static char help[] = "The variable-viscosity Stokes Problem in 2d with finite elements.\n\ We solve the Stokes problem in a square domain\n\ and compare against exact solutions from Mirko Velic.\n\n\n"; /* We discretize the variable-viscosity Stokes problem using the finite element method on an unstructured mesh. The weak form equations are \begin{align*} (\nabla v, \mu (\nabla u + {\nabla u}^T)) - (\nabla\cdot v, p) + (v, f) &= 0 \\ (q, \nabla\cdot u) &= 0 \end{align*} Free slip conditions for velocity are enforced on every wall. The pressure is constrained to have zero integral over the domain. To produce nice output, use -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 Testing the solver: ./ex69 -sol_type solkx -simplex 0 -mantle_basename /PETSc3/geophysics/MM/input_data/TwoDimSlab45cg1deguf4 -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -snes_monitor -snes_converged_reason -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_velocity_ksp_monitor_no -fieldsplit_velocity_ksp_converged_reason_no -fieldsplit_pressure_ksp_monitor -fieldsplit_pressure_ksp_converged_reason -ksp_rtol 1e-8 -fieldsplit_pressure_ksp_rtol 1e-3 -fieldsplit_pressure_pc_type lu -snes_max_it 1 -snes_error_if_not_converged 0 -snes_view -petscds_jac_pre 1 Testing the Jacobian: ./ex69 -sol_type solkx -simplex 0 -mantle_basename $PETSC_DIR/share/petsc/datafiles/mantle/small -dm_plex_separate_marker -vel_petscspace_degree 1 -pres_petscspace_degree 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -snes_monitor -snes_converged_reason -ksp_monitor -ksp_converged_reason -fieldsplit_velocity_ksp_monitor -fieldsplit_velocity_ksp_converged_reason -fieldsplit_velocity_ksp_view_pmat -fieldsplit_pressure_ksp_monitor -fieldsplit_pressure_ksp_converged_reason -fieldsplit_pressure_ksp_view_pmat -snes_test_jacobian -snes_test_jacobian_view -petscds_jac_pre 0 */ #include #include #include #include typedef enum {SOLKX, SOLCX, NUM_SOL_TYPES} SolutionType; const char *solTypes[NUM_SOL_TYPES+1] = {"solkx", "solcx", "unknown"}; typedef struct { PetscInt n, m; /* x- and y-wavelengths for variation across the domain */ /* SolKx */ PetscReal B; /* Exponential scale for viscosity variation */ /* SolCx */ PetscReal etaA, etaB; /* Two viscosities for discontinuous change */ PetscReal xc; /* The location of viscosity jump */ } Parameter; typedef struct { PetscInt debug; /* The debugging level */ PetscBool showSolution, showError; /* Domain and mesh definition */ PetscInt dim; /* The topological mesh dimension */ PetscBool simplex; /* Use simplices or tensor product cells */ PetscInt serRef; /* Number of serial refinements before the mesh gets distributed */ int verts[3]; /* The number of vertices in each dimension for mantle problems */ int perm[3] ; /* The permutation of axes for mantle problems */ /* Problem definition */ SolutionType solType; /* The type of exact solution */ PetscBag bag; /* Holds problem parameters */ } AppCtx; static PetscErrorCode zero_scalar(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx) { u[0] = 0.0; return 0; } static PetscErrorCode one_scalar(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx) { u[0] = 1.0; return 0; } static PetscErrorCode zero_vector(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx) { PetscInt d; for (d = 0; d < dim; ++d) u[d] = 0.0; return 0; } static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) { f0[0] = 0.0; f0[1] = -PetscSinScalar(constants[1]*PETSC_PI*x[1])*PetscCosScalar(constants[0]*PETSC_PI*x[0]); } static void stokes_momentum_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) { const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]); PetscInt c, d; for (c = 0; c < dim; ++c) { for (d = 0; d < dim; ++d) { f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]); } f1[c*dim+c] -= u[dim]; } } static void stokes_momentum_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) { const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]); PetscInt c, d; for (c = 0; c < dim; ++c) { for (d = 0; d < dim; ++d) { f1[c*dim+d] = mu * (u_x[c*dim+d] + u_x[d*dim+c]); } f1[c*dim+c] -= u[dim]; } } static void stokes_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) { PetscInt d; f0[0] = 0.0; for (d = 0; d < dim; ++d) f0[0] += u_x[d*dim+d]; } static void f1_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) { PetscInt d; for (d = 0; d < dim*dim; ++d) f1[d] = 0.0; } /* < q, \nabla\cdot u >, J_{pu} */ static void stokes_mass_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[]) { PetscInt d; for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */ } /* -< \nabla\cdot v, p >, J_{up} */ static void stokes_momentum_pres_J(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[]) { PetscInt d; for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */ } /* < \nabla v, \nabla u + {\nabla u}^T >, J_{uu} This just gives \nabla u, give the perdiagonal for the transpose */ static void stokes_momentum_vel_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) { const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]); PetscInt cI, d; for (cI = 0; cI < dim; ++cI) { for (d = 0; d < dim; ++d) { g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/ g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/ } } } static void stokes_momentum_vel_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) { const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]); PetscInt cI, d; for (cI = 0; cI < dim; ++cI) { for (d = 0; d < dim; ++d) { g3[((cI*dim+cI)*dim+d)*dim+d] += mu; /*g3[cI, cI, d, d]*/ g3[((cI*dim+d)*dim+d)*dim+cI] += mu; /*g3[cI, d, d, cI]*/ } } } /* 1/mu < q, I q >, Jp_{pp} */ static void stokes_identity_J_kx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) { const PetscReal mu = PetscExpReal(2.0*PetscRealPart(constants[2])*x[0]); g0[0] = 1.0/mu; } static void stokes_identity_J_cx(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) { const PetscReal mu = x[0] < PetscRealPart(constants[4]) ? PetscRealPart(constants[2]) : PetscRealPart(constants[3]); g0[0] = 1.0/mu; } /* SolKxSolution - Exact Stokes solutions for exponentially varying viscosity Input Parameters: + pos - The (x,z) coordinate at which to evaluate the solution . n - The constant defining the x-dependence of the forcing function . m - The constant defining the z-dependence of the forcing function - B - The viscosity coefficient Output Parameters: + vel - The (x,z)-velocity at (x,z), or NULL . p - The pressure at (x,z), or NULL . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL . gamma - The strain rate, or NULL - mu - The viscosity at (x,z), or NULL Note: $ The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary $ conditions everywhere. The forcing term f is given by $ $ fx = 0 $ fz = sigma*sin(km*z)*cos(kn*x) $ $ where $ $ km = m*Pi (m may be non-integral) $ kn = n*Pi $ $ meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1. $ The viscosity eta is exp(2*B*x). */ static PetscErrorCode SolKxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal B, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu) { PetscReal sigma = 1.0; PetscReal Z; PetscReal u1,u2,u3,u4,u5,u6; PetscReal sum1,sum2,sum3,sum4,sum5,sum6; PetscReal kn,km,x,z; PetscReal _PC1,_PC2,_PC3,_PC4; PetscReal Rp, UU, VV; PetscReal a,b,r,_aa,_bb,AA,BB,Rm; PetscReal num1,num2,num3,num4,den1; PetscReal t1,t2,t3,t4,t5,t6,t7,t8,t9,t10; PetscReal t11,t12,t13,t14,t15,t16,t17,t18,t19,t20; PetscReal t21,t22,t23,t24,t25,t26,t27,t28,t29,t30; PetscReal t31,t32,t33,t34,t35,t36,t37,t38,t39,t40; PetscReal t41,t42,t43,t44,t45,t46,t47,t49,t51,t53; PetscReal t56,t58,t61,t62,t63,t64,t65,t66,t67,t68; PetscReal t69,t70,t71,t72,t73,t74,t75,t76,t77,t78; PetscReal t79,t80,t81,t82,t83,t84,t85,t86,t87,t88; PetscReal t89,t90,t91,t92,t93,t94,t95,t96,t97,t99; PetscReal t100,t101,t103,t104,t105,t106,t107,t108,t109,t110; PetscReal t111,t112,t113,t114,t115,t116,t117,t118,t119,t120; PetscReal t121,t124,t125,t126,t127,t129,t130,t132,t133,t135; PetscReal t136,t138,t140,t141,t142,t143,t152,t160,t162; PetscFunctionBegin; /*************************************************************************/ /*************************************************************************/ /* rho = -sin(km*z)*cos(kn*x) */ x = pos[0]; z = pos[1]; Z = PetscExpReal( 2.0 * B * x); km = m*PETSC_PI; /* solution valid for km not zero -- should get trivial solution if km=0 */ kn = (PetscReal) n*PETSC_PI; /*************************************************************************/ /*************************************************************************/ a = B*B + km*km; b = 2.0*km*B; r = PetscSqrtReal(a*a + b*b); Rp = PetscSqrtReal( (r+a)/2.0); Rm = PetscSqrtReal( (r-a)/2.0); UU = Rp - B; VV = Rp + B; sum1=0.0; sum2=0.0; sum3=0.0; sum4=0.0; sum5=0.0; sum6=0.0; /*sum7=0.0;*/ /*******************************************/ /* calculate the constants */ /*******************************************/ t1 = kn * kn; t4 = km * km; t5 = t4 + t1; t6 = t5 * t5; t8 = pow(km + kn, 0.2e1); t9 = B * B; t16 = pow(km - kn, 0.2e1); _aa = -0.4e1 * B * t1 * sigma * t5 / (t6 + 0.4e1 * t8 * t9) / (t6 + 0.4e1 * t16 * t9); t2 = km * km; t3 = kn * kn; t5 = pow(t2 + t3, 0.2e1); t6 = km - kn; t7 = km + kn; t9 = B * B; t13 = t7 * t7; t19 = t6 * t6; _bb = sigma * kn * (t5 + 0.4e1 * t6 * t7 * t9) / (t5 + 0.4e1 * t13 * t9) / (t5 + 0.4e1 * t19 * t9); AA = _aa; BB = _bb; /*******************************************/ /* calculate the velocities etc */ /*******************************************/ t1 = Rm * Rm; t2 = B - Rp; t4 = Rp + B; t6 = UU * x; t9 = PetscExpReal(t6 - 0.4e1 * Rp); t13 = B * B; t16 = Rp * t1; t18 = Rp * Rp; t19 = B * t18; t20 = t13 * Rp; t22 = kn * kn; t24 = B * t1; t32 = 0.8e1 * t13 * BB * kn * Rp; t34 = 0.2e1 * Rm; t35 = PetscCosReal(t34); t37 = Rp * Rm; t49 = PetscSinReal(t34); t63 = PetscExpReal(t6 - 0.2e1 * Rp); t65 = Rm * t2; t67 = 0.2e1 * B * kn; t68 = B * Rm; t69 = t67 + t68 + t37; t73 = 0.3e1 * t13; t75 = 0.2e1 * B * Rp; t76 = t73 - t75 + t1 - t22 - t18; t78 = t65 * t76 * BB; t80 = Rm - kn; t81 = PetscCosReal(t80); t83 = -t67 + t68 + t37; t88 = Rm + kn; t89 = PetscCosReal(t88); t92 = t65 * t76 * AA; t97 = PetscSinReal(t80); t103 = PetscSinReal(t88); t108 = PetscExpReal(t6 - 0.3e1 * Rp - B); t110 = Rm * t4; t111 = t67 + t68 - t37; t115 = t73 + t75 + t1 - t22 - t18; t117 = t110 * t115 * BB; t120 = -t67 + t68 - t37; t127 = t110 * t115 * AA; t140 = PetscExpReal(t6 - Rp - B); 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; t1 = Rp + B; t2 = Rm * t1; t3 = B * B; t4 = 0.3e1 * t3; t5 = B * Rp; t7 = Rm * Rm; t8 = kn * kn; t9 = Rp * Rp; t10 = t4 + 0.2e1 * t5 + t7 - t8 - t9; t12 = t2 * t10 * AA; t14 = B * Rm; t20 = UU * x; t23 = PetscExpReal(t20 - 0.4e1 * Rp); t25 = Rp * Rm; t32 = Rm * kn; t37 = 0.2e1 * Rm; t38 = PetscCosReal(t37); t40 = t3 * B; t44 = B * t9; t45 = t3 * Rp; t53 = t3 * BB; t58 = PetscSinReal(t37); t69 = PetscExpReal(t20 - 0.2e1 * Rp); t72 = 0.3e1 * t40 * Rm; t73 = t9 * Rp; t74 = t73 * Rm; t75 = t7 * Rm; t76 = B * t75; t77 = t14 * t8; t78 = Rp * t75; t80 = 0.8e1 * t45 * kn; t81 = t25 * t8; t83 = 0.5e1 * t45 * Rm; t84 = t44 * Rm; t85 = t72 - t74 + t76 - t77 + t78 + t80 - t81 + t83 + t84; t88 = 0.2e1 * t9 * t3; t90 = 0.3e1 * t40 * Rp; t91 = t7 * t3; t93 = 0.2e1 * t5 * t32; t94 = t5 * t7; t95 = t5 * t8; t96 = B * t73; t97 = t7 * t9; t100 = 0.2e1 * t3 * Rm * kn; t101 = -t88 + t90 - t91 - t93 - t94 - t95 - t96 - t97 - t100; t105 = Rm - kn; t106 = PetscCosReal(t105); t108 = t72 - t80 + t83 + t76 + t84 - t81 - t74 + t78 - t77; t110 = -t97 - t96 - t88 + t100 + t90 - t95 + t93 - t91 - t94; t114 = Rm + kn; t115 = PetscCosReal(t114); t121 = PetscSinReal(t105); t127 = PetscSinReal(t114); t132 = PetscExpReal(t20 - 0.3e1 * Rp - B); t135 = 0.2e1 * B * kn; t136 = t135 + t14 - t25; t142 = -t135 + t14 - t25; t152 = t2 * t10 * BB; t162 = PetscExpReal(t20 - Rp - B); 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; t1 = Rm * Rm; t2 = B - Rp; t4 = Rp + B; t6 = VV * x; t7 = PetscExpReal(-t6); t11 = kn * kn; t13 = B * t1; t14 = Rp * Rp; t15 = B * t14; t16 = B * B; t17 = t16 * Rp; t21 = Rp * t1; t30 = 0.8e1 * t16 * BB * kn * Rp; t32 = 0.2e1 * Rm; t33 = PetscCosReal(t32); t35 = Rp * Rm; t47 = PetscSinReal(t32); t61 = PetscExpReal(-t6 - 0.2e1 * Rp); t63 = Rm * t2; t65 = 0.2e1 * B * kn; t66 = B * Rm; t67 = t65 + t66 + t35; t71 = 0.3e1 * t16; t73 = 0.2e1 * B * Rp; t74 = t71 - t73 + t1 - t11 - t14; t76 = t63 * t74 * BB; t78 = Rm - kn; t79 = PetscCosReal(t78); t81 = -t65 + t66 + t35; t86 = Rm + kn; t87 = PetscCosReal(t86); t90 = t63 * t74 * AA; t95 = PetscSinReal(t78); t101 = PetscSinReal(t86); t106 = PetscExpReal(-t6 - 0.3e1 * Rp - B); t108 = Rm * t4; t109 = t65 + t66 - t35; t113 = t71 + t73 + t1 - t11 - t14; t115 = t108 * t113 * BB; t118 = -t65 + t66 - t35; t125 = t108 * t113 * AA; t138 = PetscExpReal(-t6 - Rp - B); 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; t1 = B - Rp; t2 = Rm * t1; t3 = B * B; t4 = 0.3e1 * t3; t5 = B * Rp; t7 = Rm * Rm; t8 = kn * kn; t9 = Rp * Rp; t10 = t4 - 0.2e1 * t5 + t7 - t8 - t9; t12 = t2 * t10 * AA; t14 = B * Rm; t20 = VV * x; t21 = PetscExpReal(-t20); t23 = Rp * Rm; t30 = Rm * kn; t35 = 0.2e1 * Rm; t36 = PetscCosReal(t35); t40 = B * t9; t41 = t3 * Rp; t43 = t3 * B; t51 = t3 * BB; t56 = PetscSinReal(t35); t67 = PetscExpReal(-t20 - 0.2e1 * Rp); t70 = 0.2e1 * B * kn; t71 = t70 + t14 + t23; t76 = Rm - kn; t77 = PetscCosReal(t76); t79 = -t70 + t14 + t23; t84 = Rm + kn; t85 = PetscCosReal(t84); t91 = t2 * t10 * BB; t93 = PetscSinReal(t76); t99 = PetscSinReal(t84); t104 = PetscExpReal(-t20 - 0.3e1 * Rp - B); t107 = 0.3e1 * t43 * Rm; t108 = t9 * Rp; t109 = t108 * Rm; t110 = t7 * Rm; t111 = B * t110; t112 = t14 * t8; t113 = Rp * t110; t115 = 0.8e1 * t41 * kn; t116 = t23 * t8; t118 = 0.5e1 * t41 * Rm; t119 = t40 * Rm; t120 = t107 + t109 + t111 - t112 - t113 - t115 + t116 - t118 + t119; t124 = 0.2e1 * t3 * Rm * kn; t125 = t5 * t8; t126 = B * t108; t127 = t7 * t9; t129 = 0.2e1 * t9 * t3; t130 = t5 * t7; t132 = 0.3e1 * t43 * Rp; t133 = t7 * t3; t135 = 0.2e1 * t5 * t30; t136 = t124 - t125 - t126 + t127 + t129 - t130 + t132 + t133 - t135; t141 = t107 + t115 - t118 + t111 + t119 + t116 + t109 - t113 - t112; t143 = t132 + t129 - t125 + t133 + t127 - t124 - t130 - t126 + t135; t160 = PetscExpReal(-t20 - Rp - B); 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; t1 = Rm * Rm; t2 = Rp * Rp; t3 = t1 * t2; t4 = B * B; t5 = t1 * t4; t9 = PetscExpReal(-0.4e1 * Rp); t15 = PetscCosReal(0.2e1 * Rm); t22 = PetscExpReal(-0.2e1 * Rp); 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; _PC1=num1/den1; _PC2=num2/den1; _PC3=num3/den1; _PC4=num4/den1; t1 = Rm * x; t2 = PetscCosReal(t1); t4 = PetscSinReal(t1); t10 = PetscExpReal(-0.2e1 * x * B); t12 = kn * x; t13 = PetscCosReal(t12); t16 = PetscSinReal(t12); u1 = -km * (_PC1 * t2 + _PC2 * t4 + _PC3 * t2 + _PC4 * t4 + t10 * AA * t13 + t10 * BB * t16); t2 = Rm * x; t3 = PetscCosReal(t2); t6 = PetscSinReal(t2); t22 = PetscExpReal(-0.2e1 * x * B); t23 = B * t22; t24 = kn * x; t25 = PetscCosReal(t24); t29 = PetscSinReal(t24); 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; t3 = PetscExpReal(0.2e1 * x * B); t4 = t3 * B; t8 = km * km; t9 = t3 * t8; t11 = 0.3e1 * t9 * Rm; t12 = Rm * Rm; t14 = t3 * t12 * Rm; t15 = UU * UU; t19 = 0.4e1 * t4 * UU * Rm - t11 - t14 + 0.3e1 * t3 * t15 * Rm; t20 = Rm * x; t21 = PetscSinReal(t20); t27 = 0.2e1 * B * t9; t33 = 0.2e1 * t4 * t12; t36 = 0.3e1 * t3 * UU * t12 - t27 - 0.2e1 * t4 * t15 + 0.3e1 * t9 * UU + t33 - t3 * t15 * UU; t37 = PetscCosReal(t20); t49 = VV * VV; t53 = -0.4e1 * t4 * VV * Rm - t11 + 0.3e1 * t3 * t49 * Rm - t14; t64 = t3 * t49 * VV + t33 - 0.3e1 * t9 * VV - 0.2e1 * t4 * t49 - t27 - 0.3e1 * t3 * VV * t12; t76 = B * t8; t80 = kn * kn; t83 = B * B; t87 = t80 * kn; t90 = kn * x; t91 = PetscSinReal(t90); t106 = PetscCosReal(t90); 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; t3 = PetscExpReal(0.2e1 * x * B); t4 = km * km; t5 = t3 * t4; t6 = Rm * x; t7 = PetscCosReal(t6); t8 = _PC1 * t7; t10 = PetscSinReal(t6); t11 = _PC2 * t10; t13 = _PC3 * t7; t15 = _PC4 * t10; t18 = kn * x; t19 = PetscCosReal(t18); t22 = PetscSinReal(t18); t24 = UU * UU; t25 = t3 * t24; t28 = t3 * UU; t38 = Rm * Rm; t39 = t7 * t38; t42 = t10 * t38; 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; t45 = VV * VV; t46 = t3 * t45; t49 = t3 * VV; t62 = B * B; t78 = kn * kn; 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; u4 = t44 + t82; t3 = PetscExpReal(0.2e1 * x * B); t4 = t3 * B; t8 = km * km; t9 = t3 * t8; t10 = t9 * Rm; t11 = Rm * Rm; t13 = t3 * t11 * Rm; t14 = UU * UU; t18 = 0.4e1 * t4 * UU * Rm - t10 - t13 + 0.3e1 * t3 * t14 * Rm; t19 = Rm * x; t20 = PetscSinReal(t19); t26 = 0.2e1 * B * t9; t31 = 0.2e1 * t4 * t11; t34 = 0.3e1 * t3 * UU * t11 - t26 - 0.2e1 * t4 * t14 + t9 * UU + t31 - t3 * t14 * UU; t35 = PetscCosReal(t19); t47 = VV * VV; t51 = -0.4e1 * t4 * VV * Rm - t10 + 0.3e1 * t3 * t47 * Rm - t13; t61 = t3 * t47 * VV + t31 - t9 * VV - 0.2e1 * t4 * t47 - t26 - 0.3e1 * t3 * VV * t11; t72 = B * t8; t76 = kn * kn; t79 = B * B; t83 = t76 * kn; t86 = kn * x; t87 = PetscSinReal(t86); t101 = PetscCosReal(t86); 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; t3 = PetscExpReal(0.2e1 * x * B); t4 = UU * UU; t8 = km * km; t9 = t3 * t8; t10 = t9 * Rm; t11 = Rm * Rm; t13 = t3 * t11 * Rm; t14 = t3 * B; t18 = 0.3e1 * t3 * t4 * Rm + t10 - t13 + 0.4e1 * t14 * UU * Rm; t19 = Rm * x; t20 = PetscSinReal(t19); t28 = 0.2e1 * B * t9; t33 = 0.2e1 * t14 * t11; t34 = -0.2e1 * t4 * t14 + 0.3e1 * t3 * UU * t11 - t28 - t3 * t4 * UU - t9 * UU + t33; t35 = PetscCosReal(t19); t47 = VV * VV; t51 = -0.4e1 * t14 * VV * Rm - t13 + t10 + 0.3e1 * t3 * t47 * Rm; t61 = -0.3e1 * t3 * VV * t11 + t33 + t3 * t47 * VV + t9 * VV - 0.2e1 * t14 * t47 - t28; t71 = kn * kn; t74 = B * B; t80 = t71 * kn; t83 = kn * x; t84 = PetscSinReal(t83); t96 = PetscCosReal(t83); 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; /*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)));*/ /* u1 = Vx, u2 = Vz, u3 = txx, u4 = tzx, u5 = pressure, u6 = tzz */ sum5 += u5*PetscCosReal(km*z); /* pressure */ sum6 += u6*PetscCosReal(km*z); /* zz total stress */ u1 *= PetscCosReal(km*z); /* x velocity */ sum1 += u1; u2 *= PetscSinReal(km*z); /* z velocity */ sum2 += u2; u3 *= PetscCosReal(km*z); /* xx total stress */ sum3 += u3; u4 *= PetscSinReal(km*z); /* zx stress */ sum4 += u4; /* rho = -sigma*sin(km*z)*cos(kn*x); */ /* density */ /* sum7 += rho; */ /* Output */ if (mu) { *mu = Z; } if (vel) { vel[0] = sum1; vel[1] = sum2; } if (p) { (*p) = sum5; } if (s) { s[0] = sum3; s[1] = sum4; s[2] = sum6; } if (gamma) { /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */ gamma[0] = (sum3+sum5)/(2.0*Z); gamma[1] = (sum4)/(2.0*Z); gamma[2] = (sum6+sum5)/(2.0*Z); } PetscFunctionReturn(0); } static PetscErrorCode SolKxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx) { Parameter *s = (Parameter *) ctx; PetscErrorCode ierr; PetscFunctionBegin; ierr = SolKxSolution(x, s->m, s->n, s->B, v, NULL, NULL, NULL, NULL);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode SolKxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx) { Parameter *s = (Parameter *) ctx; PetscErrorCode ierr; PetscFunctionBegin; ierr = SolKxSolution(x, s->m, s->n, s->B, NULL, p, NULL, NULL, NULL);CHKERRQ(ierr); PetscFunctionReturn(0); } /* SolCxSolution - Exact Stokes solutions for discontinuous viscosity Input Parameters: + pos - The (x,z) coordinate at which to evaluate the solution . n - The constant defining the x-dependence of the forcing function . m - The constant defining the z-dependence of the forcing function . xc - The x coordinate at which the viscosity is discontinuous . etaA - The viscosity coefficient for x < xc - etaB - The viscosity coefficient for x > xc Output Parameters: + vel - The (x,z)-velocity at (x,z), or NULL . p - The pressure at (x,z), or NULL . s - The total stress (sigma_xx, sigma_xz, sigma_zz) at (x,z), or NULL . gamma - The strain rate, or NULL - mu - The viscosity at (x,z), or NULL Note: $ The domain is the square 0 <= x,z <= 1. We solve the Stokes equation for incompressible flow with free-slip boundary $ conditions everywhere. The forcing term f is given by $ $ fx = 0 $ fz = sigma*sin(km*z)*cos(kn*x) $ $ where $ $ km = m*Pi (m may be non-integral) $ kn = n*Pi $ $ meaning that the density rho is -sigma*sin(km*z)*cos(kn*x). Here we set sigma = 1. $ The viscosity eta jumps from etaA to etaB at x = xc. */ static PetscErrorCode SolCxSolution(const PetscReal pos[], PetscReal m, PetscInt n, PetscReal xc, PetscReal etaA, PetscReal etaB, PetscScalar vel[], PetscScalar *p, PetscScalar s[], PetscScalar gamma[], PetscScalar *mu) { PetscReal _PC1A,_PC2A,_PC3A,_PC4A,_PC1B,_PC2B,_PC3B,_PC4B,_PC1,_PC2,_PC3,_PC4; 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; 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; 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; 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; 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; 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; 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; 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; 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; 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; 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; 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; 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; 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; PetscReal t561,t562,t563,t564,t567,t568,t571,t573,t575,t576,t578,t579,t583,t590,t591,t594,t595,t596,t597,t598,t600; 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; 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; 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; 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; 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; PetscReal t801,t806,t807,t808,t809,t811,t812,t817,t818,t819,t821,t822,t824,t827,t828,t830,t834,t835,t837,t840; 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; PetscReal t884,t888,t891,t894,t900,t901,t903,t904,t907,t908,t909,t911,t914,t915,t916,t919,t920; 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; PetscReal t961,t964,t965,t966,t967,t968,t969,t971,t972,t974,t977,t978,t981,t983,t987,t988,t992,t993,t994,t997,t998; PetscReal t1001,t1003,t1005,t1006,t1009,t1010,t1012,t1013,t1015,t1016,t1017,t1018,t1020,t1021,t1029,t1031,t1032,t1033,t1040; PetscReal t1041,t1042,t1044,t1047,t1050,t1054,t1055,t1057,t1058,t1063,t1068,t1069,t1070,t1079,t1080; PetscReal t1088,t1089,t1091,t1092,t1094,t1096,t1101,t1102,t1103,t1104,t1105,t1108,t1112,t1113,t1118,t1119,t1120; 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; PetscReal t1161,t1162,t1165,t1166,t1170,t1171,t1172,t1173,t1175,t1176,t1178,t1180,t1181,t1182,t1185,t1189,t1192,t1193,t1195,t1196,t1199; PetscReal t1201,t1203,t1209,t1210,t1211,t1213,t1214,t1218,t1221,t1224,t1225,t1226,t1228,t1233,t1234,t1235,t1236,t1237,t1240; PetscReal t1241,t1242,t1243,t1244,t1245,t1248,t1251,t1252,t1257,t1258,t1259,t1260,t1263,t1268,t1269,t1272,t1280; PetscReal t1282,t1283,t1284,t1285,t1287,t1288,t1289,t1292,t1293,t1296,t1297,t1300,t1304,t1307,t1310,t1311,t1312,t1316,t1317,t1320; PetscReal t1321,t1323,t1328,t1330,t1331,t1332,t1333,t1336,t1338,t1343,t1344,t1346,t1349,t1350,t1354; PetscReal t1366,t1369,t1370,t1371,t1376,t1378,t1380,t1383,t1386,t1387,t1388,t1391,t1393,t1399; PetscReal t1411,t1412,t1420,t1427; PetscReal t1450,t1456,t1468,t1472,t1474,t1478; PetscReal t1504,t1511; PetscReal t1545; PetscReal t1564,t1583; PetscReal sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, sum6 = 0.0; PetscReal ZA = etaA, ZB = etaB; PetscInt nz = m, nx = n; PetscReal u1, u2, u3, u4, u5, u6, Z, x = pos[0], z = pos[1]; PetscFunctionBegin; /* Note that there is no Fourier sum here. */ /****************************************************************************************/ _PC1A = 0; /****************************************************************************************/ t1 = nx * 0.3141592654e1; t2 = PetscSinReal(t1); t3 = nx * t2; t4 = nz * nz; t5 = t4 * t4; t6 = 0.3141592654e1 * 0.3141592654e1; t8 = t3 * t5 * t6; t9 = ZA * xc; t12 = PetscExpReal(xc * nz * 0.3141592654e1); t13 = t12 * t12; t15 = nz * 0.3141592654e1; t16 = PetscExpReal(t15); t17 = t16 * t16; t18 = t17 * t16; t19 = ZB * t13 * t18; t20 = t9 * t19; t23 = ZA * ZA; t24 = nx * nx; t25 = t24 * nx; t26 = t23 * t25; t28 = t13 * t13; t29 = t28 * t13; t33 = nx * ZB; t34 = t1 * xc; t35 = PetscSinReal(t34); t36 = t4 * nz; t37 = t35 * t36; t38 = t33 * t37; t39 = 0.3141592654e1 * ZA; t40 = t13 * t12; t41 = t17 * t40; t45 = ZB * ZB; t46 = t45 * t24; t47 = t46 * t4; t48 = 0.3141592654e1 * xc; t49 = t13 * t17; t53 = xc * xc; t54 = t36 * t53; t56 = t54 * t6 * t45; t57 = PetscCosReal(t34); t58 = t57 * t24; t59 = t28 * t12; t60 = t17 * t59; t61 = t58 * t60; t64 = t25 * t2; t65 = t64 * t15; t72 = nx * t23; t74 = t72 * t2 * t5; t75 = t6 * t53; t76 = t16 * t29; t80 = t23 * nz; t81 = t80 * 0.3141592654e1; t82 = t18 * t28; t86 = nx * t5; t87 = t23 * t6; t89 = xc * t2; t90 = t13 * t18; t91 = t89 * t90; t94 = t28 * t28; t96 = t24 * nz; t98 = t4 * t45; t99 = t98 * 0.3141592654e1; t100 = t58 * t41; t104 = 0.3141592654e1 * t25; t105 = ZA * nz * t104; t106 = t2 * ZB; t110 = t17 * t17; t111 = ZA * t110; t116 = nz * t28; t122 = t64 * t4 * t6; t126 = t23 * t29 * t4; t128 = t24 * xc; t132 = t36 * t23; t133 = t6 * t57; t135 = t128 * t41; t138 = t6 * xc; t142 = t72 * t2; 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; t149 = ZA * t25 * t2; t150 = ZB * t28; t154 = t35 * t5; t155 = t72 * t154; t156 = t75 * t41; t159 = nx * ZA; t160 = t2 * t36; t161 = t159 * t160; t162 = 0.3141592654e1 * ZB; t163 = t28 * t16; t167 = t23 * t57; t168 = t167 * t24; t169 = nz * t110; t170 = t169 * t40; t173 = ZA * ZB; t174 = t173 * t90; t177 = t36 * 0.3141592654e1; t181 = t80 * t104; t184 = nz * t17; t188 = t17 * t29; t190 = t4 * 0.3141592654e1; t191 = t190 * t24; t206 = t138 * t60; t209 = t23 * t4; t211 = t209 * t6 * t25; t212 = t89 * t76; t216 = ZB * t16 * t29; t217 = t9 * t216; t220 = ZB * t110; t221 = ZA * t24; t222 = t221 * nz; t225 = t132 * t75; t232 = t45 * t28; t233 = t110 * t24; t234 = t233 * nz; t236 = t209 * 0.3141592654e1; t237 = t17 * xc; t239 = t237 * t13 * t24; 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; t244 = nx * t45; t245 = t244 * t37; t246 = t110 * t40; t251 = t237 * t59; t256 = t64 * t90; t260 = t36 * t45 * t133; t263 = t45 * t57; t264 = t263 * t24; t265 = t169 * t12; t269 = t6 * t36; t270 = t17 * t24; t274 = t110 * t13; t276 = t190 * t128; t279 = nx * t36; t281 = t28 * t40; t282 = t281 * t35; t286 = t138 * t41; t289 = t75 * t60; t296 = t190 * t173; t305 = t86 * t45 * t35; t312 = t33 * t154; t313 = t6 * ZA; t324 = t232 * t270; 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; t328 = t3 * t4; t331 = t72 * t37; t332 = t48 * t60; t335 = nz * t94; t345 = t72 * t35; t349 = t173 * t57; t355 = t53 * t17; t364 = t54 * t6 * ZB; t365 = t28 * t17; t369 = xc * ZB; t370 = t269 * t369; t371 = ZA * t57; t373 = t371 * t270 * t40; t385 = nx * t35; t396 = t4 * xc; t397 = t396 * t162; t415 = t37 * t48; 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; t427 = t371 * t270 * t59; t439 = t209 * t48; t440 = t110 * t12; t441 = t58 * t440; t447 = t36 * xc; t455 = t48 * t440; t471 = ZB * t17; 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; t499 = ZA * t53 * t19; t505 = t396 * 0.3141592654e1; t518 = t173 * t53 * t16 * t29; t533 = t23 * t28; t535 = t188 * t45; t538 = t24 * t4; t545 = t3 * t177; t546 = t173 * t76; t555 = t45 * t110; t557 = t72 * t160; 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; t567 = t396 * 0.3141592654e1 * t45; t568 = t58 * t246; t597 = t58 * nz; t615 = t13 * t45; t616 = t615 * t233; t619 = t94 * t45; t621 = t45 * t59; 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; t626 = t49 * t45; t660 = t29 * t45; 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; t690 = t6 * 0.3141592654e1; t691 = ZA * t690; t693 = t24 * t24; t694 = t693 * xc; t695 = t188 * t694; t698 = t23 * ZA; t699 = t698 * t690; t700 = t699 * t5; t704 = t5 * t4; t705 = t691 * t704; t709 = t691 * t5; t713 = t5 * nz; t714 = t713 * ZB; t718 = t698 * t6; t719 = t713 * t28; t722 = t699 * t704; t726 = t713 * t94; t733 = t713 * t45; t736 = t87 * t36; 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; t746 = t313 * t36; t752 = t6 * t6; t753 = t23 * t752; t759 = t698 * t752; t760 = t759 * t36; t761 = t17 * t693; t762 = xc * t28; t763 = t761 * t762; t766 = t87 * t713; t773 = t699 * t4; t774 = t110 * t693; t775 = xc * t13; t785 = t704 * t17; 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; t791 = t691 * t4; t792 = t45 * t693; t793 = t49 * t792; t796 = t759 * t713; t797 = t53 * t28; t798 = t270 * t797; t801 = t87 * nz; t818 = t5 * t36; t819 = t753 * t818; t827 = t753 * t36 * ZB; t830 = xc * t45; 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; t842 = xc * t29; t843 = t270 * t842; t849 = t759 * t818; t853 = t691 * t396; t857 = t691 * t5 * t45; t869 = t313 * nz; 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; t877 = ZA * t752; t878 = t877 * t818; 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; t916 = t110 * t28; t945 = t28 * t693 * t45 * t17; 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; t974 = t761 * t797; 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; 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; _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); /****************************************************************************************/ t1 = nz * nz; t2 = t1 * nz; t3 = t2 * 0.3141592654e1; t4 = t3 * xc; t5 = ZB * ZB; t7 = PetscExpReal(nz * 0.3141592654e1); t8 = t7 * t7; t9 = t5 * t8; t12 = PetscExpReal(xc * nz * 0.3141592654e1); t13 = t12 * t12; t14 = t13 * t13; t15 = t14 * t13; t19 = nx * nx; t21 = nx * 0.3141592654e1; t22 = PetscSinReal(t21); t23 = t19 * nx * t22; t24 = t23 * 0.3141592654e1; t25 = ZA * ZB; t26 = t7 * t15; t27 = t25 * t26; t30 = t21 * xc; t31 = PetscSinReal(t30); t32 = t31 * nx; t33 = t32 * nz; t34 = ZA * ZA; t35 = t8 * t8; t36 = t34 * t35; t40 = t2 * t34; t41 = 0.3141592654e1 * t8; t42 = t41 * t15; t45 = t1 * t5; t46 = t14 * t14; t49 = t19 * t5; t51 = t19 * t46; t53 = t19 * t34; t55 = t8 * t7; t56 = t13 * t55; t57 = t25 * t56; t60 = t2 * nx; t61 = 0.3141592654e1 * 0.3141592654e1; t63 = t60 * t31 * t61; t64 = xc * xc; t65 = ZA * t64; t66 = ZB * t8; t67 = t14 * t12; t68 = t66 * t67; t69 = t65 * t68; 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; t73 = t1 * nx; t75 = t73 * t31 * 0.3141592654e1; t76 = t8 * t67; t77 = t25 * t76; t80 = t1 * t1; t81 = t80 * t34; t83 = t61 * t14; t87 = t1 * t19; t88 = PetscCosReal(t30); t90 = t87 * t88 * t61; t91 = t5 * t64; t92 = t13 * t12; t93 = t8 * t92; t94 = t91 * t93; t100 = ZB * t64 * ZA * t8 * t92; t103 = nz * t19; t105 = t103 * t88 * 0.3141592654e1; t106 = ZA * xc; t107 = ZB * t35; t109 = t106 * t107 * t12; t112 = t34 * xc; t113 = t112 * t93; t116 = t35 * t14; t118 = t1 * ZA; t119 = ZB * t14; t122 = t1 * t46; t125 = t19 * ZB; t126 = t35 * ZA; t127 = t125 * t126; t129 = t1 * ZB; 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; t134 = t1 * t34; t136 = t34 * t64; t137 = t136 * t76; t141 = t91 * t76; t145 = t103 * t34; t146 = 0.3141592654e1 * xc; t147 = t8 * t13; t153 = t14 * ZA; t156 = xc * t5; t157 = t156 * t93; t160 = t103 * t5; t162 = t146 * t8 * t15; t166 = t34 * t7 * t15; 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; t170 = t106 * t68; t177 = t35 * t92; t178 = t112 * t177; t181 = t156 * t76; t186 = t35 * t12; t187 = t112 * t186; t193 = t5 * 0.3141592654e1; t206 = t34 * t14; t207 = t206 * t7; 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; t217 = t106 * t66 * t92; t226 = t88 * t19 * nz; t227 = 0.3141592654e1 * t34; t229 = t227 * xc * t67; t232 = t73 * t31; t234 = t146 * t5 * t67; t238 = t61 * ZB; t239 = t14 * t8; t240 = t238 * t239; t243 = t136 * t93; 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; t247 = t14 * t92; t249 = t227 * t247 * xc; t254 = t73 * t22; t259 = t60 * t22 * t61; t260 = t112 * t26; t264 = t146 * t247 * t5; t268 = xc * t14; t274 = t5 * t14; t275 = t274 * t8; t280 = nz * nx; t281 = t280 * t22; t282 = t55 * t14; t283 = t25 * t282; t290 = ZA * t247 * xc * ZB; t295 = t22 * nx * t1 * 0.3141592654e1; 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; t301 = t61 * t5; t307 = t87 * t34; t312 = t61 * xc; t313 = t312 * t239; t317 = t34 * t55 * t14; t329 = ZB * t13 * t55; t330 = t65 * t329; 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; t340 = t5 * t35; t344 = t25 * t93; t356 = t41 * t13; t360 = t23 * nz * t61; t363 = t25 * t64 * t7 * t15; t366 = t156 * t177; t369 = t14 * t7; t370 = t25 * t369; t373 = t156 * t186; 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; t382 = t112 * t76; t387 = t80 * t61; t391 = t136 * t26; 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; t423 = t153 * t8; t426 = t34 * t13; t427 = t426 * t55; t430 = t34 * t8; t437 = t80 * ZA; 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; t453 = t106 * ZB * t7 * t15; t456 = t2 * t5; t459 = t112 * t56; t462 = t126 * t14; t474 = t40 * 0.3141592654e1; t475 = xc * t8; t480 = t146 * t13 * t35; 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; t497 = t136 * t56; t504 = t9 * t13; t509 = t475 * t13; 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; t528 = t5 * t13; t529 = t528 * t35; t532 = t106 * t329; 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; t557 = t146 * t15; t562 = xc * t15; t563 = t562 * t5; 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; 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; t623 = xc * t13; 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; t632 = t61 * 0.3141592654e1; t633 = t632 * t8; t634 = t80 * nz; t638 = t632 * t634; t639 = t638 * xc; t642 = t61 * t34; t643 = t122 * t19; t649 = t61 * t61; t650 = t649 * t1; t652 = t19 * t19; t653 = t14 * t652; t654 = t653 * t9; t657 = t14 * t1; t658 = t657 * t19; t665 = t632 * t34; t666 = t665 * t2; t667 = t8 * t19; t668 = t667 * t623; t674 = t665 * nz; t675 = t652 * xc; 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; t683 = t46 * t652; t686 = t633 * t15; t691 = t35 * t80; t698 = t35 * t652; t705 = t14 * t80; t708 = t61 * t35; 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; t727 = t61 * t46; t737 = t649 * t34; t738 = t737 * t1; t739 = t8 * t652; t740 = t739 * t268; t746 = t61 * ZA; t754 = t632 * nz * xc; 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; t762 = t633 * t13; t764 = t5 * nz * t652; t767 = t80 * t1; t768 = t649 * t767; t772 = t649 * ZA; t773 = t772 * t129; t777 = t35 * t1 * t19; t780 = t632 * t5; t781 = t780 * t15; t786 = t698 * ZA; t790 = t64 * t14; t800 = t649 * t8; 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; t812 = t649 * t80; t817 = t83 * ZB; t824 = t746 * ZB; t828 = t800 * t14; 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; t858 = t35 * t19; t873 = t2 * t8; t878 = t61 * t1; 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; t903 = t739 * t790; t923 = t737 * t80; t924 = t667 * t790; t927 = t780 * t2; t937 = t15 * t19 * xc; 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; 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; _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); /****************************************************************************************/ _PC4A = 0; /****************************************************************************************/ t1 = nx * 0.3141592654e1; t2 = t1 * xc; t3 = PetscCosReal(t2); t4 = nx * nx; t6 = nz * 0.3141592654e1; t7 = t3 * t4 * t6; t8 = ZA * ZB; t9 = PetscExpReal(t6); t10 = t9 * t9; t11 = xc * nz; t13 = PetscExpReal(t11 * 0.3141592654e1); t14 = t13 * t13; t15 = t14 * t13; t16 = t14 * t14; t17 = t16 * t15; t18 = t10 * t17; t19 = t8 * t18; t22 = PetscSinReal(t2); t23 = nx * t22; t24 = t23 * nz; t25 = ZB * ZB; t30 = nz * nz; t31 = t30 * nz; t32 = t31 * nx; t33 = 0.3141592654e1 * 0.3141592654e1; t35 = t32 * t22 * t33; t36 = ZA * ZA; t37 = t36 * xc; t38 = t16 * t13; t39 = t10 * t38; t40 = t37 * t39; t43 = PetscSinReal(t1); t44 = nx * t43; t45 = t30 * 0.3141592654e1; t46 = t44 * t45; t47 = ZA * xc; t49 = ZB * t16 * t9; t54 = t4 * nx * t43; t55 = xc * xc; t57 = t54 * t30 * t55; t58 = t33 * 0.3141592654e1; t59 = t58 * t25; t60 = t16 * t9; t61 = t59 * t60; t64 = xc * t25; t65 = t14 * t9; t66 = t64 * t65; t70 = t44 * t31 * t33; t71 = t37 * t65; t74 = t10 * t15; t75 = t64 * t74; t78 = t25 * t10; t83 = t54 * nz * t33; t84 = t55 * t25; t85 = t10 * t9; t86 = t14 * t85; t87 = t84 * t86; t90 = t30 * t30; t92 = t44 * t90 * t58; t93 = t55 * xc; t94 = t93 * t25; t95 = t85 * t16; t96 = t94 * t95; t102 = t23 * t45; t103 = t10 * t10; t104 = ZB * t103; t106 = t47 * t104 * t15; t111 = t54 * 0.3141592654e1; t112 = t25 * t85; t113 = t112 * t16; t115 = t8 * t39; t118 = t16 * t14; t119 = t85 * t118; t120 = t37 * t119; t123 = t16 * t16; t124 = t36 * t123; t125 = t124 * t9; 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; t128 = t37 * t74; t131 = t44 * nz; t133 = t25 * t9 * t118; t136 = t36 * t14; t137 = t136 * t9; t140 = t30 * t4; t142 = t140 * t3 * t33; t143 = t64 * t39; t147 = t30 * nx * t43; t148 = 0.3141592654e1 * t36; t149 = t9 * t118; t153 = t44 * t31 * ZA; t154 = t33 * xc; t155 = t154 * t49; t160 = ZA * t17 * xc * ZB; t163 = t103 * t13; t164 = t64 * t163; t170 = t44 * t90 * t55; t171 = t58 * ZB; t172 = ZA * t16; t174 = t171 * t172 * t9; t177 = t36 * t55; t178 = t177 * t149; t181 = t54 * t11; t182 = t33 * t25; t186 = t25 * t14; t187 = t186 * t9; t193 = t186 * t85; t198 = ZB * t55; t199 = ZA * t103; t201 = t198 * t199 * t15; 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; t210 = t32 * t22; t211 = t33 * t55; t212 = t25 * t38; t213 = t211 * t212; t216 = nz * nx; t217 = t22 * t25; t222 = ZB * t85 * t16; t226 = t23 * t30; t227 = t13 * t10; t228 = t148 * t227; t233 = t37 * t163; t237 = nz * t4 * t3; t238 = t148 * t74; t241 = t64 * t86; t245 = t148 * xc * t15; t248 = t112 * t118; t250 = t22 * t36; t256 = 0.3141592654e1 * t25; t257 = t256 * t39; t262 = t38 * t103; t263 = t37 * t262; t267 = t148 * t17 * xc; 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; t273 = t37 * t149; t277 = t47 * t104 * t13; t285 = t31 * t36; t286 = t44 * t285; t291 = t25 * t123 * t9; t304 = 0.3141592654e1 * xc; t305 = t304 * t212; t312 = t256 * t18; t315 = t8 * t60; t319 = t54 * t30 * t58; t323 = t90 * t36; t324 = t44 * t323; t325 = t55 * t58; t326 = t325 * t60; 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; t332 = t8 * t95; t335 = t136 * t85; t337 = t256 * t227; t340 = t177 * t119; t346 = t37 * t86; t351 = t103 * t15; t352 = t177 * t351; t355 = t64 * t119; t358 = t8 * t227; t361 = t85 * 0.3141592654e1; t365 = t84 * t39; t372 = ZB * t10; t373 = t372 * t38; t374 = t47 * t373; t379 = t177 * t39; 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; t386 = t54 * t30 * t93; t387 = ZA * t85; t389 = t171 * t387 * t16; t394 = t64 * t60; t398 = t304 * t25 * t15; t401 = t361 * t25; t405 = t84 * t65; t410 = t148 * t18; t414 = t25 * t16 * t9; t417 = t84 * t74; t422 = t177 * t86; t428 = ZB * t38; t429 = t47 * t428; t432 = t148 * t39; 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; t442 = t36 * t9 * t118; t444 = t123 * t9; t445 = t8 * t444; t448 = t361 * t36; t451 = t47 * t372 * t17; t454 = t94 * t60; t457 = t25 * t103; t465 = t47 * t372 * t15; t468 = t36 * t85; t469 = t468 * t16; t474 = t43 * t85; t478 = t8 * t74; t484 = t256 * t74; t489 = t198 * ZA * t10 * t15; 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; t504 = t33 * t36 * t55 * t38; t507 = t37 * t18; t512 = t47 * ZB * t13 * t10; t518 = t59 * t95; t530 = t84 * t351; t534 = t37 * t227; 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; t557 = t468 * t118; t562 = t93 * t58; t563 = t562 * t60; t567 = t44 * t90 * t93; t575 = ZA * t55; t576 = t575 * t428; t583 = t37 * t60; t590 = t140 * t3; 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; t604 = nz * t36; t606 = t154 * t95; t625 = t36 * t103; t640 = t30 * t36; t641 = t54 * t640; t642 = t325 * t95; 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; t652 = t36 * t16; t653 = t652 * t9; t655 = t64 * t227; t658 = t182 * t95; t663 = t562 * t95; t684 = t64 * t351; t689 = t36 * t10; t695 = t154 * t222; 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; t711 = t575 * t373; t717 = t304 * t17 * t25; t736 = t177 * t74; 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; t750 = t64 * t262; t763 = t44 * t640; t770 = t84 * t119; 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; t797 = t64 * t149; 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; t827 = t84 * t149; t846 = t54 * nz * ZA; t854 = t64 * t18; 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; 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; t914 = t25 * ZB; t915 = t33 * t914; t919 = t4 * t4; t920 = t16 * t919; t929 = t123 * t90; t932 = t919 * t103; t935 = t33 * ZB; t939 = t652 * t919; t942 = t16 * t30; t943 = t942 * t4; t949 = t103 * t16; t950 = t949 * t90; 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; t954 = t171 * t36; t955 = t90 * nz; t956 = xc * t955; t957 = t118 * t10; t964 = t33 * t33; t965 = t964 * ZB; t966 = t965 * t640; t967 = t10 * t919; t968 = t55 * t16; t969 = t967 * t968; t972 = t935 * t36; t974 = t103 * t30 * t4; t977 = xc * t16; t978 = t967 * t977; t981 = t90 * t30; t983 = t16 * t10; t987 = t182 * ZA; t988 = t4 * t10; t992 = t171 * t604; t993 = xc * t14; t994 = t932 * t993; t997 = t182 * t30; t1005 = t171 * t285; t1006 = t988 * t993; t1009 = t58 * t914; t1010 = t1009 * t31; 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; t1015 = t964 * t25; t1016 = ZA * t30; t1017 = t1015 * t1016; t1020 = t967 * t993; t1031 = t1009 * t118; t1032 = t31 * t10; t1040 = t964 * t914; t1041 = t1040 * t90; t1044 = t55 * t10 * t4 * t16; t1047 = t1040 * t30; t1050 = t123 * ZA; t1054 = t977 * t988; 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; t1058 = t1009 * nz; t1063 = t932 * ZA; t1069 = t123 * t30 * t4; t1080 = t993 * t103 * t4; t1088 = t935 * t103; 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; t1113 = t955 * t118 * xc; t1120 = t4 * t118; t1125 = t981 * xc; t1133 = nz * t10; 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; t1153 = xc * t118; t1165 = t182 * t16; t1170 = t171 * t10; t1178 = ZA * t90; 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; t1195 = t1040 * t981; t1199 = t1009 * t955; t1203 = t1009 * t10; t1211 = t965 * t323; 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; 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; _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); /****************************************************************************************/ t1 = nz * nz; t2 = t1 * nz; t3 = nx * t2; t4 = 0.3141592654e1 * ZA; t5 = t3 * t4; t6 = nx * 0.3141592654e1; t7 = t6 * xc; t8 = PetscSinReal(t7); t9 = t8 * ZB; t10 = nz * 0.3141592654e1; t11 = PetscExpReal(t10); t12 = t11 * t11; t15 = PetscExpReal(xc * nz * 0.3141592654e1); t16 = t15 * t15; t17 = t16 * t16; t18 = t17 * t15; t19 = t12 * t18; t23 = t1 * t1; t24 = nx * t23; t25 = ZB * ZB; t27 = t18 * t8; t28 = 0.3141592654e1 * 0.3141592654e1; t29 = xc * xc; t30 = t28 * t29; t34 = t1 * xc; t35 = 0.3141592654e1 * ZB; t36 = t34 * t35; t37 = PetscCosReal(t7); t38 = ZA * t37; t39 = nx * nx; t40 = t39 * t12; t41 = t16 * t15; t43 = t38 * t40 * t41; t46 = t25 * nz; t47 = t46 * 0.3141592654e1; t48 = t39 * nx; t49 = PetscSinReal(t6); t50 = t48 * t49; t51 = t12 * t11; t52 = t51 * t17; t53 = t50 * t52; t56 = t34 * 0.3141592654e1 * t25; t57 = t37 * t39; t58 = t17 * t41; t59 = t12 * t58; t60 = t57 * t59; t63 = t25 * t18; t64 = t57 * nz; t67 = ZA * ZA; t68 = t67 * nz; t69 = 0.3141592654e1 * t48; t70 = t68 * t69; t71 = t49 * xc; t72 = t17 * t16; t73 = t11 * t72; t74 = t71 * t73; t77 = t1 * t67; t78 = t77 * 0.3141592654e1; t81 = nx * t25; t82 = t81 * t49; t83 = t17 * t17; t85 = t1 * t83 * t11; t87 = nx * ZB; t88 = t8 * t2; t89 = t87 * t88; t90 = 0.3141592654e1 * xc; t91 = t12 * t12; t92 = ZA * t91; t97 = ZB * ZA; t98 = t97 * t37; t99 = t39 * nz; t100 = t12 * t41; 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; t105 = t67 * t48; t106 = t49 * t51; t107 = t106 * t72; t109 = t1 * 0.3141592654e1; t110 = t109 * xc; t115 = nx * t67; t116 = t115 * t49; t117 = t1 * t16; t118 = t117 * t11; t120 = t2 * t25; t121 = t28 * 0.3141592654e1; t122 = t121 * t29; t123 = t120 * t122; t129 = t1 * ZB; t130 = t129 * t4; t131 = t57 * t100; t134 = t12 * t16; t136 = t109 * t39; t139 = ZB * t18; t141 = t39 * t1; t142 = t141 * t90; t145 = t77 * t90; t146 = t91 * t41; t147 = t57 * t146; t151 = t25 * t39 * t1; t152 = t72 * t12; t156 = t49 * t2; t158 = t83 * t11; 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; t164 = t115 * t88; t165 = t90 * t19; t168 = t25 * t48; t169 = t49 * t16; t170 = t169 * t11; t174 = ZA * nz * t69; t175 = ZB * t51; t176 = t175 * t17; t177 = t71 * t176; t180 = t1 * t29; t181 = t28 * t25; t182 = t180 * t181; t183 = t50 * t73; t186 = ZA * t1; t187 = t28 * t48; t188 = t186 * t187; t189 = ZB * t17; t190 = t189 * t11; t191 = t71 * t190; t194 = t50 * t158; t196 = t115 * t156; t197 = t90 * t73; t201 = t49 * t17 * t11; t204 = t88 * t90; t207 = t68 * 0.3141592654e1; t208 = t17 * t11; t209 = t50 * t208; 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; t212 = t2 * 0.3141592654e1; t213 = t212 * t52; t215 = t81 * t8; t216 = t212 * t59; t219 = t3 * t90; t220 = t25 * t8; t221 = t18 * t91; t225 = t71 * t52; t231 = t16 * t51; t232 = t50 * t231; t237 = ZA * t12; t243 = t67 * t28; t244 = t24 * t243; t245 = t71 * t231; 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; t252 = t25 * t37; t253 = t252 * t39; t255 = nz * t15 * t12; t258 = t2 * t29; t259 = ZB * t28; t260 = t258 * t259; t263 = t106 * t17; t265 = xc * t25; t269 = t25 * t49; t270 = t269 * t52; t273 = t1 * t25; t274 = t273 * 0.3141592654e1; t275 = t57 * t19; t278 = t24 * t30; t288 = t1 * t11 * t72; t290 = t212 * t208; t292 = t2 * xc; 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; t301 = t50 * t176; t304 = t51 * t72; t305 = t71 * t304; t308 = t25 * t41; t311 = ZA * t48; t312 = t311 * t49; t317 = t91 * t15; t318 = t57 * t317; t321 = t81 * t88; t322 = t90 * t59; t325 = t212 * t231; t327 = t15 * t12; t328 = t57 * t327; t331 = t77 * t187; t334 = t2 * ZA; t335 = t334 * t122; t336 = t50 * t190; 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; t341 = t169 * t51; t344 = t49 * t11 * t72; t346 = t77 * t30; t347 = t50 * t304; t350 = t25 * t51; t352 = nx * ZA; t353 = t49 * t23; t354 = t352 * t353; t355 = t28 * xc; t362 = t25 * t91; t365 = t23 * nz; t366 = nx * t365; t367 = t366 * t122; t368 = ZB * t49; t369 = ZA * t51; t370 = t369 * t17; t371 = t368 * t370; t374 = t115 * t353; t375 = t355 * t73; 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; t382 = t71 * t208; t394 = t2 * t67; t395 = t394 * t122; t398 = t352 * t156; t402 = t17 * t12; t403 = t39 * ZA; t404 = t402 * t403; t407 = t269 * t208; t411 = t49 * t83 * t11; t413 = t46 * t69; 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; t424 = t16 * t11; t425 = t212 * t424; t427 = t258 * t181; t430 = t67 * t29; t431 = t366 * t430; t432 = t121 * t49; t433 = t432 * t52; t436 = nz * t12; t437 = t436 * t18; t440 = t29 * xc; t441 = t440 * t121; t442 = t394 * t441; t445 = t67 * t37; t446 = t445 * t39; t448 = nz * t18 * t91; t453 = t352 * t49; t458 = t8 * t23; t462 = t81 * t458; t463 = t30 * t19; 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; t470 = t436 * t58; t475 = t2 * t121 * t440 * t25; t485 = t212 * t73; t488 = t67 * t72 * t1; t490 = t39 * xc; 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; t503 = t115 * t8; t510 = t355 * t19; t513 = t432 * t208; t525 = t38 * t40 * t18; 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; t536 = t28 * t37; t538 = t490 * t100; t541 = t334 * t441; t547 = t394 * t30; t550 = t212 * t19; t553 = t366 * t441; t556 = nz * t17; 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; t583 = t90 * t317; t594 = t212 * t158; t596 = t152 * t67; t602 = t67 * t17; 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; t613 = t83 * t25; t616 = t81 * t156; t627 = t90 * t231; t630 = t91 * t16; 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; t643 = t77 * t355; t648 = t115 * t458; t651 = t134 * t67; t657 = t30 * t304; t660 = t30 * t146; t665 = t25 * t17; t668 = t50 * t424; 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; t672 = t90 * t424; t676 = t120 * t536; t680 = t436 * t41; t688 = t366 * t67 * t440; t696 = xc * t12; t697 = t696 * t18; t701 = t252 * t141; t702 = t90 * t221; 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; t712 = t24 * t430; t713 = t28 * t49; t721 = t1 * t17 * t11; t726 = ZB * xc; t737 = nz * t91; 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; t745 = t269 * t231; t749 = t1 * t28 * t265; t757 = t16 * t39; t758 = t696 * t757; t762 = t69 * t49; t772 = t355 * t100; t775 = t81 * t353; 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; t790 = t212 * t304; t793 = t156 * 0.3141592654e1; t795 = t355 * t304; t800 = t91 * t39; t801 = t800 * nz; t807 = t2 * t28; t808 = t807 * t726; 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; t812 = t117 * t51; t821 = t24 * t355; t827 = t90 * t304; t840 = t800 * t41; 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; t849 = t1 * t51; t850 = t849 * t17; t860 = t269 * t424; t863 = t273 * t187; 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; t879 = xc * ZA; t888 = t67 * t51; t901 = ZA * t17; t903 = t368 * t901 * t11; 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; t923 = t71 * t424; t926 = t87 * t458; t927 = t28 * ZA; 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; t948 = t90 * t327; t961 = t30 * t100; t964 = t29 * t49; t981 = t106 * t1; 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; 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; t1018 = t212 * t100; t1029 = t212 * t327; 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; 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; t1079 = t58 * t8; t1091 = t807 * t29; t1092 = t665 * t40; t1101 = ZB * t91; t1102 = t403 * nz; 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; t1108 = t849 * t72; t1121 = t737 * t15; t1124 = t29 * t12; 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; t1134 = t394 * t28; 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; t1161 = nz * t83; t1173 = ZB * t12; 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; 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; t1234 = t25 * ZB; t1235 = t1234 * t28; t1236 = t365 * t91; t1240 = ZB * t121; t1241 = t1240 * t77; t1242 = t39 * t39; t1243 = t12 * t1242; t1244 = xc * t72; t1245 = t1243 * t1244; t1248 = t365 * t25; t1252 = t243 * nz; t1257 = t23 * t1; t1258 = t1240 * t1257; t1259 = t67 * t12; t1260 = xc * t16; t1268 = t1234 * t121; t1269 = t1268 * t23; t1272 = t1242 * t91; t1280 = t67 * xc; t1284 = t28 * t28; t1285 = t67 * t1284; t1287 = t1285 * t2 * ZB; t1288 = t17 * xc; t1289 = t1243 * t1288; 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; t1293 = t365 * t83; t1300 = ZA * t1284; t1304 = t17 * t1242 * t25 * t12; t1307 = t927 * t2; t1311 = t23 * t2; t1312 = t1300 * t1311; t1316 = t1234 * t1284; t1317 = t1316 * t1311; t1321 = t1240 * t23; t1331 = t1240 * t23 * t67; t1332 = t40 * t1244; t1338 = t1243 * t1260; 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; t1346 = t1316 * t2; t1349 = t927 * nz; t1350 = t25 * t1242; t1354 = t1268 * t1257; t1366 = t1268 * t1; t1370 = t29 * t17; t1371 = t1243 * t1370; 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; t1387 = t1257 * t12; t1391 = t1240 * t1; t1399 = t1272 * t1260; t1412 = t1285 * t1311; 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; t1456 = t365 * ZB; 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; t1472 = t1316 * t365; t1474 = t1124 * t39 * t17; t1478 = t17 * t91; t1504 = t72 * t39; 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; 