 = Rp * Rp; 509: t3 = t1 * t2; 510: t4 = B * B; 511: t5 = t1 * t4; 512: t9 = PetscExpReal(-0.4e1 * Rp); 513: t15 = PetscCosReal(0.2e1 * Rm); 514: t22 = PetscExpReal(-0.2e1 * Rp); 515: 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; 517: _PC1=num1/den1; _PC2=num2/den1; _PC3=num3/den1; _PC4=num4/den1; 519: t1 = Rm * x; 520: t2 = PetscCosReal(t1); 521: t4 = PetscSinReal(t1); 522: t10 = PetscExpReal(-0.2e1 * x * B); 523: t12 = kn * x; 524: t13 = PetscCosReal(t12); 525: t16 = PetscSinReal(t12); 526: u1 = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16); 528: t2 = Rm * x; 529: t3 = PetscCosReal(t2); 530: t6 = PetscSinReal(t2); 531: t22 = PetscExpReal(-0.2e1 * x * B); 532: t23 = B * t22; 533: t24 = kn * x; 534: t25 = PetscCosReal(t24); 535: t29 = PetscSinReal(t24); 536: 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; 538: t3 = PetscExpReal(0.2e1 * x * B); 539: t4 = t3 * B; 540: t8 = km * km; 541: t9 = t3 * t8; 542: t11 = 0.3e1 * t9 * Rm; 543: t12 = Rm * Rm; 544: t14 = t3 * t12 * Rm; 545: t15 = UU * UU; 546: t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm; 547: t20 = Rm * x; 548: t21 = PetscSinReal(t20); 549: t27 = 0.2e1 * B * t9; 550: t33 = 0.2e1 * t4 * t12; 551: t36 = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU; 552: t37 = PetscCosReal(t20); 553: t49 = VV * VV; 554: t53 = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14; 555: t64 = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12; 556: t76 = B * t8; 557: t80 = kn * kn; 558: t83 = B * B; 559: t87 = t80 * kn; 560: t90 = kn * x; 561: t91 = PetscSinReal(t90); 562: t106 = PetscCosReal(t90); 563: 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; 565: t3 = PetscExpReal(0.2e1 * x * B); 566: t4 = km * km; 567: t5 = t3 * t4; 568: t6 = Rm * x; 569: t7 = PetscCosReal(t6); 570: t8 = _PC1 * t7; 571: t10 = PetscSinReal(t6); 572: t11 = _PC2 * t10; 573: t13 = _PC3 * t7; 574: t15 = _PC4 * t10; 575: t18 = kn * x; 576: t19 = PetscCosReal(t18); 577: t22 = PetscSinReal(t18); 578: t24 = UU * UU; 579: t25 = t3 * t24; 580: t28 = t3 * UU; 581: t38 = Rm * Rm; 582: t39 = t7 * t38; 583: t42 = t10 * t38; 584: 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; 585: t45 = VV * VV; 586: t46 = t3 * t45; 587: t49 = t3 * VV; 588: t62 = B * B; 589: t78 = kn * kn; 590: 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; 591: u4 = t44 + t82; 593: t3 = PetscExpReal(0.2e1 * x * B); 594: t4 = t3 * B; 595: t8 = km * km; 596: t9 = t3 * t8; 597: t10 = t9 * Rm; 598: t11 = Rm * Rm; 599: t13 = t3 * t11 * Rm; 600: t14 = UU * UU; 601: t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm; 602: t19 = Rm * x; 603: t20 = PetscSinReal(t19); 604: t26 = 0.2e1 * B * t9; 605: t31 = 0.2e1 * t4 * t11; 606: t34 = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU; 607: t35 = PetscCosReal(t19); 608: t47 = VV * VV; 609: t51 = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13; 610: t61 = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11; 611: t72 = B * t8; 612: t76 = kn * kn; 613: t79 = B * B; 614: t83 = t76 * kn; 615: t86 = kn * x; 616: t87 = PetscSinReal(t86); 617: t101 = PetscCosReal(t86); 618: 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; 620: t3 = PetscExpReal(0.2e1 * x * B); 621: t4 = UU * UU; 622: t8 = km * km; 623: t9 = t3 * t8; 624: t10 = t9 * Rm; 625: t11 = Rm * Rm; 626: t13 = t3 * t11 * Rm; 627: t14 = t3 * B; 628: t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm; 629: t19 = Rm * x; 630: t20 = PetscSinReal(t19); 631: t28 = 0.2e1 * B * t9; 632: t33 = 0.2e1 * t14 * t11; 633: t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33; 634: t35 = PetscCosReal(t19); 635: t47 = VV * VV; 636: t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm; 637: t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28; 638: t71 = kn * kn; 639: t74 = B * B; 640: t80 = t71 * kn; 641: t83 = kn * x; 642: t84 = PetscSinReal(t83); 643: t96 = PetscCosReal(t83); 644: 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; 646: /*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)));*/ 648: /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */ 650: sum5 += u5*PetscCosReal(km*z); /* pressure */ 651: sum6 += u6*PetscCosReal(km*z); /* zz total stress */ 653: u1 *= PetscCosReal(km*z); /* x velocity */ 654: sum1 += u1; 655: u2 *= PetscSinReal(km*z); /* z velocity */ 656: sum2 += u2; 658: u3 *= PetscCosReal(km*z); /* xx total stress */ 659: sum3 += u3; 660: u4 *= PetscSinReal(km*z); /* zx stress */ 661: sum4 += u4; 663: /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */ 664: /* sum7 += rho; */ 666: /* Output */ 667: if (mu) { 668: *mu = Z; 669: } 670: if (vel) { 671: vel[0] = sum1; 672: vel[1] = sum2; 673: } 674: if (p) { 675: (*p) = sum5; 676: } 677: if (s) { 678: s[0] = sum3; 679: s[1] = sum4; 680: s[2] = sum6; 681: } 682: if (gamma) { 683: /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */ 684: gamma[0] = (sum3+sum5)/(2.0*Z); 685: gamma[1] = (sum4)/(2.0*Z); 686: gamma[2] = (sum6+sum5)/(2.0*Z); 687: } 688: return 0; 689: } 691: static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx) 692: { 693: Parameter *s = (Parameter *) ctx; 695: SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL); 696: return 0; 697: } 699: static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx) 700: { 701: Parameter *s = (Parameter *) ctx; 703: SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL); 704: return 0; 705: } 707: /* 708: SolCxSolution - Exact Stokes solutions for discontinuous viscosity 710: Input Parameters: 711: + pos - The (x,z) coordinate at which to evaluate the solution 712: . n - The constant defining the x-dependence of the forcing function 713: . m - The constant defining the z-dependence of the forcing function 714: . xc - The x coordinate at which the viscosity is discontinuous 715: . etaA - The viscosity coefficient for x < xc 716: - etaB - The viscosity coefficient for x > xc 718: Output Parameters: 719: + vel - The (x,z)-velocity at (x,z), or NULL 720: . p - The pressure at (x,z), or NULL 721: . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL 722: . gamma - The strain rate, or NULL 723: - mu - The viscosity at (x,z), or NULL 725: Note: 726:$  The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary
727: $conditions everywhere. The forcing term f is given by 728:$
729: $fx = 0 730:$    fz = sigma*sin(km*z)*cos(kn*x)
731: $732:$  where
733: $734:$    km = m*Pi (m may be non-integral)
735: $kn = n*Pi 736:$
737: $meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1. 738:$  The viscosity eta jumps from etaA to etaB at x = xc.
739: */
740: static PetscErrorCode SolCxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal xc, PetscReal etaA, PetscReal etaB,
741:                                     PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu)
742: {
743:   PetscReal _PC1A,_PC2A,_PC3A,_PC4A,_PC1B,_PC2B,_PC3B,_PC4B,_PC1,_PC2,_PC3,_PC4;
744:   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;
745:   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;
746:   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;
747:   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;
748:   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;
749:   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;
750:   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;
751:   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;
752:   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;
753:   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;
754:   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;
755:   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;
756:   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;
757:   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;
758:   PetscReal t561,t562,t563,t564,t567,t568,t571,t573,t575,t576,t578,t579,t583,t590,t591,t594,t595,t596,t597,t598,t600;
759:   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;
760:   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;
761:   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;
762:   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;
763:   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;
764:   PetscReal t801,t806,t807,t808,t809,t811,t812,t817,t818,t819,t821,t822,t824,t827,t828,t830,t834,t835,t837,t840;
765:   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;
766:   PetscReal t884,t888,t891,t894,t900,t901,t903,t904,t907,t908,t909,t911,t914,t915,t916,t919,t920;
767:   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;
768:   PetscReal t961,t964,t965,t966,t967,t968,t969,t971,t972,t974,t977,t978,t981,t983,t987,t988,t992,t993,t994,t997,t998;
769:   PetscReal t1001,t1003,t1005,t1006,t1009,t1010,t1012,t1013,t1015,t1016,t1017,t1018,t1020,t1021,t1029,t1031,t1032,t1033,t1040;
770:   PetscReal t1041,t1042,t1044,t1047,t1050,t1054,t1055,t1057,t1058,t1063,t1068,t1069,t1070,t1079,t1080;
771:   PetscReal t1088,t1089,t1091,t1092,t1094,t1096,t1101,t1102,t1103,t1104,t1105,t1108,t1112,t1113,t1118,t1119,t1120;
772:   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;
773:   PetscReal t1161,t1162,t1165,t1166,t1170,t1171,t1172,t1173,t1175,t1176,t1178,t1180,t1181,t1182,t1185,t1189,t1192,t1193,t1195,t1196,t1199;
774:   PetscReal t1201,t1203,t1209,t1210,t1211,t1213,t1214,t1218,t1221,t1224,t1225,t1226,t1228,t1233,t1234,t1235,t1236,t1237,t1240;
775:   PetscReal t1241,t1242,t1243,t1244,t1245,t1248,t1251,t1252,t1257,t1258,t1259,t1260,t1263,t1268,t1269,t1272,t1280;
776:   PetscReal t1282,t1283,t1284,t1285,t1287,t1288,t1289,t1292,t1293,t1296,t1297,t1300,t1304,t1307,t1310,t1311,t1312,t1316,t1317,t1320;
777:   PetscReal t1321,t1323,t1328,t1330,t1331,t1332,t1333,t1336,t1338,t1343,t1344,t1346,t1349,t1350,t1354;
778:   PetscReal t1366,t1369,t1370,t1371,t1376,t1378,t1380,t1383,t1386,t1387,t1388,t1391,t1393,t1399;
779:   PetscReal t1411,t1412,t1420,t1427;
780:   PetscReal t1450,t1456,t1468,t1472,t1474,t1478;
781:   PetscReal t1504,t1511;
782:   PetscReal t1545;
783:   PetscReal t1564,t1583;

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

790:   /* Note that there is no Fourier sum here. */
791:   /****************************************************************************************/
792:   _PC1A = 0;
793:   /****************************************************************************************/
794:   t1 = nx * 0.3141592654e1;
795:   t2 = PetscSinReal(t1);
796:   t3 = nx * t2;
797:   t4 = nz * nz;
798:   t5 = t4 * t4;
799:   t6 = 0.3141592654e1 * 0.3141592654e1;
800:   t8 = t3 * t5 * t6;
801:   t9 = ZA * xc;
802:   t12 = PetscExpReal(xc * nz * 0.3141592654e1);
803:   t13 = t12 * t12;
804:   t15 = nz * 0.3141592654e1;
805:   t16 = PetscExpReal(t15);
806:   t17 = t16 * t16;
807:   t18 = t17 * t16;
808:   t19 = ZB * t13 * t18;
809:   t20 = t9 * t19;
810:   t23 = ZA * ZA;
811:   t24 = nx * nx;
812:   t25 = t24 * nx;
813:   t26 = t23 * t25;
814:   t28 = t13 * t13;
815:   t29 = t28 * t13;
816:   t33 = nx * ZB;
817:   t34 = t1 * xc;
818:   t35 = PetscSinReal(t34);
819:   t36 = t4 * nz;
820:   t37 = t35 * t36;
821:   t38 = t33 * t37;
822:   t39 = 0.3141592654e1 * ZA;
823:   t40 = t13 * t12;
824:   t41 = t17 * t40;
825:   t45 = ZB * ZB;
826:   t46 = t45 * t24;
827:   t47 = t46 * t4;
828:   t48 = 0.3141592654e1 * xc;
829:   t49 = t13 * t17;
830:   t53 = xc * xc;
831:   t54 = t36 * t53;
832:   t56 = t54 * t6 * t45;
833:   t57 = PetscCosReal(t34);
834:   t58 = t57 * t24;
835:   t59 = t28 * t12;
836:   t60 = t17 * t59;
837:   t61 = t58 * t60;
838:   t64 = t25 * t2;
839:   t65 = t64 * t15;
840:   t72 = nx * t23;
841:   t74 = t72 * t2 * t5;
842:   t75 = t6 * t53;
843:   t76 = t16 * t29;
844:   t80 = t23 * nz;
845:   t81 = t80 * 0.3141592654e1;
846:   t82 = t18 * t28;
847:   t86 = nx * t5;
848:   t87 = t23 * t6;
849:   t89 = xc * t2;
850:   t90 = t13 * t18;
851:   t91 = t89 * t90;
852:   t94 = t28 * t28;
853:   t96 = t24 * nz;
854:   t98 = t4 * t45;
855:   t99 = t98 * 0.3141592654e1;
856:   t100 = t58 * t41;
857:   t104 = 0.3141592654e1 * t25;
858:   t105 = ZA * nz * t104;
859:   t106 = t2 * ZB;
860:   t110 = t17 * t17;
861:   t111 = ZA * t110;
862:   t116 = nz * t28;
863:   t122 = t64 * t4 * t6;
864:   t126 = t23 * t29 * t4;
865:   t128 = t24 * xc;
866:   t132 = t36 * t23;
867:   t133 = t6 * t57;
868:   t135 = t128 * t41;
869:   t138 = t6 * xc;
870:   t142 = t72 * t2;
871:   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;
872:   t149 = ZA * t25 * t2;
873:   t150 = ZB * t28;
874:   t154 = t35 * t5;
875:   t155 = t72 * t154;
876:   t156 = t75 * t41;
877:   t159 = nx * ZA;
878:   t160 = t2 * t36;
879:   t161 = t159 * t160;
880:   t162 = 0.3141592654e1 * ZB;
881:   t163 = t28 * t16;
882:   t167 = t23 * t57;
883:   t168 = t167 * t24;
884:   t169 = nz * t110;
885:   t170 = t169 * t40;
886:   t173 = ZA * ZB;
887:   t174 = t173 * t90;
888:   t177 = t36 * 0.3141592654e1;
889:   t181 = t80 * t104;
890:   t184 = nz * t17;
891:   t188 = t17 * t29;
892:   t190 = t4 * 0.3141592654e1;
893:   t191 = t190 * t24;
894:   t206 = t138 * t60;
895:   t209 = t23 * t4;
896:   t211 = t209 * t6 * t25;
897:   t212 = t89 * t76;
898:   t216 = ZB * t16 * t29;
899:   t217 = t9 * t216;
900:   t220 = ZB * t110;
901:   t221 = ZA * t24;
902:   t222 = t221 * nz;
903:   t225 = t132 * t75;
904:   t232 = t45 * t28;
905:   t233 = t110 * t24;
906:   t234 = t233 * nz;
907:   t236 = t209 * 0.3141592654e1;
908:   t237 = t17 * xc;
909:   t239 = t237 * t13 * t24;
910:   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;
911:   t244 = nx * t45;
912:   t245 = t244 * t37;
913:   t246 = t110 * t40;
914:   t251 = t237 * t59;
915:   t256 = t64 * t90;
916:   t260 = t36 * t45 * t133;
917:   t263 = t45 * t57;
918:   t264 = t263 * t24;
919:   t265 = t169 * t12;
920:   t269 = t6 * t36;
921:   t270 = t17 * t24;
922:   t274 = t110 * t13;
923:   t276 = t190 * t128;
924:   t279 = nx * t36;
925:   t281 = t28 * t40;
926:   t282 = t281 * t35;
927:   t286 = t138 * t41;
928:   t289 = t75 * t60;
929:   t296 = t190 * t173;
930:   t305 = t86 * t45 * t35;
931:   t312 = t33 * t154;
932:   t313 = t6 * ZA;
933:   t324 = t232 * t270;
934:   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;
935:   t328 = t3 * t4;
936:   t331 = t72 * t37;
937:   t332 = t48 * t60;
938:   t335 = nz * t94;
939:   t345 = t72 * t35;
940:   t349 = t173 * t57;
941:   t355 = t53 * t17;
942:   t364 = t54 * t6 * ZB;
943:   t365 = t28 * t17;
944:   t369 = xc * ZB;
945:   t370 = t269 * t369;
946:   t371 = ZA * t57;
947:   t373 = t371 * t270 * t40;
948:   t385 = nx * t35;
949:   t396 = t4 * xc;
950:   t397 = t396 * t162;
951:   t415 = t37 * t48;
952:   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;
953:   t427 = t371 * t270 * t59;
954:   t439 = t209 * t48;
955:   t440 = t110 * t12;
956:   t441 = t58 * t440;
957:   t447 = t36 * xc;
958:   t455 = t48 * t440;
959:   t471 = ZB * t17;
960:   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;
961:   t499 = ZA * t53 * t19;
962:   t505 = t396 * 0.3141592654e1;
963:   t518 = t173 * t53 * t16 * t29;
964:   t533 = t23 * t28;
965:   t535 = t188 * t45;
966:   t538 = t24 * t4;
967:   t545 = t3 * t177;
968:   t546 = t173 * t76;
969:   t555 = t45 * t110;
970:   t557 = t72 * t160;
971:   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;
972:   t567 = t396 * 0.3141592654e1 * t45;
973:   t568 = t58 * t246;
974:   t597 = t58 * nz;
975:   t615 = t13 * t45;
976:   t616 = t615 * t233;
977:   t619 = t94 * t45;
978:   t621 = t45 * t59;
979:   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;
980:   t626 = t49 * t45;
981:   t660 = t29 * t45;
982:   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;
983:   t690 = t6 * 0.3141592654e1;
984:   t691 = ZA * t690;
985:   t693 = t24 * t24;
986:   t694 = t693 * xc;
987:   t695 = t188 * t694;
988:   t698 = t23 * ZA;
989:   t699 = t698 * t690;
990:   t700 = t699 * t5;
991:   t704 = t5 * t4;
992:   t705 = t691 * t704;
993:   t709 = t691 * t5;
994:   t713 = t5 * nz;
995:   t714 = t713 * ZB;
996:   t718 = t698 * t6;
997:   t719 = t713 * t28;
998:   t722 = t699 * t704;
999:   t726 = t713 * t94;
1000:   t733 = t713 * t45;
1001:   t736 = t87 * t36;
1002:   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;
1003:   t746 = t313 * t36;
1004:   t752 = t6 * t6;
1005:   t753 = t23 * t752;
1006:   t759 = t698 * t752;
1007:   t760 = t759 * t36;
1008:   t761 = t17 * t693;
1009:   t762 = xc * t28;
1010:   t763 = t761 * t762;
1011:   t766 = t87 * t713;
1012:   t773 = t699 * t4;
1013:   t774 = t110 * t693;
1014:   t775 = xc * t13;
1015:   t785 = t704 * t17;
1016:   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;
1017:   t791 = t691 * t4;
1018:   t792 = t45 * t693;
1019:   t793 = t49 * t792;
1020:   t796 = t759 * t713;
1021:   t797 = t53 * t28;
1022:   t798 = t270 * t797;
1023:   t801 = t87 * nz;
1024:   t818 = t5 * t36;
1025:   t819 = t753 * t818;
1026:   t827 = t753 * t36 * ZB;
1027:   t830 = xc * t45;
1028:   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;
1029:   t842 = xc * t29;
1030:   t843 = t270 * t842;
1031:   t849 = t759 * t818;
1032:   t853 = t691 * t396;
1033:   t857 = t691 * t5 * t45;
1034:   t869 = t313 * nz;
1035:   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;
1036:   t877 = ZA * t752;
1037:   t878 = t877 * t818;
1038:   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;
1039:   t916 = t110 * t28;
1040:   t945 = t28 * t693 * t45 * t17;
1041:   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;
1042:   t974 = t761 * t797;
1043:   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;
1044:   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;

1046:   _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);
1047:   /****************************************************************************************/
1048:   t1 = nz * nz;
1049:   t2 = t1 * nz;
1050:   t3 = t2 * 0.3141592654e1;
1051:   t4 = t3 * xc;
1052:   t5 = ZB * ZB;
1053:   t7 = PetscExpReal(nz * 0.3141592654e1);
1054:   t8 = t7 * t7;
1055:   t9 = t5 * t8;
1056:   t12 = PetscExpReal(xc * nz * 0.3141592654e1);
1057:   t13 = t12 * t12;
1058:   t14 = t13 * t13;
1059:   t15 = t14 * t13;
1060:   t19 = nx * nx;
1061:   t21 = nx * 0.3141592654e1;
1062:   t22 = PetscSinReal(t21);
1063:   t23 = t19 * nx * t22;
1064:   t24 = t23 * 0.3141592654e1;
1065:   t25 = ZA * ZB;
1066:   t26 = t7 * t15;
1067:   t27 = t25 * t26;
1068:   t30 = t21 * xc;
1069:   t31 = PetscSinReal(t30);
1070:   t32 = t31 * nx;
1071:   t33 = t32 * nz;
1072:   t34 = ZA * ZA;
1073:   t35 = t8 * t8;
1074:   t36 = t34 * t35;
1075:   t40 = t2 * t34;
1076:   t41 = 0.3141592654e1 * t8;
1077:   t42 = t41 * t15;
1078:   t45 = t1 * t5;
1079:   t46 = t14 * t14;
1080:   t49 = t19 * t5;
1081:   t51 = t19 * t46;
1082:   t53 = t19 * t34;
1083:   t55 = t8 * t7;
1084:   t56 = t13 * t55;
1085:   t57 = t25 * t56;
1086:   t60 = t2 * nx;
1087:   t61 = 0.3141592654e1 * 0.3141592654e1;
1088:   t63 = t60 * t31 * t61;
1089:   t64 = xc * xc;
1090:   t65 = ZA * t64;
1091:   t66 = ZB * t8;
1092:   t67 = t14 * t12;
1093:   t68 = t66 * t67;
1094:   t69 = t65 * t68;
1095:   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;
1096:   t73 = t1 * nx;
1097:   t75 = t73 * t31 * 0.3141592654e1;
1098:   t76 = t8 * t67;
1099:   t77 = t25 * t76;
1100:   t80 = t1 * t1;
1101:   t81 = t80 * t34;
1102:   t83 = t61 * t14;
1103:   t87 = t1 * t19;
1104:   t88 = PetscCosReal(t30);
1105:   t90 = t87 * t88 * t61;
1106:   t91 = t5 * t64;
1107:   t92 = t13 * t12;
1108:   t93 = t8 * t92;
1109:   t94 = t91 * t93;
1110:   t100 = ZB * t64 * ZA * t8 * t92;
1111:   t103 = nz * t19;
1112:   t105 = t103 * t88 * 0.3141592654e1;
1113:   t106 = ZA * xc;
1114:   t107 = ZB * t35;
1115:   t109 = t106 * t107 * t12;
1116:   t112 = t34 * xc;
1117:   t113 = t112 * t93;
1118:   t116 = t35 * t14;
1119:   t118 = t1 * ZA;
1120:   t119 = ZB * t14;
1121:   t122 = t1 * t46;
1122:   t125 = t19 * ZB;
1123:   t126 = t35 * ZA;
1124:   t127 = t125 * t126;
1125:   t129 = t1 * ZB;
1126:   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;
1127:   t134 = t1 * t34;
1128:   t136 = t34 * t64;
1129:   t137 = t136 * t76;
1130:   t141 = t91 * t76;
1131:   t145 = t103 * t34;
1132:   t146 = 0.3141592654e1 * xc;
1133:   t147 = t8 * t13;
1134:   t153 = t14 * ZA;
1135:   t156 = xc * t5;
1136:   t157 = t156 * t93;
1137:   t160 = t103 * t5;
1138:   t162 = t146 * t8 * t15;
1139:   t166 = t34 * t7 * t15;
1140:   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;
1141:   t170 = t106 * t68;
1142:   t177 = t35 * t92;
1143:   t178 = t112 * t177;
1144:   t181 = t156 * t76;
1145:   t186 = t35 * t12;
1146:   t187 = t112 * t186;
1147:   t193 = t5 * 0.3141592654e1;
1148:   t206 = t34 * t14;
1149:   t207 = t206 * t7;
1150:   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;
1151:   t217 = t106 * t66 * t92;
1152:   t226 = t88 * t19 * nz;
1153:   t227 = 0.3141592654e1 * t34;
1154:   t229 = t227 * xc * t67;
1155:   t232 = t73 * t31;
1156:   t234 = t146 * t5 * t67;
1157:   t238 = t61 * ZB;
1158:   t239 = t14 * t8;
1159:   t240 = t238 * t239;
1160:   t243 = t136 * t93;
1161:   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;
1162:   t247 = t14 * t92;
1163:   t249 = t227 * t247 * xc;
1164:   t254 = t73 * t22;
1165:   t259 = t60 * t22 * t61;
1166:   t260 = t112 * t26;
1167:   t264 = t146 * t247 * t5;
1168:   t268 = xc * t14;
1169:   t274 = t5 * t14;
1170:   t275 = t274 * t8;
1171:   t280 = nz * nx;
1172:   t281 = t280 * t22;
1173:   t282 = t55 * t14;
1174:   t283 = t25 * t282;
1175:   t290 = ZA * t247 * xc * ZB;
1176:   t295 = t22 * nx * t1 * 0.3141592654e1;
1177:   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;
1178:   t301 = t61 * t5;
1179:   t307 = t87 * t34;
1180:   t312 = t61 * xc;
1181:   t313 = t312 * t239;
1182:   t317 = t34 * t55 * t14;
1183:   t329 = ZB * t13 * t55;
1184:   t330 = t65 * t329;
1185:   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;
1186:   t340 = t5 * t35;
1187:   t344 = t25 * t93;
1188:   t356 = t41 * t13;
1189:   t360 = t23 * nz * t61;
1190:   t363 = t25 * t64 * t7 * t15;
1191:   t366 = t156 * t177;
1192:   t369 = t14 * t7;
1193:   t370 = t25 * t369;
1194:   t373 = t156 * t186;
1195:   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;
1196:   t382 = t112 * t76;
1197:   t387 = t80 * t61;
1198:   t391 = t136 * t26;
1199:   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;
1200:   t423 = t153 * t8;
1201:   t426 = t34 * t13;
1202:   t427 = t426 * t55;
1203:   t430 = t34 * t8;
1204:   t437 = t80 * ZA;
1205:   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;
1206:   t453 = t106 * ZB * t7 * t15;
1207:   t456 = t2 * t5;
1208:   t459 = t112 * t56;
1209:   t462 = t126 * t14;
1210:   t474 = t40 * 0.3141592654e1;
1211:   t475 = xc * t8;
1212:   t480 = t146 * t13 * t35;
1213:   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;
1214:   t497 = t136 * t56;
1215:   t504 = t9 * t13;
1216:   t509 = t475 * t13;
1217:   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;
1218:   t528 = t5 * t13;
1219:   t529 = t528 * t35;
1220:   t532 = t106 * t329;
1221:   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;
1222:   t557 = t146 * t15;
1223:   t562 = xc * t15;
1224:   t563 = t562 * t5;
1225:   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;
1226:   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;
1227:   t623 = xc * t13;
1228:   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;
1229:   t632 = t61 * 0.3141592654e1;
1230:   t633 = t632 * t8;
1231:   t634 = t80 * nz;
1232:   t638 = t632 * t634;
1233:   t639 = t638 * xc;
1234:   t642 = t61 * t34;
1235:   t643 = t122 * t19;
1236:   t649 = t61 * t61;
1237:   t650 = t649 * t1;
1238:   t652 = t19 * t19;
1239:   t653 = t14 * t652;
1240:   t654 = t653 * t9;
1241:   t657 = t14 * t1;
1242:   t658 = t657 * t19;
1243:   t665 = t632 * t34;
1244:   t666 = t665 * t2;
1245:   t667 = t8 * t19;
1246:   t668 = t667 * t623;
1247:   t674 = t665 * nz;
1248:   t675 = t652 * xc;
1249:   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;
1250:   t683 = t46 * t652;
1251:   t686 = t633 * t15;
1252:   t691 = t35 * t80;
1253:   t698 = t35 * t652;
1254:   t705 = t14 * t80;
1255:   t708 = t61 * t35;
1256:   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;
1257:   t727 = t61 * t46;
1258:   t737 = t649 * t34;
1259:   t738 = t737 * t1;
1260:   t739 = t8 * t652;
1261:   t740 = t739 * t268;
1262:   t746 = t61 * ZA;
1263:   t754 = t632 * nz * xc;
1264:   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;
1265:   t762 = t633 * t13;
1266:   t764 = t5 * nz * t652;
1267:   t767 = t80 * t1;
1268:   t768 = t649 * t767;
1269:   t772 = t649 * ZA;
1270:   t773 = t772 * t129;
1271:   t777 = t35 * t1 * t19;
1272:   t780 = t632 * t5;
1273:   t781 = t780 * t15;
1274:   t786 = t698 * ZA;
1275:   t790 = t64 * t14;
1276:   t800 = t649 * t8;
1277:   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;
1278:   t812 = t649 * t80;
1279:   t817 = t83 * ZB;
1280:   t824 = t746 * ZB;
1281:   t828 = t800 * t14;
1282:   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;
1283:   t858 = t35 * t19;
1284:   t873 = t2 * t8;
1285:   t878 = t61 * t1;
1286:   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;
1287:   t903 = t739 * t790;
1288:   t923 = t737 * t80;
1289:   t924 = t667 * t790;
1290:   t927 = t780 * t2;
1291:   t937 = t15 * t19 * xc;
1292:   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;
1293:   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;

1295:   _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);
1296:   /****************************************************************************************/
1297:   _PC4A = 0;
1298:   /****************************************************************************************/
1299:   t1 = nx * 0.3141592654e1;
1300:   t2 = t1 * xc;
1301:   t3 = PetscCosReal(t2);
1302:   t4 = nx * nx;
1303:   t6 = nz * 0.3141592654e1;
1304:   t7 = t3 * t4 * t6;
1305:   t8 = ZA * ZB;
1306:   t9 = PetscExpReal(t6);
1307:   t10 = t9 * t9;
1308:   t11 = xc * nz;
1309:   t13 = PetscExpReal(t11 * 0.3141592654e1);
1310:   t14 = t13 * t13;
1311:   t15 = t14 * t13;
1312:   t16 = t14 * t14;
1313:   t17 = t16 * t15;
1314:   t18 = t10 * t17;
1315:   t19 = t8 * t18;
1316:   t22 = PetscSinReal(t2);
1317:   t23 = nx * t22;
1318:   t24 = t23 * nz;
1319:   t25 = ZB * ZB;
1320:   t30 = nz * nz;
1321:   t31 = t30 * nz;
1322:   t32 = t31 * nx;
1323:   t33 = 0.3141592654e1 * 0.3141592654e1;
1324:   t35 = t32 * t22 * t33;
1325:   t36 = ZA * ZA;
1326:   t37 = t36 * xc;
1327:   t38 = t16 * t13;
1328:   t39 = t10 * t38;
1329:   t40 = t37 * t39;
1330:   t43 = PetscSinReal(t1);
1331:   t44 = nx * t43;
1332:   t45 = t30 * 0.3141592654e1;
1333:   t46 = t44 * t45;
1334:   t47 = ZA * xc;
1335:   t49 = ZB * t16 * t9;
1336:   t54 = t4 * nx * t43;
1337:   t55 = xc * xc;
1338:   t57 = t54 * t30 * t55;
1339:   t58 = t33 * 0.3141592654e1;
1340:   t59 = t58 * t25;
1341:   t60 = t16 * t9;
1342:   t61 = t59 * t60;
1343:   t64 = xc * t25;
1344:   t65 = t14 * t9;
1345:   t66 = t64 * t65;
1346:   t70 = t44 * t31 * t33;
1347:   t71 = t37 * t65;
1348:   t74 = t10 * t15;
1349:   t75 = t64 * t74;
1350:   t78 = t25 * t10;
1351:   t83 = t54 * nz * t33;
1352:   t84 = t55 * t25;
1353:   t85 = t10 * t9;
1354:   t86 = t14 * t85;
1355:   t87 = t84 * t86;
1356:   t90 = t30 * t30;
1357:   t92 = t44 * t90 * t58;
1358:   t93 = t55 * xc;
1359:   t94 = t93 * t25;
1360:   t95 = t85 * t16;
1361:   t96 = t94 * t95;
1362:   t102 = t23 * t45;
1363:   t103 = t10 * t10;
1364:   t104 = ZB * t103;
1365:   t106 = t47 * t104 * t15;
1366:   t111 = t54 * 0.3141592654e1;
1367:   t112 = t25 * t85;
1368:   t113 = t112 * t16;
1369:   t115 = t8 * t39;
1370:   t118 = t16 * t14;
1371:   t119 = t85 * t118;
1372:   t120 = t37 * t119;
1373:   t123 = t16 * t16;
1374:   t124 = t36 * t123;
1375:   t125 = t124 * t9;
1376:   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;
1377:   t128 = t37 * t74;
1378:   t131 = t44 * nz;
1379:   t133 = t25 * t9 * t118;
1380:   t136 = t36 * t14;
1381:   t137 = t136 * t9;
1382:   t140 = t30 * t4;
1383:   t142 = t140 * t3 * t33;
1384:   t143 = t64 * t39;
1385:   t147 = t30 * nx * t43;
1386:   t148 = 0.3141592654e1 * t36;
1387:   t149 = t9 * t118;
1388:   t153 = t44 * t31 * ZA;
1389:   t154 = t33 * xc;
1390:   t155 = t154 * t49;
1391:   t160 = ZA * t17 * xc * ZB;
1392:   t163 = t103 * t13;
1393:   t164 = t64 * t163;
1394:   t170 = t44 * t90 * t55;
1395:   t171 = t58 * ZB;
1396:   t172 = ZA * t16;
1397:   t174 = t171 * t172 * t9;
1398:   t177 = t36 * t55;
1399:   t178 = t177 * t149;
1400:   t181 = t54 * t11;
1401:   t182 = t33 * t25;
1402:   t186 = t25 * t14;
1403:   t187 = t186 * t9;
1404:   t193 = t186 * t85;
1405:   t198 = ZB * t55;
1406:   t199 = ZA * t103;
1407:   t201 = t198 * t199 * t15;
1408:   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;
1409:   t210 = t32 * t22;
1410:   t211 = t33 * t55;
1411:   t212 = t25 * t38;
1412:   t213 = t211 * t212;
1413:   t216 = nz * nx;
1414:   t217 = t22 * t25;
1415:   t222 = ZB * t85 * t16;
1416:   t226 = t23 * t30;
1417:   t227 = t13 * t10;
1418:   t228 = t148 * t227;
1419:   t233 = t37 * t163;
1420:   t237 = nz * t4 * t3;
1421:   t238 = t148 * t74;
1422:   t241 = t64 * t86;
1423:   t245 = t148 * xc * t15;
1424:   t248 = t112 * t118;
1425:   t250 = t22 * t36;
1426:   t256 = 0.3141592654e1 * t25;
1427:   t257 = t256 * t39;
1428:   t262 = t38 * t103;
1429:   t263 = t37 * t262;
1430:   t267 = t148 * t17 * xc;
1431:   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;
1432:   t273 = t37 * t149;
1433:   t277 = t47 * t104 * t13;
1434:   t285 = t31 * t36;
1435:   t286 = t44 * t285;
1436:   t291 = t25 * t123 * t9;
1437:   t304 = 0.3141592654e1 * xc;
1438:   t305 = t304 * t212;
1439:   t312 = t256 * t18;
1440:   t315 = t8 * t60;
1441:   t319 = t54 * t30 * t58;
1442:   t323 = t90 * t36;
1443:   t324 = t44 * t323;
1444:   t325 = t55 * t58;
1445:   t326 = t325 * t60;
1446:   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;
1447:   t332 = t8 * t95;
1448:   t335 = t136 * t85;
1449:   t337 = t256 * t227;
1450:   t340 = t177 * t119;
1451:   t346 = t37 * t86;
1452:   t351 = t103 * t15;
1453:   t352 = t177 * t351;
1454:   t355 = t64 * t119;
1455:   t358 = t8 * t227;
1456:   t361 = t85 * 0.3141592654e1;
1457:   t365 = t84 * t39;
1458:   t372 = ZB * t10;
1459:   t373 = t372 * t38;
1460:   t374 = t47 * t373;
1461:   t379 = t177 * t39;
1462:   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;
1463:   t386 = t54 * t30 * t93;
1464:   t387 = ZA * t85;
1465:   t389 = t171 * t387 * t16;
1466:   t394 = t64 * t60;
1467:   t398 = t304 * t25 * t15;
1468:   t401 = t361 * t25;
1469:   t405 = t84 * t65;
1470:   t410 = t148 * t18;
1471:   t414 = t25 * t16 * t9;
1472:   t417 = t84 * t74;
1473:   t422 = t177 * t86;
1474:   t428 = ZB * t38;
1475:   t429 = t47 * t428;
1476:   t432 = t148 * t39;
1477:   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;
1478:   t442 = t36 * t9 * t118;
1479:   t444 = t123 * t9;
1480:   t445 = t8 * t444;
1481:   t448 = t361 * t36;
1482:   t451 = t47 * t372 * t17;
1483:   t454 = t94 * t60;
1484:   t457 = t25 * t103;
1485:   t465 = t47 * t372 * t15;
1486:   t468 = t36 * t85;
1487:   t469 = t468 * t16;
1488:   t474 = t43 * t85;
1489:   t478 = t8 * t74;
1490:   t484 = t256 * t74;
1491:   t489 = t198 * ZA * t10 * t15;
1492:   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;
1493:   t504 = t33 * t36 * t55 * t38;
1494:   t507 = t37 * t18;
1495:   t512 = t47 * ZB * t13 * t10;
1496:   t518 = t59 * t95;
1497:   t530 = t84 * t351;
1498:   t534 = t37 * t227;
1499:   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;
1500:   t557 = t468 * t118;
1501:   t562 = t93 * t58;
1502:   t563 = t562 * t60;
1503:   t567 = t44 * t90 * t93;
1504:   t575 = ZA * t55;
1505:   t576 = t575 * t428;
1506:   t583 = t37 * t60;
1507:   t590 = t140 * t3;
1508:   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;
1509:   t604 = nz * t36;
1510:   t606 = t154 * t95;
1511:   t625 = t36 * t103;
1512:   t640 = t30 * t36;
1513:   t641 = t54 * t640;
1514:   t642 = t325 * t95;
1515:   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;
1516:   t652 = t36 * t16;
1517:   t653 = t652 * t9;
1518:   t655 = t64 * t227;
1519:   t658 = t182 * t95;
1520:   t663 = t562 * t95;
1521:   t684 = t64 * t351;
1522:   t689 = t36 * t10;
1523:   t695 = t154 * t222;
1524:   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;
1525:   t711 = t575 * t373;
1526:   t717 = t304 * t17 * t25;
1527:   t736 = t177 * t74;
1528:   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;
1529:   t750 = t64 * t262;
1530:   t763 = t44 * t640;
1531:   t770 = t84 * t119;
1532:   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;
1533:   t797 = t64 * t149;
1534:   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;
1535:   t827 = t84 * t149;
1536:   t846 = t54 * nz * ZA;
1537:   t854 = t64 * t18;
1538:   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;
1539:   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;
1540:   t914 = t25 * ZB;
1541:   t915 = t33 * t914;
1542:   t919 = t4 * t4;
1543:   t920 = t16 * t919;
1544:   t929 = t123 * t90;
1545:   t932 = t919 * t103;
1546:   t935 = t33 * ZB;
1547:   t939 = t652 * t919;
1548:   t942 = t16 * t30;
1549:   t943 = t942 * t4;
1550:   t949 = t103 * t16;
1551:   t950 = t949 * t90;
1552:   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;
1553:   t954 = t171 * t36;
1554:   t955 = t90 * nz;
1555:   t956 = xc * t955;
1556:   t957 = t118 * t10;
1557:   t964 = t33 * t33;
1558:   t965 = t964 * ZB;
1559:   t966 = t965 * t640;
1560:   t967 = t10 * t919;
1561:   t968 = t55 * t16;
1562:   t969 = t967 * t968;
1563:   t972 = t935 * t36;
1564:   t974 = t103 * t30 * t4;
1565:   t977 = xc * t16;
1566:   t978 = t967 * t977;
1567:   t981 = t90 * t30;
1568:   t983 = t16 * t10;
1569:   t987 = t182 * ZA;
1570:   t988 = t4 * t10;
1571:   t992 = t171 * t604;
1572:   t993 = xc * t14;
1573:   t994 = t932 * t993;
1574:   t997 = t182 * t30;
1575:   t1005 = t171 * t285;
1576:   t1006 = t988 * t993;
1577:   t1009 = t58 * t914;
1578:   t1010 = t1009 * t31;
1579:   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;
1580:   t1015 = t964 * t25;
1581:   t1016 = ZA * t30;
1582:   t1017 = t1015 * t1016;
1583:   t1020 = t967 * t993;
1584:   t1031 = t1009 * t118;
1585:   t1032 = t31 * t10;
1586:   t1040 = t964 * t914;
1587:   t1041 = t1040 * t90;
1588:   t1044 = t55 * t10 * t4 * t16;
1589:   t1047 = t1040 * t30;
1590:   t1050 = t123 * ZA;
1591:   t1054 = t977 * t988;
1592:   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;
1593:   t1058 = t1009 * nz;
1594:   t1063 = t932 * ZA;
1595:   t1069 = t123 * t30 * t4;
1596:   t1080 = t993 * t103 * t4;
1597:   t1088 = t935 * t103;
1598:   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;
1599:   t1113 = t955 * t118 * xc;
1600:   t1120 = t4 * t118;
1601:   t1125 = t981 * xc;
1602:   t1133 = nz * t10;
1603:   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;
1604:   t1153 = xc * t118;
1605:   t1165 = t182 * t16;
1606:   t1170 = t171 * t10;
1607:   t1178 = ZA * t90;
1608:   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;
1609:   t1195 = t1040 * t981;
1610:   t1199 = t1009 * t955;
1611:   t1203 = t1009 * t10;
1612:   t1211 = t965 * t323;
1613:   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;
1614:   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;

1616:   _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);
1617:   /****************************************************************************************/
1618:   t1 = nz * nz;
1619:   t2 = t1 * nz;
1620:   t3 = nx * t2;
1621:   t4 = 0.3141592654e1 * ZA;
1622:   t5 = t3 * t4;
1623:   t6 = nx * 0.3141592654e1;
1624:   t7 = t6 * xc;
1625:   t8 = PetscSinReal(t7);
1626:   t9 = t8 * ZB;
1627:   t10 = nz * 0.3141592654e1;
1628:   t11 = PetscExpReal(t10);
1629:   t12 = t11 * t11;
1630:   t15 = PetscExpReal(xc * nz * 0.3141592654e1);
1631:   t16 = t15 * t15;
1632:   t17 = t16 * t16;
1633:   t18 = t17 * t15;
1634:   t19 = t12 * t18;
1635:   t23 = t1 * t1;
1636:   t24 = nx * t23;
1637:   t25 = ZB * ZB;
1638:   t27 = t18 * t8;
1639:   t28 = 0.3141592654e1 * 0.3141592654e1;
1640:   t29 = xc * xc;
1641:   t30 = t28 * t29;
1642:   t34 = t1 * xc;
1643:   t35 = 0.3141592654e1 * ZB;
1644:   t36 = t34 * t35;
1645:   t37 = PetscCosReal(t7);
1646:   t38 = ZA * t37;
1647:   t39 = nx * nx;
1648:   t40 = t39 * t12;
1649:   t41 = t16 * t15;
1650:   t43 = t38 * t40 * t41;
1651:   t46 = t25 * nz;
1652:   t47 = t46 * 0.3141592654e1;
1653:   t48 = t39 * nx;
1654:   t49 = PetscSinReal(t6);
1655:   t50 = t48 * t49;
1656:   t51 = t12 * t11;
1657:   t52 = t51 * t17;
1658:   t53 = t50 * t52;
1659:   t56 = t34 * 0.3141592654e1 * t25;
1660:   t57 = t37 * t39;
1661:   t58 = t17 * t41;
1662:   t59 = t12 * t58;
1663:   t60 = t57 * t59;
1664:   t63 = t25 * t18;
1665:   t64 = t57 * nz;
1666:   t67 = ZA * ZA;
1667:   t68 = t67 * nz;
1668:   t69 = 0.3141592654e1 * t48;
1669:   t70 = t68 * t69;
1670:   t71 = t49 * xc;
1671:   t72 = t17 * t16;
1672:   t73 = t11 * t72;
1673:   t74 = t71 * t73;
1674:   t77 = t1 * t67;
1675:   t78 = t77 * 0.3141592654e1;
1676:   t81 = nx * t25;
1677:   t82 = t81 * t49;
1678:   t83 = t17 * t17;
1679:   t85 = t1 * t83 * t11;
1680:   t87 = nx * ZB;
1681:   t88 = t8 * t2;
1682:   t89 = t87 * t88;
1683:   t90 = 0.3141592654e1 * xc;
1684:   t91 = t12 * t12;
1685:   t92 = ZA * t91;
1686:   t97 = ZB * ZA;
1687:   t98 = t97 * t37;
1688:   t99 = t39 * nz;
1689:   t100 = t12 * t41;
1690:   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;
1691:   t105 = t67 * t48;
1692:   t106 = t49 * t51;
1693:   t107 = t106 * t72;
1694:   t109 = t1 * 0.3141592654e1;
1695:   t110 = t109 * xc;
1696:   t115 = nx * t67;
1697:   t116 = t115 * t49;
1698:   t117 = t1 * t16;
1699:   t118 = t117 * t11;
1700:   t120 = t2 * t25;
1701:   t121 = t28 * 0.3141592654e1;
1702:   t122 = t121 * t29;
1703:   t123 = t120 * t122;
1704:   t129 = t1 * ZB;
1705:   t130 = t129 * t4;
1706:   t131 = t57 * t100;
1707:   t134 = t12 * t16;
1708:   t136 = t109 * t39;
1709:   t139 = ZB * t18;
1710:   t141 = t39 * t1;
1711:   t142 = t141 * t90;
1712:   t145 = t77 * t90;
1713:   t146 = t91 * t41;
1714:   t147 = t57 * t146;
1715:   t151 = t25 * t39 * t1;
1716:   t152 = t72 * t12;
1717:   t156 = t49 * t2;
1718:   t158 = t83 * t11;
1719:   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;
1720:   t164 = t115 * t88;
1721:   t165 = t90 * t19;
1722:   t168 = t25 * t48;
1723:   t169 = t49 * t16;
1724:   t170 = t169 * t11;
1725:   t174 = ZA * nz * t69;
1726:   t175 = ZB * t51;
1727:   t176 = t175 * t17;
1728:   t177 = t71 * t176;
1729:   t180 = t1 * t29;
1730:   t181 = t28 * t25;
1731:   t182 = t180 * t181;
1732:   t183 = t50 * t73;
1733:   t186 = ZA * t1;
1734:   t187 = t28 * t48;
1735:   t188 = t186 * t187;
1736:   t189 = ZB * t17;
1737:   t190 = t189 * t11;
1738:   t191 = t71 * t190;
1739:   t194 = t50 * t158;
1740:   t196 = t115 * t156;
1741:   t197 = t90 * t73;
1742:   t201 = t49 * t17 * t11;
1743:   t204 = t88 * t90;
1744:   t207 = t68 * 0.3141592654e1;
1745:   t208 = t17 * t11;
1746:   t209 = t50 * t208;
1747:   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;
1748:   t212 = t2 * 0.3141592654e1;
1749:   t213 = t212 * t52;
1750:   t215 = t81 * t8;
1751:   t216 = t212 * t59;
1752:   t219 = t3 * t90;
1753:   t220 = t25 * t8;
1754:   t221 = t18 * t91;
1755:   t225 = t71 * t52;
1756:   t231 = t16 * t51;
1757:   t232 = t50 * t231;
1758:   t237 = ZA * t12;
1759:   t243 = t67 * t28;
1760:   t244 = t24 * t243;
1761:   t245 = t71 * t231;
1762:   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;
1763:   t252 = t25 * t37;
1764:   t253 = t252 * t39;
1765:   t255 = nz * t15 * t12;
1766:   t258 = t2 * t29;
1767:   t259 = ZB * t28;
1768:   t260 = t258 * t259;
1769:   t263 = t106 * t17;
1770:   t265 = xc * t25;
1771:   t269 = t25 * t49;
1772:   t270 = t269 * t52;
1773:   t273 = t1 * t25;
1774:   t274 = t273 * 0.3141592654e1;
1775:   t275 = t57 * t19;
1776:   t278 = t24 * t30;
1777:   t288 = t1 * t11 * t72;
1778:   t290 = t212 * t208;
1779:   t292 = t2 * xc;
1780:   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;
1781:   t301 = t50 * t176;
1782:   t304 = t51 * t72;
1783:   t305 = t71 * t304;
1784:   t308 = t25 * t41;
1785:   t311 = ZA * t48;
1786:   t312 = t311 * t49;
1787:   t317 = t91 * t15;
1788:   t318 = t57 * t317;
1789:   t321 = t81 * t88;
1790:   t322 = t90 * t59;
1791:   t325 = t212 * t231;
1792:   t327 = t15 * t12;
1793:   t328 = t57 * t327;
1794:   t331 = t77 * t187;
1795:   t334 = t2 * ZA;
1796:   t335 = t334 * t122;
1797:   t336 = t50 * t190;
1798:   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;
1799:   t341 = t169 * t51;
1800:   t344 = t49 * t11 * t72;
1801:   t346 = t77 * t30;
1802:   t347 = t50 * t304;
1803:   t350 = t25 * t51;
1804:   t352 = nx * ZA;
1805:   t353 = t49 * t23;
1806:   t354 = t352 * t353;
1807:   t355 = t28 * xc;
1808:   t362 = t25 * t91;
1809:   t365 = t23 * nz;
1810:   t366 = nx * t365;
1811:   t367 = t366 * t122;
1812:   t368 = ZB * t49;
1813:   t369 = ZA * t51;
1814:   t370 = t369 * t17;
1815:   t371 = t368 * t370;
1816:   t374 = t115 * t353;
1817:   t375 = t355 * t73;
1818:   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;
1819:   t382 = t71 * t208;
1820:   t394 = t2 * t67;
1821:   t395 = t394 * t122;
1822:   t398 = t352 * t156;
1823:   t402 = t17 * t12;
1824:   t403 = t39 * ZA;
1825:   t404 = t402 * t403;
1826:   t407 = t269 * t208;
1827:   t411 = t49 * t83 * t11;
1828:   t413 = t46 * t69;
1829:   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;
1830:   t424 = t16 * t11;
1831:   t425 = t212 * t424;
1832:   t427 = t258 * t181;
1833:   t430 = t67 * t29;
1834:   t431 = t366 * t430;
1835:   t432 = t121 * t49;
1836:   t433 = t432 * t52;
1837:   t436 = nz * t12;
1838:   t437 = t436 * t18;
1839:   t440 = t29 * xc;
1840:   t441 = t440 * t121;
1841:   t442 = t394 * t441;
1842:   t445 = t67 * t37;
1843:   t446 = t445 * t39;
1844:   t448 = nz * t18 * t91;
1845:   t453 = t352 * t49;
1846:   t458 = t8 * t23;
1847:   t462 = t81 * t458;
1848:   t463 = t30 * t19;
1849:   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;
1850:   t470 = t436 * t58;
1851:   t475 = t2 * t121 * t440 * t25;
1852:   t485 = t212 * t73;
1853:   t488 = t67 * t72 * t1;
1854:   t490 = t39 * xc;
1855:   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;
1856:   t503 = t115 * t8;
1857:   t510 = t355 * t19;
1858:   t513 = t432 * t208;
1859:   t525 = t38 * t40 * t18;
1860:   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;
1861:   t536 = t28 * t37;
1862:   t538 = t490 * t100;
1863:   t541 = t334 * t441;
1864:   t547 = t394 * t30;
1865:   t550 = t212 * t19;
1866:   t553 = t366 * t441;
1867:   t556 = nz * t17;
1868:   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;
1869:   t583 = t90 * t317;
1870:   t594 = t212 * t158;
1871:   t596 = t152 * t67;
1872:   t602 = t67 * t17;
1873:   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;
1874:   t613 = t83 * t25;
1875:   t616 = t81 * t156;
1876:   t627 = t90 * t231;
1877:   t630 = t91 * t16;
1878:   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;
1879:   t643 = t77 * t355;
1880:   t648 = t115 * t458;
1881:   t651 = t134 * t67;
1882:   t657 = t30 * t304;
1883:   t660 = t30 * t146;
1884:   t665 = t25 * t17;
1885:   t668 = t50 * t424;
1886:   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;
1887:   t672 = t90 * t424;
1888:   t676 = t120 * t536;
1889:   t680 = t436 * t41;
1890:   t688 = t366 * t67 * t440;
1891:   t696 = xc * t12;
1892:   t697 = t696 * t18;
1893:   t701 = t252 * t141;
1894:   t702 = t90 * t221;
1895:   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;
1896:   t712 = t24 * t430;
1897:   t713 = t28 * t49;
1898:   t721 = t1 * t17 * t11;
1899:   t726 = ZB * xc;
1900:   t737 = nz * t91;
1901:   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;
1902:   t745 = t269 * t231;
1903:   t749 = t1 * t28 * t265;
1904:   t757 = t16 * t39;
1905:   t758 = t696 * t757;
1906:   t762 = t69 * t49;
1907:   t772 = t355 * t100;
1908:   t775 = t81 * t353;
1909:   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;
1910:   t790 = t212 * t304;
1911:   t793 = t156 * 0.3141592654e1;
1912:   t795 = t355 * t304;
1913:   t800 = t91 * t39;
1914:   t801 = t800 * nz;
1915:   t807 = t2 * t28;
1916:   t808 = t807 * t726;
1917:   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;
1918:   t812 = t117 * t51;
1919:   t821 = t24 * t355;
1920:   t827 = t90 * t304;
1921:   t840 = t800 * t41;
1922:   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;
1923:   t849 = t1 * t51;
1924:   t850 = t849 * t17;
1925:   t860 = t269 * t424;
1926:   t863 = t273 * t187;
1927:   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;
1928:   t879 = xc * ZA;
1929:   t888 = t67 * t51;
1930:   t901 = ZA * t17;
1931:   t903 = t368 * t901 * t11;
1932:   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;
1933:   t923 = t71 * t424;
1934:   t926 = t87 * t458;
1935:   t927 = t28 * ZA;
1936:   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;
1937:   t948 = t90 * t327;
1938:   t961 = t30 * t100;
1939:   t964 = t29 * t49;
1940:   t981 = t106 * t1;
1941:   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;
1942:   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;
1943:   t1018 = t212 * t100;
1944:   t1029 = t212 * t327;
1945:   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;
1946:   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;
1947:   t1079 = t58 * t8;
1948:   t1091 = t807 * t29;
1949:   t1092 = t665 * t40;
1950:   t1101 = ZB * t91;
1951:   t1102 = t403 * nz;
1952:   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;
1953:   t1108 = t849 * t72;
1954:   t1121 = t737 * t15;
1955:   t1124 = t29 * t12;
1956:   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;
1957:   t1134 = t394 * t28;
1958:   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;
1959:   t1161 = nz * t83;
1960:   t1173 = ZB * t12;
1961:   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;
1962:   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;
1963:   t1234 = t25 * ZB;
1964:   t1235 = t1234 * t28;
1965:   t1236 = t365 * t91;
1966:   t1240 = ZB * t121;
1967:   t1241 = t1240 * t77;
1968:   t1242 = t39 * t39;
1969:   t1243 = t12 * t1242;
1970:   t1244 = xc * t72;
1971:   t1245 = t1243 * t1244;
1972:   t1248 = t365 * t25;
1973:   t1252 = t243 * nz;
1974:   t1257 = t23 * t1;
1975:   t1258 = t1240 * t1257;
1976:   t1259 = t67 * t12;
1977:   t1260 = xc * t16;
1978:   t1268 = t1234 * t121;
1979:   t1269 = t1268 * t23;
1980:   t1272 = t1242 * t91;
1981:   t1280 = t67 * xc;
1982:   t1284 = t28 * t28;
1983:   t1285 = t67 * t1284;
1984:   t1287 = t1285 * t2 * ZB;
1985:   t1288 = t17 * xc;
1986:   t1289 = t1243 * t1288;
1987:   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;
1988:   t1293 = t365 * t83;
1989:   t1300 = ZA * t1284;
1990:   t1304 = t17 * t1242 * t25 * t12;
1991:   t1307 = t927 * t2;
1992:   t1311 = t23 * t2;
1993:   t1312 = t1300 * t1311;
1994:   t1316 = t1234 * t1284;
1995:   t1317 = t1316 * t1311;
1996:   t1321 = t1240 * t23;
1997:   t1331 = t1240 * t23 * t67;
1998:   t1332 = t40 * t1244;
1999:   t1338 = t1243 * t1260;
2000:   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;
2001:   t1346 = t1316 * t2;
2002:   t1349 = t927 * nz;
2003:   t1350 = t25 * t1242;
2004:   t1354 = t1268 * t1257;
2005:   t1366 = t1268 * t1;
2006:   t1370 = t29 * t17;
2007:   t1371 = t1243 * t1370;
2008:   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;
2009:   t1387 = t1257 * t12;
2010:   t1391 = t1240 * t1;
2011:   t1399 = t1272 * t1260;
2012:   t1412 = t1285 * t1311;
2013:   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;
2014:   t1456 = t365 * ZB;
2015:   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;
2016:   t1472 = t1316 * t365;
2017:   t1474 = t1124 * t39 * t17;
2018:   t1478 = t17 * t91;
2019:   t1504 = t72 * t39;
2020:   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;
2021:   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;
2022:   t1564 = t1260 * t800;
2023:   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;

2025:   _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);
2026:   /****************************************************************************************/
2027:   t1 = nz * nz;
2028:   t2 = t1 * nz;
2029:   t3 = t2 * nx;
2030:   t4 = nx * 0.3141592654e1;
2031:   t5 = t4 * xc;
2032:   t6 = PetscSinReal(t5);
2033:   t7 = 0.3141592654e1 * 0.3141592654e1;
2034:   t9 = t3 * t6 * t7;
2035:   t10 = xc * xc;
2036:   t11 = ZA * ZA;
2037:   t12 = t10 * t11;
2038:   t13 = nz * 0.3141592654e1;
2039:   t14 = PetscExpReal(t13);
2040:   t15 = t14 * t14;
2041:   t16 = xc * nz;
2042:   t18 = PetscExpReal(t16 * 0.3141592654e1);
2043:   t19 = t18 * t18;
2044:   t20 = t19 * t18;
2045:   t21 = t15 * t20;
2046:   t22 = t12 * t21;
2047:   t25 = nx * t6;
2048:   t26 = t1 * 0.3141592654e1;
2049:   t27 = t25 * t26;
2050:   t28 = ZA * ZB;
2051:   t29 = t18 * t15;
2052:   t30 = t28 * t29;
2053:   t33 = t25 * nz;
2054:   t34 = t11 * t15;
2055:   t35 = t19 * t19;
2056:   t36 = t35 * t18;
2057:   t40 = t25 * t1;
2058:   t41 = 0.3141592654e1 * t11;
2059:   t42 = t15 * t36;
2060:   t43 = t41 * t42;
2061:   t46 = nx * nx;
2062:   t47 = t1 * t46;
2063:   t48 = t47 * t11;
2064:   t49 = t7 * xc;
2065:   t50 = t35 * t15;
2066:   t51 = t49 * t50;
2067:   t55 = PetscSinReal(t4);
2068:   t56 = t46 * nx * t55;
2069:   t58 = t56 * nz * t7;
2070:   t59 = ZB * ZB;
2071:   t60 = t10 * t59;
2072:   t61 = t15 * t14;
2073:   t62 = t19 * t61;
2074:   t63 = t60 * t62;
2075:   t66 = t19 * t14;
2076:   t67 = t60 * t66;
2077:   t70 = t28 * t42;
2078:   t73 = PetscCosReal(t5);
2079:   t74 = t47 * t73;
2080:   t75 = t7 * t11;
2081:   t77 = t75 * t10 * t36;
2082:   t80 = t73 * t46;
2083:   t81 = t80 * nz;
2084:   t82 = 0.3141592654e1 * t59;
2085:   t83 = t82 * t42;
2086:   t87 = xc * t11;
2087:   t88 = t87 * t62;
2088:   t91 = nz * nx;
2089:   t92 = t55 * t61;
2090:   t96 = nx * t55;
2091:   t98 = t96 * t2 * t7;
2092:   t101 = xc * t59;
2093:   t102 = t101 * t62;
2094:   t108 = t1 * t1;
2095:   t109 = t108 * t7;
2096:   t111 = t59 * t35;
2097:   t112 = t111 * t15;
2098:   t115 = t35 * t20;
2099:   t123 = t1 * nx * t55;
2100:   t124 = t61 * t35;
2101:   t127 = t35 * t19;
2102:   t128 = t61 * t127;
2103:   t129 = t60 * t128;
2104:   t132 = t56 * t16;
2105:   t133 = t7 * t59;
2106:   t134 = t133 * t124;
2107:   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;
2108:   t139 = t56 * 0.3141592654e1;
2109:   t140 = t111 * t14;
2110:   t144 = t49 * t124;
2111:   t147 = t91 * t55;
2112:   t148 = t61 * ZA;
2113:   t154 = ZA * t115 * xc * ZB;
2114:   t157 = t7 * 0.3141592654e1;
2115:   t159 = t96 * t108 * t157;
2116:   t160 = t10 * xc;
2117:   t161 = t160 * t59;
2118:   t162 = t35 * t14;
2119:   t163 = t161 * t162;
2120:   t166 = t28 * t162;
2121:   t169 = t80 * t13;
2122:   t170 = t101 * t42;
2123:   t173 = t2 * t11;
2124:   t174 = t96 * t173;
2125:   t175 = t7 * t10;
2126:   t179 = t59 * t15;
2127:   t184 = t15 * t15;
2128:   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;
2129:   t194 = t173 * 0.3141592654e1;
2130:   t195 = xc * t15;
2131:   t196 = t195 * t19;
2132:   t202 = t15 * t115;
2133:   t203 = t28 * t202;
2134:   t206 = t96 * t26;
2135:   t207 = t14 * t127;
2136:   t208 = t101 * t207;
2137:   t211 = t12 * t128;
2138:   t218 = t11 * t61;
2139:   t219 = t218 * t35;
2140:   t221 = t108 * ZA;
2141:   t223 = t7 * ZB;
2142:   t224 = t223 * t50;
2143:   t227 = ZA * xc;
2144:   t228 = ZB * t15;
2145:   t229 = t228 * t36;
2146:   t230 = t227 * t229;
2147:   t233 = t87 * t207;
2148:   t236 = t6 * t11;
2149:   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;
2150:   t244 = t227 * t228 * t20;
2151:   t252 = t184 * t18;
2152:   t253 = t101 * t252;
2153:   t256 = t35 * t35;
2154:   t257 = t256 * t14;
2155:   t258 = t28 * t257;
2156:   t261 = t108 * t11;
2157:   t263 = t7 * t35;
2158:   t268 = ZB * t61 * t35;
2159:   t273 = t96 * t108 * t160;
2160:   t274 = t157 * ZB;
2161:   t276 = t274 * t148 * t35;
2162:   t279 = t101 * t21;
2163:   t282 = 0.3141592654e1 * xc;
2164:   t283 = t59 * t36;
2165:   t284 = t282 * t283;
2166:   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;
2167:   t290 = t1 * t11;
2168:   t291 = t96 * t290;
2169:   t297 = t59 * t61;
2170:   t298 = t297 * t127;
2171:   t300 = ZB * t36;
2172:   t301 = t227 * t300;
2173:   t304 = t1 * t59;
2174:   t305 = t184 * t35;
2175:   t310 = t46 * ZB;
2176:   t311 = t184 * ZA;
2177:   t312 = t310 * t311;
2178:   t314 = t60 * t21;
2179:   t317 = t1 * ZA;
2180:   t318 = ZB * t35;
2181:   t321 = t1 * t256;
2182:   t324 = t96 * t261;
2183:   t325 = t10 * t157;
2184:   t326 = t325 * t124;
2185:   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;
2186:   t331 = t28 * t124;
2187:   t334 = 0.3141592654e1 * t15;
2188:   t335 = t334 * t127;
2189:   t338 = t35 * ZA;
2190:   t341 = t46 * t256;
2191:   t344 = t46 * t11;
2192:   t346 = t46 * t59;
2193:   t348 = t297 * t35;
2194:   t351 = ZA * t10;
2195:   t352 = t351 * t300;
2196:   t355 = t1 * ZB;
2197:   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;
2198:   t363 = t36 * t184;
2199:   t364 = t87 * t363;
2200:   t368 = t47 * t73 * t7;
2201:   t373 = t160 * t157;
2202:   t374 = t373 * t124;
2203:   t377 = t311 * t35;
2204:   t380 = t12 * t62;
2205:   t386 = ZB * t10 * ZA * t15 * t20;
2206:   t389 = t87 * t66;
2207:   t393 = t56 * t1 * t10;
2208:   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;
2209:   t412 = t11 * t14 * t127;
2210:   t416 = t11 * t19;
2211:   t417 = t416 * t61;
2212:   t421 = t96 * t2 * ZA;
2213:   t426 = t56 * nz * ZA;
2214:   t427 = t318 * t14;
2215:   t428 = t49 * t427;
2216:   t431 = t82 * t29;
2217:   t434 = t87 * t21;
2218:   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;
2219:   t443 = t184 * t20;
2220:   t447 = t61 * 0.3141592654e1;
2221:   t448 = t447 * t11;
2222:   t450 = t49 * t268;
2223:   t453 = t60 * t42;
2224:   t456 = t41 * t202;
2225:   t463 = t101 * t443;
2226:   t469 = t41 * xc * t20;
2227:   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;
2228:   t482 = t108 * t10;
2229:   t492 = nz * t46;
2230:   t493 = t492 * t11;
2231:   t495 = t282 * t19 * t184;
2232:   t498 = t56 * t290;
2233:   t499 = t325 * t162;
2234:   t502 = t416 * t14;
2235:   t504 = t60 * t207;
2236:   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;
2237:   t508 = t101 * t162;
2238:   t512 = t41 * t115 * xc;
2239:   t515 = t87 * t42;
2240:   t520 = ZB * t184;
2241:   t522 = t227 * t520 * t18;
2242:   t525 = t492 * t59;
2243:   t528 = t6 * t59;
2244:   t532 = t520 * t20;
2245:   t533 = t351 * t532;
2246:   t539 = t447 * t59;
2247:   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;
2248:   t551 = t87 * t162;
2249:   t554 = t351 * t229;
2250:   t560 = t59 * t19;
2251:   t561 = t560 * t14;
2252:   t564 = t101 * t202;
2253:   t567 = t87 * t252;
2254:   t573 = t227 * t228 * t115;
2255:   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;
2256:   t579 = t82 * t202;
2257:   t591 = t282 * t115 * t59;
2258:   t598 = t101 * t66;
2259:   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;
2260:   t608 = t373 * t162;
2261:   t611 = t59 * t184;
2262:   t617 = t101 * t29;
2263:   t624 = t227 * ZB * t18 * t15;
2264:   t629 = t157 * t59;
2265:   t630 = t629 * t124;
2266:   t633 = t3 * t6;
2267:   t634 = t175 * t283;
2268:   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;
2269:   t645 = t41 * t29;
2270:   t648 = t2 * 0.3141592654e1;
2271:   t649 = t648 * xc;
2272:   t650 = t560 * t184;
2273:   t656 = t56 * t1 * t157;
2274:   t659 = t87 * t128;
2275:   t662 = t96 * t482;
2276:   t663 = t629 * t162;
2277:   t671 = t161 * t124;
2278:   t674 = t218 * t127;
2279:   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;
2280:   t714 = t334 * t19;
2281:   t719 = t12 * t42;
2282:   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;
2283:   t730 = xc * t19;
2284:   t735 = t59 * t256 * t14;
2285:   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;
2286:   t755 = t28 * t21;
2287:   t759 = t274 * t338 * t14;
2288:   t767 = t11 * t35;
2289:   t768 = t767 * t14;
2290:   t778 = t560 * t61;
2291:   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;
2292:   t786 = t12 * t443;
2293:   t790 = t282 * t59 * t20;
2294:   t796 = t59 * t14 * t127;
2295:   t806 = t41 * t21;
2296:   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;
2297:   t819 = t282 * t15 * t127;
2298:   t822 = t101 * t363;
2299:   t830 = t11 * t256 * t14;
2300:   t835 = t227 * t532;
2301:   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;
2302:   t845 = t87 * t202;
2303:   t854 = t338 * t15;
2304:   t859 = t12 * t207;
2305:   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;
2306:   t880 = t60 * t443;
2307:   t891 = t101 * t128;
2308:   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;
2309:   t903 = t179 * t19;
2310:   t920 = t56 * t1 * t160;
2311:   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;
2312:   t932 = t87 * t29;
2313:   t945 = t82 * t21;
2314:   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;
2315:   t971 = t282 * t127;
2316:   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;
2317:   t997 = xc * t127;
2318:   t998 = t997 * t59;
2319:   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;
2320:   t1006 = t2 * t59;
2321:   t1017 = xc * t35;
2322:   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;
2323:   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;
2324:   t1070 = t15 * t19;
2325:   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;
2326:   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;
2327:   t1119 = t321 * t46;
2328:   t1122 = t157 * t11;
2329:   t1123 = t1122 * t2;
2330:   t1124 = t184 * t46;
2331:   t1128 = t108 * nz;
2332:   t1132 = t7 * t7;
2333:   t1133 = t1132 * t11;
2334:   t1134 = t1133 * t108;
2335:   t1135 = t15 * t46;
2336:   t1139 = t7 * ZA;
2337:   t1140 = t1139 * ZB;
2338:   t1141 = t1 * t35;
2339:   t1145 = t629 * t2;
2340:   t1146 = t1135 * t730;
2341:   t1149 = t157 * t1128;
2342:   t1150 = t1149 * xc;
2343:   t1153 = t46 * xc;
2344:   t1154 = t1153 * t127;
2345:   t1158 = t184 * t1 * t46;
2346:   t1161 = t46 * t46;
2347:   t1162 = t35 * t1161;
2348:   t1166 = t7 * t1;
2349:   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;
2350:   t1171 = t1161 * t184;
2351:   t1175 = t1122 * nz;
2352:   t1176 = t15 * t1161;
2353:   t1180 = t1132 * ZA;
2354:   t1181 = t1180 * t355;
2355:   t1182 = t1176 * t1017;
2356:   t1185 = t1161 * xc;
2357:   t1189 = t1133 * t1;
2358:   t1192 = t108 * t1;
2359:   t1193 = t1132 * t1192;
2360:   t1195 = t10 * t35;
2361:   t1199 = t157 * t15;
2362:   t1203 = t1141 * t46;
2363:   t1211 = t184 * t108;
2364:   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;
2365:   t1221 = t256 * t1161;
2366:   t1224 = t35 * t108;
2367:   t1233 = t7 * t256;
2368:   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;
2369:   t1240 = t1135 * t1195;
2370:   t1252 = t629 * t127;
2371:   t1263 = t1171 * ZA;
2372:   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;
2373:   t1283 = t1199 * t19;
2374:   t1287 = t1199 * t127;
2375:   t1289 = t59 * nz * t1161;
2376:   t1293 = t157 * nz * xc;
2377:   t1304 = t1132 * t108;
2378:   t1310 = t263 * ZB;
2379:   t1316 = t2 * t15;
2380:   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;
2381:   t1330 = t1132 * t15;
2382:   t1336 = t1132 * t1;
2383:   t1338 = t1162 * t179;
2384:   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;
2385:   t1376 = t7 * t184;
2386:   t1380 = t1176 * t1195;
2387:   t1393 = t1330 * t35;
2388:   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;
2389:   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;
2390:   _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);
2391:   /****************************************************************************************/
2392:   t1 = nz * nz;
2393:   t2 = t1 * xc;
2394:   t3 = ZB * ZB;
2395:   t5 = t2 * 0.3141592654e1 * t3;
2396:   t6 = nx * 0.3141592654e1;
2397:   t7 = t6 * xc;
2398:   t8 = PetscCosReal(t7);
2399:   t9 = nx * nx;
2400:   t10 = t8 * t9;
2401:   t11 = nz * 0.3141592654e1;
2402:   t12 = PetscExpReal(t11);
2403:   t13 = t12 * t12;
2404:   t16 = PetscExpReal(xc * nz * 0.3141592654e1);
2405:   t17 = t16 * t16;
2406:   t18 = t17 * t16;
2407:   t19 = t17 * t17;
2408:   t20 = t19 * t18;
2409:   t21 = t13 * t20;
2410:   t22 = t10 * t21;
2411:   t25 = ZA * ZA;
2412:   t26 = t1 * t25;
2413:   t27 = xc * 0.3141592654e1;
2414:   t28 = t26 * t27;
2415:   t29 = t19 * t16;
2416:   t30 = t13 * t13;
2417:   t31 = t29 * t30;
2418:   t35 = t9 * nx;
2419:   t36 = t3 * t35;
2420:   t37 = PetscSinReal(t6);
2421:   t38 = t13 * t12;
2422:   t39 = t37 * t38;
2423:   t40 = t39 * t19;
2424:   t42 = t1 * t1;
2425:   t43 = nx * t42;
2426:   t44 = xc * xc;
2427:   t45 = t25 * t44;
2428:   t46 = t43 * t45;
2429:   t47 = 0.3141592654e1 * 0.3141592654e1;
2430:   t48 = t47 * t37;
2431:   t49 = t17 * t38;
2432:   t54 = 0.3141592654e1 * t35;
2433:   t55 = ZA * nz * t54;
2434:   t56 = t37 * ZB;
2435:   t57 = t19 * t12;
2436:   t61 = t25 * t8;
2437:   t62 = t61 * t9;
2438:   t63 = nz * t30;
2439:   t64 = t63 * t16;
2440:   t67 = t1 * nz;
2441:   t69 = t47 * ZB;
2442:   t70 = t67 * t44 * t69;
2443:   t75 = nx * t3;
2444:   t76 = t75 * t37;
2445:   t77 = t67 * 0.3141592654e1;
2446:   t78 = t19 * t19;
2447:   t79 = t78 * t12;
2448:   t80 = t77 * t79;
2449:   t82 = t3 * t38;
2450:   t84 = t54 * t37;
2451:   t87 = PetscSinReal(t7);
2452:   t88 = t29 * t87;
2453:   t89 = t47 * t44;
2454:   t93 = nx * t25;
2455:   t94 = t87 * t42;
2456:   t95 = t93 * t94;
2457:   t96 = t47 * xc;
2458:   t97 = t13 * t29;
2459:   t98 = t96 * t97;
2460:   t101 = t87 * t67;
2461:   t102 = t93 * t101;
2462:   t103 = t13 * t18;
2463:   t107 = t47 * t35;
2464:   t108 = t26 * t107;
2465:   t109 = t37 * t44;
2466:   t110 = t19 * t17;
2467:   t111 = t12 * t110;
2468:   t116 = t37 * t19 * t12;
2469:   t118 = t37 * xc;
2470:   t119 = ZB * t19;
2471:   t120 = t119 * t12;
2472:   t121 = t118 * t120;
2473:   t125 = xc * t3;
2474:   t126 = t1 * t47 * t125;
2475:   t127 = t35 * t37;
2476:   t128 = t38 * t19;
2477:   t129 = t127 * t128;
2478:   t132 = t26 * 0.3141592654e1;
2479:   t133 = t16 * t13;
2480:   t134 = t10 * t133;
2481:   t137 = 0.3141592654e1 * ZB;
2482:   t138 = t2 * t137;
2483:   t139 = ZA * t8;
2484:   t140 = t9 * t13;
2485:   t145 = t30 * t18;
2486:   t146 = t10 * t145;
2487:   t149 = t3 * t8;
2488:   t150 = t149 * t9;
2489:   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;
2490:   t154 = t42 * nz;
2491:   t155 = nx * t154;
2492:   t156 = t44 * xc;
2493:   t157 = t47 * 0.3141592654e1;
2494:   t158 = t156 * t157;
2495:   t159 = t155 * t158;
2496:   t162 = t56 * ZA * t19 * t12;
2497:   t165 = t77 * t49;
2498:   t167 = t1 * t3;
2499:   t168 = t167 * t89;
2500:   t169 = t127 * t49;
2501:   t172 = t37 * t67;
2502:   t173 = t75 * t172;
2503:   t174 = t38 * t110;
2504:   t175 = t27 * t174;
2505:   t179 = t47 * t25;
2506:   t181 = t10 * t97;
2507:   t184 = t27 * t31;
2508:   t187 = t67 * t47;
2509:   t188 = t44 * t3;
2510:   t189 = t187 * t188;
2511:   t192 = t25 * t35;
2512:   t193 = t37 * t17;
2513:   t194 = t193 * t12;
2514:   t196 = nx * ZA;
2515:   t197 = t196 * t172;
2516:   t198 = ZB * t38;
2517:   t199 = t198 * t19;
2518:   t204 = t1 * t12 * t110;
2519:   t207 = nx * ZB;
2520:   t209 = t1 * ZA;
2521:   t215 = t67 * t3;
2522:   t216 = t47 * t8;
2523:   t217 = t215 * t216;
2524:   t218 = t9 * xc;
2525:   t222 = nx * t67;
2526:   t223 = t222 * t27;
2527:   t224 = t3 * t87;
2528:   t228 = t167 * t107;
2529:   t232 = t26 * t96;
2530:   t235 = t207 * t94;
2531:   t236 = t47 * ZA;
2532:   t243 = xc * t13;
2533:   t244 = t243 * t29;
2534:   t248 = t25 * nz;
2535:   t249 = t248 * 0.3141592654e1;
2536:   t253 = ZB * ZA;
2537:   t254 = t253 * t8;
2538:   t255 = t9 * nz;
2539:   t256 = t30 * t16;
2540:   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;
2541:   t263 = t43 * t179;
2542:   t267 = t3 * nz;
2543:   t268 = t267 * t54;
2544:   t269 = t118 * t57;
2545:   t272 = t39 * t1;
2546:   t274 = t67 * t25;
2547:   t275 = t274 * t158;
2548:   t278 = t75 * t87;
2549:   t279 = t77 * t103;
2550:   t282 = t25 * t38;
2551:   t285 = ZA * t38;
2552:   t290 = t267 * 0.3141592654e1;
2553:   t296 = t77 * t111;
2554:   t298 = t196 * t37;
2555:   t299 = t1 * ZB;
2556:   t303 = t37 * t42;
2557:   t304 = t196 * t303;
2558:   t308 = t77 * t57;
2559:   t310 = t26 * t89;
2560:   t313 = t77 * t128;
2561:   t316 = t101 * t27;
2562:   t319 = t93 * t87;
2563:   t320 = t77 * t97;
2564:   t323 = t127 * t57;
2565:   t326 = t10 * nz;
2566:   t329 = t118 * t174;
2567:   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;
2568:   t335 = t75 * t101;
2569:   t336 = t27 * t21;
2570:   t342 = t77 * t133;
2571:   t347 = t209 * t137;
2572:   t350 = t9 * t1;
2573:   t351 = t149 * t350;
2574:   t355 = t37 * t78 * t12;
2575:   t359 = t93 * t303;
2576:   t367 = t172 * 0.3141592654e1;
2577:   t369 = t96 * t103;
2578:   t376 = t209 * t107;
2579:   t379 = t10 * t103;
2580:   t383 = t207 * t101;
2581:   t389 = 0.3141592654e1 * ZA;
2582:   t390 = t222 * t389;
2583:   t391 = t87 * ZB;
2584:   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;
2585:   t402 = t39 * t110;
2586:   t404 = t193 * t38;
2587:   t406 = t127 * t174;
2588:   t408 = t167 * 0.3141592654e1;
2589:   t411 = t44 * t157;
2590:   t412 = t155 * t411;
2591:   t413 = t285 * t19;
2592:   t414 = t56 * t413;
2593:   t417 = ZA * t30;
2594:   t424 = t93 * t37;
2595:   t426 = t248 * t54;
2596:   t427 = t17 * t12;
2597:   t428 = t118 * t427;
2598:   t431 = t77 * t21;
2599:   t438 = ZA * t13;
2600:   t443 = t93 * t172;
2601:   t444 = t27 * t427;
2602:   t448 = t1 * t78 * t12;
2603:   t455 = t274 * t89;
2604:   t461 = t118 * t111;
2605:   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;
2606:   t469 = nz * t16 * t13;
2607:   t474 = t1 * t38;
2608:   t475 = t474 * t19;
2609:   t480 = t89 * t103;
2610:   t483 = t67 * ZA;
2611:   t484 = t483 * t411;
2612:   t485 = t127 * t120;
2613:   t488 = t127 * t111;
2614:   t497 = t77 * t427;
2615:   t502 = t27 * t97;
2616:   t508 = t1 * t19 * t12;
2617:   t511 = t155 * t25 * t156;
2618:   t512 = t157 * t37;
2619:   t513 = t512 * t128;
2620:   t527 = t1 * t17;
2621:   t528 = t527 * t38;
2622:   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;
2623:   t535 = t44 * t13;
2624:   t542 = t527 * t12;
2625:   t544 = nz * t13;
2626:   t545 = t544 * t20;
2627:   t548 = t75 * t303;
2628:   t549 = t96 * t111;
2629:   t552 = ZA * t35;
2630:   t553 = t552 * t37;
2631:   t562 = t43 * t96;
2632:   t563 = t3 * t37;
2633:   t564 = t563 * t128;
2634:   t579 = t474 * t110;
2635:   t590 = t9 * t30;
2636:   t591 = t590 * t18;
2637:   t595 = t127 * t427;
2638:   t598 = t77 * t174;
2639:   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;
2640:   t601 = t27 * t49;
2641:   t604 = t127 * t79;
2642:   t606 = ZB * t29;
2643:   t616 = t139 * t140 * t18;
2644:   t638 = t10 * t256;
2645:   t643 = t118 * t199;
2646:   t653 = t544 * t29;
2647:   t658 = t3 * t29;
2648:   t660 = t350 * t27;
2649:   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;
2650:   t670 = t274 * t411;
2651:   t673 = t118 * t49;
2652:   t694 = t155 * t45;
2653:   t713 = nz * t29 * t30;
2654:   t717 = t20 * t87;
2655:   t723 = t512 * t57;
2656:   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;
2657:   t734 = t43 * t89;
2658:   t735 = t563 * t427;
2659:   t740 = t75 * t94;
2660:   t744 = ZB * xc;
2661:   t750 = t563 * t57;
2662:   t754 = t218 * t103;
2663:   t771 = t127 * t199;
2664:   t776 = t89 * t174;
2665:   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;
2666:   t794 = t483 * t158;
2667:   t801 = t2 * 0.3141592654e1;
2668:   t818 = t215 * t411;
2669:   t827 = t96 * t174;
2670:   t837 = t37 * t12 * t110;
2671:   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;
2672:   t864 = t544 * t18;
2673:   t867 = t3 * t18;
2674:   t884 = t27 * t256;
2675:   t891 = t187 * t744;
2676:   t894 = t563 * t49;
2677:   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;
2678:   t904 = t27 * t111;
2679:   t907 = t118 * t128;
2680:   t915 = t89 * t145;
2681:   t947 = t139 * t140 * t29;
2682:   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;
2683:   t969 = t67 * t157 * t156 * t3;
2684:   t974 = t27 * t133;
2685:   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;
2686:   t1042 = t89 * t97;
2687:   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;
2688:   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;
2689:   t1103 = t42 * t1 * t157;
2690:   t1104 = t1103 * t25;
2691:   t1108 = t3 * t19;
2692:   t1112 = nz * t47;
2693:   t1113 = t9 * t9;
2694:   t1118 = t42 * t157;
2695:   t1119 = t1118 * t9;
2696:   t1120 = t25 * xc;
2697:   t1121 = t13 * t110;
2698:   t1122 = t1120 * t1121;
2699:   t1125 = t47 * t47;
2700:   t1126 = t67 * t1125;
2701:   t1127 = t1113 * ZA;
2702:   t1128 = t1126 * t1127;
2703:   t1129 = t19 * t13;
2704:   t1130 = t744 * t1129;
2705:   t1133 = t154 * t1125;
2706:   t1134 = t1133 * t9;
2707:   t1135 = t45 * t1129;
2708:   t1138 = t154 * t47;
2709:   t1139 = t25 * t30;
2710:   t1142 = t1126 * t1113;
2711:   t1145 = t125 * t1129;
2712:   t1148 = t1103 * xc;
2713:   t1149 = t3 * t13;
2714:   t1150 = t1149 * t17;
2715:   t1153 = t25 * t78;
2716:   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;
2717:   t1157 = t25 * t13;
2718:   t1158 = t1157 * t17;
2719:   t1161 = t13 * t17;
2720:   t1162 = t1120 * t1161;
2721:   t1165 = t3 * t78;
2722:   t1170 = t42 * t67 * t1125;
2723:   t1172 = t1108 * t13;
2724:   t1175 = t1 * t157;
2725:   t1176 = t1175 * t1113;
2726:   t1182 = t1120 * t1129;
2727:   t1189 = t110 * t9 * xc;
2728:   t1192 = t1149 * t110;
2729:   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;
2730:   t1209 = t17 * t30;
2731:   t1210 = t125 * t1209;
2732:   t1213 = t1138 * ZA;
2733:   t1214 = ZB * t30;
2734:   t1218 = t1157 * t110;
2735:   t1226 = t3 * t30;
2736:   t1237 = t1170 * t25;
2737:   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;
2738:   t1251 = t125 * t1121;
2739:   t1260 = t1120 * t1209;
2740:   t1263 = t1139 * t19;
2741:   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;
2742:   t1287 = t188 * t1129;
2743:   t1292 = t25 * t19;
2744:   t1296 = t187 * t9;
2745:   t1297 = t1226 * t19;
2746:   t1311 = t1112 * t1113;
2747:   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;
2748:   t1320 = t253 * t1129;
2749:   t1328 = t253 * t30 * t19;
2750:   t1333 = t125 * t1161;
2751:   t1343 = ZB * t44 * t1129;
2752:   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;
2753:   t1369 = t1133 * t9 * ZA;
2754:   t1378 = t187 * ZA;
2755:   t1383 = t1170 * ZA;
2756:   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;
2757:   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;

2759:   _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);
2760:   /****************************************************************************************/
2761:   /****************************************************************************************/

2763:   if (x>xc) {
2764:     _PC1=_PC1B; _PC2=_PC2B; _PC3=_PC3B; _PC4=_PC4B; Z=ZB;
2765:   }
2766:   else {
2767:     _PC1=_PC1A; _PC2=_PC2A; _PC3=_PC3A; _PC4=_PC4A; Z=ZA;
2768:   }
2769:   /****************************************************************************************/
2770:   /****************************************************************************************/
2771:   t1 = nz * nz;
2772:   t2 = t1 * t1;
2773:   t3 = t2 * nz;
2774:   t4 = x * t3;
2775:   t5 = 0.3141592654e1 * 0.3141592654e1;
2776:   t6 = t5 * 0.3141592654e1;
2777:   t11 = _PC3 * t6;
2778:   t12 = x * nz;
2779:   t13 = nx * nx;
2780:   t14 = t13 * t13;
2781:   t15 = t12 * t14;
2782:   t19 = PetscExpReal(t12 * 0.3141592654e1);
2783:   t20 = t19 * t19;
2784:   t21 = t4 * t20;
2785:   t24 = _PC1 * t5;
2786:   t25 = Z * t20;
2787:   t29 = _PC1 * t6;
2788:   t30 = t29 * Z;
2789:   t31 = t1 * nz;
2790:   t32 = x * t31;
2791:   t33 = t32 * t13;
2792:   t36 = t11 * x;
2793:   t41 = nz * t20;
2794:   t45 = t6 * _PC4;
2795:   t49 = t20 * t1;
2796:   t51 = _PC2 * Z;
2797:   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;
2798:   t58 = t32 * t6;
2799:   t59 = _PC4 * t20;
2800:   t63 = t20 * t13;
2801:   t67 = t12 * t6;
2802:   t68 = t20 * t14;
2803:   t87 = t49 * t13;
2804:   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;
2805:   t106 = _PC3 * t5;
2806:   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;
2807:   t129 = PetscSinReal(nx * 0.3141592654e1 * x);
2808:   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;
2809:   t158 = t5 * Z;

2811:   u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14);
2812:   /****************************************************************************************/
2813:   /****************************************************************************************/
2814:   t1 = nz * nz;
2815:   t2 = t1 * nz;
2816:   t3 = x * t2;
2817:   t4 = 0.3141592654e1 * 0.3141592654e1;
2818:   t5 = t4 * 0.3141592654e1;
2819:   t6 = t3 * t5;
2820:   t7 = _PC2 * Z;
2821:   t8 = nx * nx;
2822:   t12 = t1 * t1;
2823:   t13 = t12 * nz;
2824:   t14 = x * t13;
2825:   t15 = t5 * _PC4;
2826:   t16 = x * nz;
2827:   t18 = PetscExpReal(t16 * 0.3141592654e1);
2828:   t19 = t18 * t18;
2829:   t23 = t16 * t5;
2830:   t24 = t8 * t8;
2831:   t28 = _PC3 * t5;
2832:   t29 = t14 * t19;
2833:   t32 = _PC1 * t5;
2834:   t33 = t32 * Z;
2835:   t34 = t16 * t24;
2836:   t37 = _PC4 * t19;
2837:   t45 = _PC2 * t4;
2838:   t53 = t19 * t8;
2839:   t58 = _PC4 * t4;
2840:   t60 = t1 * t19 * t8;
2841:   t63 = t19 * t24;
2842:   t67 = t3 * t8;
2843:   t73 = nz * t19;
2844:   t86 = t28 * x;
2845:   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;
2846:   t94 = Z * t12;
2847:   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;
2848:   t146 = PetscCosReal(nx * 0.3141592654e1 * x);
2849:   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;
2850:   t159 = t4 * Z;

2852:   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);
2853:   /****************************************************************************************/
2854:   /****************************************************************************************/
2855:   t1 = 0.3141592654e1 * 0.3141592654e1;
2856:   t2 = t1 * 0.3141592654e1;
2857:   t3 = _PC1 * t2;
2858:   t4 = t3 * Z;
2859:   t5 = nz * nz;
2860:   t6 = t5 * t5;
2861:   t7 = t6 * nz;
2862:   t8 = x * t7;
2863:   t9 = x * nz;
2864:   t11 = PetscExpReal(t9 * 0.3141592654e1);
2865:   t12 = t11 * t11;
2866:   t13 = t8 * t12;
2867:   t16 = t5 * nz;
2868:   t17 = x * t16;
2869:   t18 = t17 * t2;
2870:   t19 = _PC4 * t12;
2871:   t20 = nx * nx;
2872:   t24 = t2 * _PC4;
2873:   t28 = _PC3 * t2;
2874:   t29 = t28 * x;
2875:   t30 = t12 * nz;
2876:   t31 = t20 * t20;
2877:   t40 = _PC2 * Z;
2878:   t44 = t9 * t2;
2879:   t48 = t12 * t20;
2880:   t52 = t17 * t20;
2881:   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;
2882:   t58 = t9 * t31;
2883:   t61 = _PC3 * t1;
2884:   t62 = t12 * t31;
2885:   t73 = t5 * t20;
2886:   t78 = _PC1 * t1;
2887:   t90 = Z * t12;
2888:   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;
2889:   t101 = PetscCosReal(nx * 0.3141592654e1 * x);
2890:   t102 = t11 * t101;
2891:   t109 = t12 * t5;
2892:   t110 = t109 * t20;
2893:   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;
2894:   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;
2895:   t159 = t1 * t11;

2897:   u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31);
2898:   /****************************************************************************************/
2899:   /****************************************************************************************/
2900:   t1 = _PC2 * Z;
2901:   t2 = 0.3141592654e1 * 0.3141592654e1;
2902:   t3 = t2 * 0.3141592654e1;
2903:   t4 = nz * nz;
2904:   t5 = t4 * t4;
2905:   t6 = t5 * t4;
2906:   t8 = t3 * t6 * x;
2907:   t11 = x * t4;
2908:   t12 = t11 * t3;
2909:   t15 = PetscExpReal(x * nz * 0.3141592654e1);
2910:   t16 = t15 * t15;
2911:   t17 = _PC3 * t16;
2912:   t18 = nx * nx;
2913:   t19 = t18 * t18;
2914:   t23 = t5 * nz;
2915:   t24 = t2 * t23;
2916:   t28 = t1 * t3;
2917:   t29 = t6 * x;
2918:   t30 = t29 * t16;
2919:   t33 = _PC4 * t3;
2920:   t34 = t5 * x;
2921:   t35 = t34 * t18;
2922:   t41 = PetscSinReal(nx * 0.3141592654e1 * x);
2923:   t47 = t11 * t19;
2924:   t54 = t3 * _PC3;
2925:   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;
2926:   t58 = 0.3141592654e1 * t16;
2927:   t60 = t2 * _PC4;
2928:   t69 = t4 * nz;
2929:   t73 = t1 * t2;
2930:   t75 = t69 * t16 * t18;
2931:   t79 = x * t16;
2932:   t83 = nz * t16;
2933:   t84 = t83 * t19;
2934:   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;
2935:   t97 = t34 * t3;
2936:   t101 = Z * _PC1;
2937:   t102 = t16 * t19;
2938:   t106 = t16 * t18;
2939:   t127 = t2 * t69;
2940:   t131 = t2 * nz;
2941:   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;
2942:   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;

2944:   u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19);

2946:   /****************************************************************************************/
2947:   /****************************************************************************************/

2949:   u5 = (PetscReal)(-2*Z*nz*PETSC_PI*u2-u3*2*nz*PETSC_PI)*PetscCosReal(nz*PETSC_PI*z); /* pressure */

2951:   u6 = (PetscReal)(u3*2*nz*PETSC_PI + 4*Z*nz*PETSC_PI*u2)*PetscCosReal(nz*PETSC_PI*z); /* zz stress */
2952:   sum5 +=u5;
2953:   sum6 +=u6;

2955:   u1 *= PetscCosReal(nz*PETSC_PI*z); /* x velocity */
2956:   sum1 += u1;
2957:   u2 *= PetscSinReal(nz*PETSC_PI*z); /* z velocity */
2958:   sum2 += u2;
2959:   u3 *= 2*nz*PETSC_PI*PetscCosReal(nz*PETSC_PI*z); /* xx stress */
2960:   sum3 += u3;
2961:   u4 *= 2*nz*PETSC_PI*PetscSinReal(nz*PETSC_PI*z); /* zx stress */
2962:   sum4 += u4;

2964:   /* Output */
2965:   if (mu) {
2966:     *mu = Z;
2967:   }
2968:   if (vel) {
2969:     vel[0] = sum1;
2970:     vel[1] = sum2;
2971:   }
2972:   if (p) {
2973:     (*p) = sum5;
2974:   }
2975:   if (s) {
2976:     s[0] = sum3;
2977:     s[1] = sum4;
2978:     s[2] = sum6;
2979:   }
2980:   if (gamma) {
2981:     /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */
2982:     gamma[0] = (sum3+sum5)/(2.0*Z);
2983:     gamma[1] = (sum4)/(2.0*Z);
2984:     gamma[2] = (sum6+sum5)/(2.0*Z);
2985:   }
2986:   return 0;
2987: }

2989: static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx)
2990: {
2991:   Parameter     *s = (Parameter *) ctx;

2993:   SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL);
2994:   return 0;
2995: }

2997: static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx)
2998: {
2999:   Parameter     *s = (Parameter *) ctx;

3001:   SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL);
3002:   return 0;
3003: }

3005: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
3006: {
3007:   PetscInt       sol;

3011:   options->solType = SOLKX;

3013:   PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");
3014:   sol  = options->solType;
3015:   PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL);
3016:   options->solType = (SolutionType) sol;
3017:   PetscOptionsEnd();
3018:   return 0;
3019: }

3021: static PetscErrorCode SetUpParameters(AppCtx *user)
3022: {
3023:   PetscBag       bag;
3024:   Parameter     *p;

3027:   /* setup PETSc parameter bag */
3028:   PetscBagGetData(user->bag, (void **) &p);
3029:   PetscBagSetName(user->bag, "par", "Problem parameters");
3030:   bag  = user->bag;
3031:   switch (user->solType) {
3032:   case SOLKX:
3033:     PetscBagRegisterInt(bag,  &p->n, 1,   "n", "x-wavelength for forcing variation");
3034:     PetscBagRegisterInt(bag,  &p->m, 1,   "m", "z-wavelength for forcing variation");
3035:     PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation");
3036:     break;
3037:   case SOLCX:
3038:     PetscBagRegisterInt(bag,  &p->n,    1,   "n",    "x-wavelength for forcing variation");
3039:     PetscBagRegisterInt(bag,  &p->m,    1,   "m",    "z-wavelength for forcing variation");
3040:     PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc");
3041:     PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc");
3042:     PetscBagRegisterReal(bag, &p->xc,   0.5, "xc",   "x-coordinate of the viscosity jump");
3043:     break;
3044:   default:
3045:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3046:   }
3047:   PetscBagSetFromOptions(bag);
3048:   PetscBagViewFromOptions(bag, NULL, "-param_view");
3049:   return 0;
3050: }

3052: /* Make split labels so that we can have corners in multiple labels */
3053: static PetscErrorCode CreateSplitLabels(DM dm)
3054: {
3055:   const char    *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"};
3056:   PetscInt       ids[4]   = {1, 2, 3, 4};
3057:   DMLabel        label;
3058:   IS             is;
3059:   PetscInt       f;

3062:   for (f = 0; f < 4; ++f) {
3063:     DMCreateLabel(dm, names[f]);
3064:     DMGetStratumIS(dm, "marker", ids[f],  &is);
3065:     if (!is) continue;
3066:     DMGetLabel(dm, names[f], &label);
3067:     DMLabelInsertIS(label, is, 1);
3068:     ISDestroy(&is);
3069:   }
3070:   return 0;
3071: }

3073: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
3074: {
3075:   DM             cdm;

3078:   DMCreate(comm, dm);
3079:   DMSetType(*dm, DMPLEX);
3080:   DMSetFromOptions(*dm);
3081:   cdm  = *dm;
3082:   while (cdm) {
3083:     CreateSplitLabels(cdm);
3084:     DMGetCoarseDM(cdm, &cdm);
3085:   }
3086:   DMViewFromOptions(*dm, NULL, "-dm_view");
3087:   return 0;
3088: }

3090: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
3091: {
3092:   PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3093:   PetscDS        prob;
3094:   DMLabel        label;
3095:   const PetscInt id  = 1;
3096:   PetscInt       dim, comp;
3097:   Parameter     *ctx;
3098:   void          *data;

3101:   DMGetDimension(dm, &dim);
3102:   DMGetDS(dm, &prob);
3103:   switch (user->solType) {
3104:   case SOLKX:
3105:     PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx);
3106:     PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);
3107:     PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  stokes_momentum_vel_J_kx);
3108:     PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  stokes_momentum_pres_J, NULL);
3109:     PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL,  NULL);
3110:     PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);
3111:     PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL);
3112:     break;
3113:   case SOLCX:
3114:     PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx);
3115:     PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);
3116:     PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  stokes_momentum_vel_J_cx);
3117:     PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  stokes_momentum_pres_J, NULL);
3118:     PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL,  NULL);
3119:     PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);
3120:     PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL);
3121:     break;
3122:   default:
3123:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3124:   }
3125:   PetscBagGetData(user->bag, &data);
3126:   switch (dim) {
3127:   case 2:
3128:     switch (user->solType) {
3129:     case SOLKX:
3130:       PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data);
3131:       PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data);
3132:       break;
3133:     case SOLCX:
3134:       PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data);
3135:       PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data);
3136:       break;
3137:     default:
3138:       SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]);
3139:     }
3140:     break;
3141:   default:
3142:     SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %D", dim);
3143:   }
3144:   /* Setup constants */
3145:   {
3146:     Parameter *param;

3148:     PetscBagGetData(user->bag, (void **) &param);
3149:     switch (user->solType) {
3150:     case SOLKX:
3151:     {
3152:       PetscScalar constants[3];

3154:       constants[0] = param->m;
3155:       constants[1] = param->n;
3156:       constants[2] = param->B;
3157:       PetscDSSetConstants(prob, 3, constants);
3158:     }
3159:     break;
3160:     case SOLCX:
3161:     {
3162:       PetscScalar constants[5];

3164:       constants[0] = param->m;
3165:       constants[1] = param->n;
3166:       constants[2] = param->etaA;
3167:       constants[3] = param->etaB;
3168:       constants[4] = param->xc;
3169:       PetscDSSetConstants(prob, 5, constants);
3170:     }
3171:     break;
3172:     default: SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType);
3173:     }
3174:   }
3175:   /* Setup Boundary Conditions */
3176:   PetscDSGetExactSolution(prob, 0, &exactFunc, (void **) &ctx);
3177:   comp = 1;
3178:   DMGetLabel(dm, "markerBottom", &label);
3179:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3180:   comp = 0;
3181:   DMGetLabel(dm, "markerRight", &label);
3182:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3183:   comp = 1;
3184:   DMGetLabel(dm, "markerTop", &label);
3185:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3186:   comp = 0;
3187:   DMGetLabel(dm, "markerLeft", &label);
3188:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", label, 1, &id, 0, 1, &comp, (void (*)(void)) exactFunc, NULL, ctx, NULL);
3189:   return 0;
3190: }

3192: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt origField, PetscInt field, MatNullSpace *nullspace)
3193: {
3194:   Vec              vec;
3195:   PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, one};

3199:   funcs[field] = one;
3200:   {
3201:     PetscDS ds;
3202:     DMGetDS(dm, &ds);
3203:     PetscObjectViewFromOptions((PetscObject) ds, NULL, "-ds_view");
3204:   }
3205:   DMCreateGlobalVector(dm, &vec);
3206:   DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
3207:   VecNormalize(vec, NULL);
3208:   MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullspace);
3209:   VecDestroy(&vec);
3210:   /* New style for field null spaces */
3211:   {
3212:     PetscObject  pressure;
3213:     MatNullSpace nullspacePres;

3215:     DMGetField(dm, field, NULL, &pressure);
3216:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);
3217:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nullspacePres);
3218:     MatNullSpaceDestroy(&nullspacePres);
3219:   }
3220:   return 0;
3221: }

3223: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
3224: {
3225:   DM             cdm = dm;
3226:   PetscFE        fe[2];
3227:   DMPolytopeType ct;
3228:   PetscInt       dim, cStart;
3229:   PetscBool      simplex;

3232:   DMGetDimension(dm, &dim);
3233:   DMPlexGetHeightStratum(dm, 0, &cStart, NULL);
3234:   DMPlexGetCellType(dm, cStart, &ct);
3235:   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE;
3236:   /* Create discretization of solution fields */
3237:   PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]);
3238:   PetscObjectSetName((PetscObject) fe[0], "velocity");
3239:   PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]);
3241:   PetscObjectSetName((PetscObject) fe[1], "pressure");
3242:   /* Set discretization and boundary conditions for each mesh */
3243:   DMSetField(dm, 0, NULL, (PetscObject) fe[0]);
3244:   DMSetField(dm, 1, NULL, (PetscObject) fe[1]);
3245:   DMCreateDS(dm);
3246:   SetupProblem(dm, user);
3247:   while (cdm) {
3248:     DMCopyDisc(dm, cdm);
3249:     DMSetNullSpaceConstructor(cdm, 1, CreatePressureNullSpace);
3250:     DMGetCoarseDM(cdm, &cdm);
3251:   }
3252:   PetscFEDestroy(&fe[0]);
3253:   PetscFEDestroy(&fe[1]);
3254:   {
3255:     PetscObject  pressure;
3256:     MatNullSpace nullSpacePres;

3258:     DMGetField(dm, 1, NULL, &pressure);
3259:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres);
3260:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nullSpacePres);
3261:     MatNullSpaceDestroy(&nullSpacePres);
3262:   }
3263:   return 0;
3264: }

3266: /* Add a vector in the nullspace to make the continuum integral 0.

3268:    If int(u) = a and int(n) = b, then int(u - a/b n) = a - a/b b = 0
3269: */
3270: static void pressure(PetscInt dim, PetscInt Nf, PetscInt NfAux,
3271:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
3272:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
3273:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar p[])
3274: {
3275:   p[0] = u[uOff[1]];
3276: }
3277: static PetscErrorCode CorrectDiscretePressure(DM dm, MatNullSpace nullspace, Vec u, AppCtx *user)
3278: {
3279:   PetscDS        ds;
3280:   const Vec     *nullvecs;
3281:   PetscScalar    pintd, intc[2], intn[2];
3282:   MPI_Comm       comm;

3285:   PetscObjectGetComm((PetscObject) dm, &comm);
3286:   DMGetDS(dm, &ds);
3287:   PetscDSSetObjective(ds, 1, pressure);
3288:   MatNullSpaceGetVecs(nullspace, NULL, NULL, &nullvecs);
3289:   VecDot(nullvecs[0], u, &pintd);
3291:   DMPlexComputeIntegralFEM(dm, nullvecs[0], intn, user);
3292:   DMPlexComputeIntegralFEM(dm, u, intc, user);
3293:   VecAXPY(u, -intc[1]/intn[1], nullvecs[0]);
3294:   DMPlexComputeIntegralFEM(dm, u, intc, user);
3296:   return 0;
3297: }

3299: static PetscErrorCode SNESConvergenceCorrectPressure(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gnorm, PetscReal f, SNESConvergedReason *reason, void *user)
3300: {
3302:   SNESConvergedDefault(snes, it, xnorm, gnorm, f, reason, user);
3303:   if (*reason > 0) {
3304:     DM           dm;
3305:     Mat          J;
3306:     Vec          u;
3307:     MatNullSpace nullspace;

3309:     SNESGetDM(snes, &dm);
3310:     SNESGetSolution(snes, &u);
3311:     SNESGetJacobian(snes, &J, NULL, NULL, NULL);
3312:     MatGetNullSpace(J, &nullspace);
3314:     CorrectDiscretePressure(dm, nullspace, u, (AppCtx *) user);
3315:   }
3316:   return 0;
3317: }

3319: int main(int argc, char **argv)
3320: {
3321:   SNES            snes;      /* nonlinear solver */
3322:   DM              dm;        /* problem definition */
3323:   Vec             u,r;       /* solution, residual vectors */
3324:   Mat             J, M;      /* Jacobian and preconditiong matrix */
3325:   MatNullSpace    nullSpace; /* May be necessary for pressure */
3326:   AppCtx          user;      /* user-defined work context */
3327:   PetscErrorCode  (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero, zero};

3329:   PetscInitialize(&argc, &argv, NULL,help);
3330:   ProcessOptions(PETSC_COMM_WORLD, &user);
3331:   SNESCreate(PETSC_COMM_WORLD, &snes);
3332:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
3333:   SNESSetDM(snes, dm);
3334:   DMSetApplicationContext(dm, &user);
3335:   /* Setup problem parameters */
3336:   PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);
3337:   SetUpParameters(&user);
3338:   /* Setup problem */
3339:   SetupDiscretization(dm, &user);
3340:   DMPlexCreateClosureIndex(dm, NULL);

3342:   DMCreateGlobalVector(dm, &u);
3343:   VecDuplicate(u, &r);

3345:   DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
3346:   CreatePressureNullSpace(dm, 1, 1, &nullSpace);

3348:   { /* set tolerances */
3349:     KSP ksp;

3351:     SNESGetKSP(snes, &ksp);
3352:     KSPSetTolerances(ksp,1.e-2*PETSC_SMALL,PETSC_SMALL,PETSC_DEFAULT,PETSC_DEFAULT);
3353:   }

3355:   /* There should be a way to express this using the DM */
3356:   SNESSetFromOptions(snes);
3357:   SNESSetUp(snes);
3358:   SNESGetJacobian(snes, &J, &M, NULL, NULL);
3359:   MatSetNullSpace(J, nullSpace);
3360:   PetscObjectSetOptionsPrefix((PetscObject) M, "prec_");
3361:   MatSetFromOptions(M);
3362:   SNESSetConvergenceTest(snes, SNESConvergenceCorrectPressure, &user, NULL);

3364:   DMSNESCheckFromOptions(snes, u);
3365:   DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
3366:   PetscObjectSetName((PetscObject) u, "Solution");
3367:   SNESSolve(snes, NULL, u);
3368:   {
3369:     PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
3370:     void            *ectxs[2];
3371:     PetscDS          ds;
3372:     Vec              e;

3374:     DMGetDS(dm, &ds);
3375:     PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]);
3376:     PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]);

3378:     DMGetGlobalVector(dm, &e);
3379:     PetscObjectCompose((PetscObject) e, "__Vec_bc_zero__", (PetscObject) dm);
3380:     DMPlexComputeL2DiffVec(dm, 0.0, exacts, ectxs, u, e);
3381:     PetscObjectSetName((PetscObject) e, "Solution Error");
3382:     VecViewFromOptions(e, NULL, "-error_vec_view");
3383:     PetscObjectCompose((PetscObject) e, "__Vec_bc_zero__", NULL);
3384:     DMRestoreGlobalVector(dm, &e);
3385:   }
3386:   VecViewFromOptions(u, NULL, "-sol_vec_view");

3388:   MatNullSpaceDestroy(&nullSpace);
3389:   VecDestroy(&u);
3390:   VecDestroy(&r);
3391:   SNESDestroy(&snes);
3392:   DMDestroy(&dm);
3393:   PetscBagDestroy(&user.bag);
3394:   PetscFinalize();
3395:   return 0;
3396: }

3398: /*TEST

3400:   # 2D serial discretization tests
3401:   test:
3402:     suffix: p2p1
3403:     requires: triangle
3404:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3405:       -snes_error_if_not_converged -dmsnes_check .001 \
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: p2p1_gmg
3412:     requires: triangle
3413:     args: -dm_plex_separate_marker -dm_refine_hierarchy 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3414:       -snes_error_if_not_converged -dmsnes_check .001 \
3415:       -ksp_type fgmres -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 mg \
3418:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3419:   test:
3420:     suffix: p2p1_conv
3421:     requires: triangle
3422:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.2]
3423:     args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
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
3429:   test:
3430:     suffix: q2q1_conv
3431:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.1]
3432:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3433:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3434:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3435:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3436:         -fieldsplit_velocity_pc_type lu \
3437:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3438:   test:
3439:     suffix: q1p0_conv
3440:     # -dm_refine 2 gives L_2 convergence rate: [2.0, 1.0]
3441:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
3442:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3443:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3444:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3445:         -fieldsplit_velocity_pc_type lu \
3446:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu
3447:   test:
3448:     suffix: q2p1_conv
3449:     # -dm_refine 2 gives L_2 convergence rate: [3.0, 2.0]
3450:     args: -dm_plex_simplex 0 -dm_plex_separate_marker \
3451:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 \
3452:       -snes_error_if_not_converged -snes_convergence_estimate -convest_num_refine 2 \
3453:       -ksp_rtol 1.e-9 -ksp_error_if_not_converged -pc_use_amat \
3454:       -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 \
3455:         -fieldsplit_velocity_pc_type lu \
3456:         -fieldsplit_pressure_ksp_rtol 1.e-9 -fieldsplit_pressure_pc_type lu

3458:   # FETI-DP tests
3459:   testset:
3460:     output_file: output/ex69_q2p1fetidp.out
3461:     suffix: q2p1fetidp
3462:     requires: !single
3463:     nsize: 5
3464:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3465:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3466:       -snes_error_if_not_converged \
3467:       -ksp_error_if_not_converged \
3468:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3469:       -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
3470:     test:
3471:       suffix: aij
3472:       args: -matis_localmat_type aij
3473:     test:
3474:       requires: viennacl !CUDA_VERSION_11PLUS
3475:       suffix: aijviennacl
3476:       args: -matis_localmat_type aijviennacl
3477:     test:
3478:       requires: cuda
3479:       suffix: aijcusparse
3480:       args: -matis_localmat_type aijcusparse

3482:   testset:
3483:     suffix: q2p1fetidp_deluxe
3484:     output_file: output/ex69_q2p1fetidp_deluxe.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_deluxe_zerorows \
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: -matis_localmat_type aij
3497:     test:
3498:       suffix: aij_seqdense
3499:       args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3500:     test:
3501:       requires: viennacl !CUDA_VERSION_11PLUS
3502:       suffix: aijviennacl
3503:       args: -matis_localmat_type aijviennacl
3504:     test:
3505:       requires: cuda
3506:       suffix: aijcusparse
3507:       args: -matis_localmat_type aijcusparse

3509:   testset:
3512:     requires: mumps double
3513:     nsize: 5
3514:     args: -dm_plex_simplex 0 -dm_plex_separate_marker -dm_refine_pre 1 -dm_mat_type is -dm_view -petscpartitioner_type simple \
3515:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 \
3516:       -snes_error_if_not_converged \
3517:       -ksp_error_if_not_converged \
3518:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural \
3519:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_pc_bddc_adaptive_userdefined -fetidp_bddc_pc_bddc_adaptive_threshold 1.3 \
3520:       -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
3521:     test:
3522:       suffix: aij
3523:       args: -matis_localmat_type aij
3524:     test:
3525:       suffix: aij_seqdense
3526:       args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense
3527:     test:
3528:       requires: viennacl !CUDA_VERSION_11PLUS
3529:       suffix: aijviennacl
3530:       args: -matis_localmat_type aijviennacl
3531:     test:
3532:       requires: cuda
3533:       suffix: aijcusparse
3534:       args: -matis_localmat_type aijcusparse

3536:   test:
3537:     suffix: p2p1fetidp
3538:     requires: triangle
3539:     nsize: 4
3540:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3541:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3542:       -snes_error_if_not_converged \
3543:       -ksp_error_if_not_converged \
3544:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3545:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3546:       -fetidp_fieldsplit_lag_ksp_type preonly \
3547:       -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

3549:   test:
3550:     suffix: p2p1fetidp_allp
3551:     requires: triangle
3552:     nsize: 4
3553:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3554:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3555:       -snes_error_if_not_converged \
3556:       -ksp_error_if_not_converged \
3557:       -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 \
3558:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3559:       -fetidp_fieldsplit_lag_ksp_type preonly \
3560:       -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

3562:   test:
3563:     suffix: p2p1fetidp_discharm
3564:     requires: triangle
3565:     nsize: 4
3566:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3567:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3568:       -snes_error_if_not_converged \
3569:       -ksp_error_if_not_converged \
3570:       -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 \
3571:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3572:       -fetidp_fieldsplit_lag_ksp_type preonly \
3573:       -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

3575:   test:
3576:     suffix: p2p1fetidp_lumped
3577:     requires: triangle
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 -fetidp_pc_lumped \
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_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd

3588:   test:
3589:     suffix: p2p1fetidp_deluxe
3590:     requires: triangle mumps
3591:     nsize: 4
3592:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3593:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3594:       -snes_error_if_not_converged \
3595:       -ksp_error_if_not_converged \
3596:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3597:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3598:       -fetidp_fieldsplit_lag_ksp_type preonly \
3599:       -fetidp_bddc_pc_bddc_detect_disconnected -fetidp_bddc_pc_bddc_symmetric -fetidp_bddc_pc_bddc_vertex_size 3 -fetidp_bddc_pc_bddc_graph_maxcount 2 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat \
3600:       -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0

3602:   test:
3603:     suffix: p2p1fetidp_deluxe_discharm
3604:     requires: triangle mumps
3605:     nsize: 4
3606:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3607:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3608:       -snes_error_if_not_converged \
3609:       -ksp_error_if_not_converged \
3610:       -ksp_type fetidp -ksp_fetidp_saddlepoint -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -fetidp_pc_fieldsplit_schur_fact_type diag \
3611:       -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_p_ksp_type preonly \
3612:       -fetidp_fieldsplit_lag_ksp_type preonly \
3613:       -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 \
3614:       -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0  -fetidp_bddc_sub_schurs_discrete_harmonic

3616:   testset:
3617:     nsize: 4
3618:     requires: triangle
3619:     output_file: output/ex69_p2p1fetidp_olof.out
3620:     args: -dm_plex_separate_marker -dm_refine_pre 2 -dm_refine_uniform_pre -dm_mat_type is -dm_view -petscpartitioner_type simple \
3621:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
3622:       -snes_error_if_not_converged \
3623:       -ksp_error_if_not_converged \
3624:       -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 \
3625:       -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none -fetidp_fieldsplit_p_ksp_type preonly \
3626:       -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 \
3627:       -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
3628:     test:
3629:       suffix: p2p1fetidp_olof_full
3630:       args: -fetidp_pc_fieldsplit_schur_fact_type full
3631:     test:
3632:       suffix: p2p1fetidp_olof_diag
3633:       args: -fetidp_pc_fieldsplit_schur_fact_type diag
3634:     test:

3638:   #BDDC with benign trick
3639:   testset:
3640:     suffix: q2p1bddc
3641:     output_file: output/ex69_q2p1fetidp_deluxe.out
3642:     nsize: 5
3643:     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
3644:     test:
3645:       requires: double
3646:       suffix: benign_card
3647:       # no native support for saddle point factorizations from PETSc
3648:       args: -pc_bddc_dirichlet_pc_type svd -pc_bddc_neumann_pc_type svd
3649:     test:
3650:       requires: mumps double
3651:       suffix: benign_deluxe_mumps
3652:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mumps -sub_schurs_mat_mumps_icntl_14 1000
3653:     test:
3654:       requires: mumps double
3656:       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
3657:     test:
3658:       TODO: broken (INDEFINITE PC)
3659:       requires: mkl_pardiso double !complex
3660:       suffix: benign_deluxe_mkl
3661:       args: -pc_bddc_use_deluxe_scaling -pc_bddc_deluxe_zerorows -sub_schurs_mat_solver_type mkl_pardiso -snes_rtol 1.e-7
3662:     test:
3663:       TODO: broken (INDEFINITE PC)
3664:       requires: mkl_pardiso double !complex