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; t1564 = t1260 * t800; 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; _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); /****************************************************************************************/ t1 = nz * nz; t2 = t1 * nz; t3 = t2 * nx; t4 = nx * 0.3141592654e1; t5 = t4 * xc; t6 = PetscSinReal(t5); t7 = 0.3141592654e1 * 0.3141592654e1; t9 = t3 * t6 * t7; t10 = xc * xc; t11 = ZA * ZA; t12 = t10 * t11; t13 = nz * 0.3141592654e1; t14 = PetscExpReal(t13); t15 = t14 * t14; t16 = xc * nz; t18 = PetscExpReal(t16 * 0.3141592654e1); t19 = t18 * t18; t20 = t19 * t18; t21 = t15 * t20; t22 = t12 * t21; t25 = nx * t6; t26 = t1 * 0.3141592654e1; t27 = t25 * t26; t28 = ZA * ZB; t29 = t18 * t15; t30 = t28 * t29; t33 = t25 * nz; t34 = t11 * t15; t35 = t19 * t19; t36 = t35 * t18; t40 = t25 * t1; t41 = 0.3141592654e1 * t11; t42 = t15 * t36; t43 = t41 * t42; t46 = nx * nx; t47 = t1 * t46; t48 = t47 * t11; t49 = t7 * xc; t50 = t35 * t15; t51 = t49 * t50; t55 = PetscSinReal(t4); t56 = t46 * nx * t55; t58 = t56 * nz * t7; t59 = ZB * ZB; t60 = t10 * t59; t61 = t15 * t14; t62 = t19 * t61; t63 = t60 * t62; t66 = t19 * t14; t67 = t60 * t66; t70 = t28 * t42; t73 = PetscCosReal(t5); t74 = t47 * t73; t75 = t7 * t11; t77 = t75 * t10 * t36; t80 = t73 * t46; t81 = t80 * nz; t82 = 0.3141592654e1 * t59; t83 = t82 * t42; t87 = xc * t11; t88 = t87 * t62; t91 = nz * nx; t92 = t55 * t61; t96 = nx * t55; t98 = t96 * t2 * t7; t101 = xc * t59; t102 = t101 * t62; t108 = t1 * t1; t109 = t108 * t7; t111 = t59 * t35; t112 = t111 * t15; t115 = t35 * t20; t123 = t1 * nx * t55; t124 = t61 * t35; t127 = t35 * t19; t128 = t61 * t127; t129 = t60 * t128; t132 = t56 * t16; t133 = t7 * t59; t134 = t133 * t124; 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; t139 = t56 * 0.3141592654e1; t140 = t111 * t14; t144 = t49 * t124; t147 = t91 * t55; t148 = t61 * ZA; t154 = ZA * t115 * xc * ZB; t157 = t7 * 0.3141592654e1; t159 = t96 * t108 * t157; t160 = t10 * xc; t161 = t160 * t59; t162 = t35 * t14; t163 = t161 * t162; t166 = t28 * t162; t169 = t80 * t13; t170 = t101 * t42; t173 = t2 * t11; t174 = t96 * t173; t175 = t7 * t10; t179 = t59 * t15; t184 = t15 * t15; 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; t194 = t173 * 0.3141592654e1; t195 = xc * t15; t196 = t195 * t19; t202 = t15 * t115; t203 = t28 * t202; t206 = t96 * t26; t207 = t14 * t127; t208 = t101 * t207; t211 = t12 * t128; t218 = t11 * t61; t219 = t218 * t35; t221 = t108 * ZA; t223 = t7 * ZB; t224 = t223 * t50; t227 = ZA * xc; t228 = ZB * t15; t229 = t228 * t36; t230 = t227 * t229; t233 = t87 * t207; t236 = t6 * t11; 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; t244 = t227 * t228 * t20; t252 = t184 * t18; t253 = t101 * t252; t256 = t35 * t35; t257 = t256 * t14; t258 = t28 * t257; t261 = t108 * t11; t263 = t7 * t35; t268 = ZB * t61 * t35; t273 = t96 * t108 * t160; t274 = t157 * ZB; t276 = t274 * t148 * t35; t279 = t101 * t21; t282 = 0.3141592654e1 * xc; t283 = t59 * t36; t284 = t282 * t283; 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; t290 = t1 * t11; t291 = t96 * t290; t297 = t59 * t61; t298 = t297 * t127; t300 = ZB * t36; t301 = t227 * t300; t304 = t1 * t59; t305 = t184 * t35; t310 = t46 * ZB; t311 = t184 * ZA; t312 = t310 * t311; t314 = t60 * t21; t317 = t1 * ZA; t318 = ZB * t35; t321 = t1 * t256; t324 = t96 * t261; t325 = t10 * t157; t326 = t325 * t124; 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; t331 = t28 * t124; t334 = 0.3141592654e1 * t15; t335 = t334 * t127; t338 = t35 * ZA; t341 = t46 * t256; t344 = t46 * t11; t346 = t46 * t59; t348 = t297 * t35; t351 = ZA * t10; t352 = t351 * t300; t355 = t1 * ZB; 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; t363 = t36 * t184; t364 = t87 * t363; t368 = t47 * t73 * t7; t373 = t160 * t157; t374 = t373 * t124; t377 = t311 * t35; t380 = t12 * t62; t386 = ZB * t10 * ZA * t15 * t20; t389 = t87 * t66; t393 = t56 * t1 * t10; 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; t412 = t11 * t14 * t127; t416 = t11 * t19; t417 = t416 * t61; t421 = t96 * t2 * ZA; t426 = t56 * nz * ZA; t427 = t318 * t14; t428 = t49 * t427; t431 = t82 * t29; t434 = t87 * t21; 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; t443 = t184 * t20; t447 = t61 * 0.3141592654e1; t448 = t447 * t11; t450 = t49 * t268; t453 = t60 * t42; t456 = t41 * t202; t463 = t101 * t443; t469 = t41 * xc * t20; 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; t482 = t108 * t10; t492 = nz * t46; t493 = t492 * t11; t495 = t282 * t19 * t184; t498 = t56 * t290; t499 = t325 * t162; t502 = t416 * t14; t504 = t60 * t207; 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; t508 = t101 * t162; t512 = t41 * t115 * xc; t515 = t87 * t42; t520 = ZB * t184; t522 = t227 * t520 * t18; t525 = t492 * t59; t528 = t6 * t59; t532 = t520 * t20; t533 = t351 * t532; t539 = t447 * t59; 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; t551 = t87 * t162; t554 = t351 * t229; t560 = t59 * t19; t561 = t560 * t14; t564 = t101 * t202; t567 = t87 * t252; t573 = t227 * t228 * t115; 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; t579 = t82 * t202; t591 = t282 * t115 * t59; t598 = t101 * t66; 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; t608 = t373 * t162; t611 = t59 * t184; t617 = t101 * t29; t624 = t227 * ZB * t18 * t15; t629 = t157 * t59; t630 = t629 * t124; t633 = t3 * t6; t634 = t175 * t283; 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; t645 = t41 * t29; t648 = t2 * 0.3141592654e1; t649 = t648 * xc; t650 = t560 * t184; t656 = t56 * t1 * t157; t659 = t87 * t128; t662 = t96 * t482; t663 = t629 * t162; t671 = t161 * t124; t674 = t218 * t127; 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; t714 = t334 * t19; t719 = t12 * t42; 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; t730 = xc * t19; t735 = t59 * t256 * t14; 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; t755 = t28 * t21; t759 = t274 * t338 * t14; t767 = t11 * t35; t768 = t767 * t14; t778 = t560 * t61; 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; t786 = t12 * t443; t790 = t282 * t59 * t20; t796 = t59 * t14 * t127; t806 = t41 * t21; 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; t819 = t282 * t15 * t127; t822 = t101 * t363; t830 = t11 * t256 * t14; t835 = t227 * t532; 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; t845 = t87 * t202; t854 = t338 * t15; t859 = t12 * t207; 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; t880 = t60 * t443; t891 = t101 * t128; 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; t903 = t179 * t19; t920 = t56 * t1 * t160; 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; t932 = t87 * t29; t945 = t82 * t21; 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; t971 = t282 * t127; 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; t997 = xc * t127; t998 = t997 * t59; 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; t1006 = t2 * t59; t1017 = xc * t35; 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; 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; t1070 = t15 * t19; 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; 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; t1119 = t321 * t46; t1122 = t157 * t11; t1123 = t1122 * t2; t1124 = t184 * t46; t1128 = t108 * nz; t1132 = t7 * t7; t1133 = t1132 * t11; t1134 = t1133 * t108; t1135 = t15 * t46; t1139 = t7 * ZA; t1140 = t1139 * ZB; t1141 = t1 * t35; t1145 = t629 * t2; t1146 = t1135 * t730; t1149 = t157 * t1128; t1150 = t1149 * xc; t1153 = t46 * xc; t1154 = t1153 * t127; t1158 = t184 * t1 * t46; t1161 = t46 * t46; t1162 = t35 * t1161; t1166 = t7 * t1; 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; t1171 = t1161 * t184; t1175 = t1122 * nz; t1176 = t15 * t1161; t1180 = t1132 * ZA; t1181 = t1180 * t355; t1182 = t1176 * t1017; t1185 = t1161 * xc; t1189 = t1133 * t1; t1192 = t108 * t1; t1193 = t1132 * t1192; t1195 = t10 * t35; t1199 = t157 * t15; t1203 = t1141 * t46; t1211 = t184 * t108; 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; t1221 = t256 * t1161; t1224 = t35 * t108; t1233 = t7 * t256; 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; t1240 = t1135 * t1195; t1252 = t629 * t127; t1263 = t1171 * ZA; 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; t1283 = t1199 * t19; t1287 = t1199 * t127; t1289 = t59 * nz * t1161; t1293 = t157 * nz * xc; t1304 = t1132 * t108; t1310 = t263 * ZB; t1316 = t2 * t15; 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; t1330 = t1132 * t15; t1336 = t1132 * t1; t1338 = t1162 * t179; 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; t1376 = t7 * t184; t1380 = t1176 * t1195; t1393 = t1330 * t35; 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; 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; _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); /****************************************************************************************/ t1 = nz * nz; t2 = t1 * xc; t3 = ZB * ZB; t5 = t2 * 0.3141592654e1 * t3; t6 = nx * 0.3141592654e1; t7 = t6 * xc; t8 = PetscCosReal(t7); t9 = nx * nx; t10 = t8 * t9; t11 = nz * 0.3141592654e1; t12 = PetscExpReal(t11); t13 = t12 * t12; t16 = PetscExpReal(xc * nz * 0.3141592654e1); t17 = t16 * t16; t18 = t17 * t16; t19 = t17 * t17; t20 = t19 * t18; t21 = t13 * t20; t22 = t10 * t21; t25 = ZA * ZA; t26 = t1 * t25; t27 = xc * 0.3141592654e1; t28 = t26 * t27; t29 = t19 * t16; t30 = t13 * t13; t31 = t29 * t30; t35 = t9 * nx; t36 = t3 * t35; t37 = PetscSinReal(t6); t38 = t13 * t12; t39 = t37 * t38; t40 = t39 * t19; t42 = t1 * t1; t43 = nx * t42; t44 = xc * xc; t45 = t25 * t44; t46 = t43 * t45; t47 = 0.3141592654e1 * 0.3141592654e1; t48 = t47 * t37; t49 = t17 * t38; t54 = 0.3141592654e1 * t35; t55 = ZA * nz * t54; t56 = t37 * ZB; t57 = t19 * t12; t61 = t25 * t8; t62 = t61 * t9; t63 = nz * t30; t64 = t63 * t16; t67 = t1 * nz; t69 = t47 * ZB; t70 = t67 * t44 * t69; t75 = nx * t3; t76 = t75 * t37; t77 = t67 * 0.3141592654e1; t78 = t19 * t19; t79 = t78 * t12; t80 = t77 * t79; t82 = t3 * t38; t84 = t54 * t37; t87 = PetscSinReal(t7); t88 = t29 * t87; t89 = t47 * t44; t93 = nx * t25; t94 = t87 * t42; t95 = t93 * t94; t96 = t47 * xc; t97 = t13 * t29; t98 = t96 * t97; t101 = t87 * t67; t102 = t93 * t101; t103 = t13 * t18; t107 = t47 * t35; t108 = t26 * t107; t109 = t37 * t44; t110 = t19 * t17; t111 = t12 * t110; t116 = t37 * t19 * t12; t118 = t37 * xc; t119 = ZB * t19; t120 = t119 * t12; t121 = t118 * t120; t125 = xc * t3; t126 = t1 * t47 * t125; t127 = t35 * t37; t128 = t38 * t19; t129 = t127 * t128; t132 = t26 * 0.3141592654e1; t133 = t16 * t13; t134 = t10 * t133; t137 = 0.3141592654e1 * ZB; t138 = t2 * t137; t139 = ZA * t8; t140 = t9 * t13; t145 = t30 * t18; t146 = t10 * t145; t149 = t3 * t8; t150 = t149 * t9; 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; t154 = t42 * nz; t155 = nx * t154; t156 = t44 * xc; t157 = t47 * 0.3141592654e1; t158 = t156 * t157; t159 = t155 * t158; t162 = t56 * ZA * t19 * t12; t165 = t77 * t49; t167 = t1 * t3; t168 = t167 * t89; t169 = t127 * t49; t172 = t37 * t67; t173 = t75 * t172; t174 = t38 * t110; t175 = t27 * t174; t179 = t47 * t25; t181 = t10 * t97; t184 = t27 * t31; t187 = t67 * t47; t188 = t44 * t3; t189 = t187 * t188; t192 = t25 * t35; t193 = t37 * t17; t194 = t193 * t12; t196 = nx * ZA; t197 = t196 * t172; t198 = ZB * t38; t199 = t198 * t19; t204 = t1 * t12 * t110; t207 = nx * ZB; t209 = t1 * ZA; t215 = t67 * t3; t216 = t47 * t8; t217 = t215 * t216; t218 = t9 * xc; t222 = nx * t67; t223 = t222 * t27; t224 = t3 * t87; t228 = t167 * t107; t232 = t26 * t96; t235 = t207 * t94; t236 = t47 * ZA; t243 = xc * t13; t244 = t243 * t29; t248 = t25 * nz; t249 = t248 * 0.3141592654e1; t253 = ZB * ZA; t254 = t253 * t8; t255 = t9 * nz; t256 = t30 * t16; 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; t263 = t43 * t179; t267 = t3 * nz; t268 = t267 * t54; t269 = t118 * t57; t272 = t39 * t1; t274 = t67 * t25; t275 = t274 * t158; t278 = t75 * t87; t279 = t77 * t103; t282 = t25 * t38; t285 = ZA * t38; t290 = t267 * 0.3141592654e1; t296 = t77 * t111; t298 = t196 * t37; t299 = t1 * ZB; t303 = t37 * t42; t304 = t196 * t303; t308 = t77 * t57; t310 = t26 * t89; t313 = t77 * t128; t316 = t101 * t27; t319 = t93 * t87; t320 = t77 * t97; t323 = t127 * t57; t326 = t10 * nz; t329 = t118 * t174; 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; t335 = t75 * t101; t336 = t27 * t21; t342 = t77 * t133; t347 = t209 * t137; t350 = t9 * t1; t351 = t149 * t350; t355 = t37 * t78 * t12; t359 = t93 * t303; t367 = t172 * 0.3141592654e1; t369 = t96 * t103; t376 = t209 * t107; t379 = t10 * t103; t383 = t207 * t101; t389 = 0.3141592654e1 * ZA; t390 = t222 * t389; t391 = t87 * ZB; 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; t402 = t39 * t110; t404 = t193 * t38; t406 = t127 * t174; t408 = t167 * 0.3141592654e1; t411 = t44 * t157; t412 = t155 * t411; t413 = t285 * t19; t414 = t56 * t413; t417 = ZA * t30; t424 = t93 * t37; t426 = t248 * t54; t427 = t17 * t12; t428 = t118 * t427; t431 = t77 * t21; t438 = ZA * t13; t443 = t93 * t172; t444 = t27 * t427; t448 = t1 * t78 * t12; t455 = t274 * t89; t461 = t118 * t111; 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; t469 = nz * t16 * t13; t474 = t1 * t38; t475 = t474 * t19; t480 = t89 * t103; t483 = t67 * ZA; t484 = t483 * t411; t485 = t127 * t120; t488 = t127 * t111; t497 = t77 * t427; t502 = t27 * t97; t508 = t1 * t19 * t12; t511 = t155 * t25 * t156; t512 = t157 * t37; t513 = t512 * t128; t527 = t1 * t17; t528 = t527 * t38; 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; t535 = t44 * t13; t542 = t527 * t12; t544 = nz * t13; t545 = t544 * t20; t548 = t75 * t303; t549 = t96 * t111; t552 = ZA * t35; t553 = t552 * t37; t562 = t43 * t96; t563 = t3 * t37; t564 = t563 * t128; t579 = t474 * t110; t590 = t9 * t30; t591 = t590 * t18; t595 = t127 * t427; t598 = t77 * t174; 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; t601 = t27 * t49; t604 = t127 * t79; t606 = ZB * t29; t616 = t139 * t140 * t18; t638 = t10 * t256; t643 = t118 * t199; t653 = t544 * t29; t658 = t3 * t29; t660 = t350 * t27; 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; t670 = t274 * t411; t673 = t118 * t49; t694 = t155 * t45; t713 = nz * t29 * t30; t717 = t20 * t87; t723 = t512 * t57; 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; t734 = t43 * t89; t735 = t563 * t427; t740 = t75 * t94; t744 = ZB * xc; t750 = t563 * t57; t754 = t218 * t103; t771 = t127 * t199; t776 = t89 * t174; 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; t794 = t483 * t158; t801 = t2 * 0.3141592654e1; t818 = t215 * t411; t827 = t96 * t174; t837 = t37 * t12 * t110; 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; t864 = t544 * t18; t867 = t3 * t18; t884 = t27 * t256; t891 = t187 * t744; t894 = t563 * t49; 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; t904 = t27 * t111; t907 = t118 * t128; t915 = t89 * t145; t947 = t139 * t140 * t29; 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; t969 = t67 * t157 * t156 * t3; t974 = t27 * t133; 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; t1042 = t89 * t97; 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; 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; t1103 = t42 * t1 * t157; t1104 = t1103 * t25; t1108 = t3 * t19; t1112 = nz * t47; t1113 = t9 * t9; t1118 = t42 * t157; t1119 = t1118 * t9; t1120 = t25 * xc; t1121 = t13 * t110; t1122 = t1120 * t1121; t1125 = t47 * t47; t1126 = t67 * t1125; t1127 = t1113 * ZA; t1128 = t1126 * t1127; t1129 = t19 * t13; t1130 = t744 * t1129; t1133 = t154 * t1125; t1134 = t1133 * t9; t1135 = t45 * t1129; t1138 = t154 * t47; t1139 = t25 * t30; t1142 = t1126 * t1113; t1145 = t125 * t1129; t1148 = t1103 * xc; t1149 = t3 * t13; t1150 = t1149 * t17; t1153 = t25 * t78; 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; t1157 = t25 * t13; t1158 = t1157 * t17; t1161 = t13 * t17; t1162 = t1120 * t1161; t1165 = t3 * t78; t1170 = t42 * t67 * t1125; t1172 = t1108 * t13; t1175 = t1 * t157; t1176 = t1175 * t1113; t1182 = t1120 * t1129; t1189 = t110 * t9 * xc; t1192 = t1149 * t110; 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; t1209 = t17 * t30; t1210 = t125 * t1209; t1213 = t1138 * ZA; t1214 = ZB * t30; t1218 = t1157 * t110; t1226 = t3 * t30; t1237 = t1170 * t25; 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; t1251 = t125 * t1121; t1260 = t1120 * t1209; t1263 = t1139 * t19; 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; t1287 = t188 * t1129; t1292 = t25 * t19; t1296 = t187 * t9; t1297 = t1226 * t19; t1311 = t1112 * t1113; 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; t1320 = t253 * t1129; t1328 = t253 * t30 * t19; t1333 = t125 * t1161; t1343 = ZB * t44 * t1129; 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; t1369 = t1133 * t9 * ZA; t1378 = t187 * ZA; t1383 = t1170 * ZA; 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; 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; _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); /****************************************************************************************/ /****************************************************************************************/ if (x>xc) { _PC1=_PC1B; _PC2=_PC2B; _PC3=_PC3B; _PC4=_PC4B; Z=ZB; } else { _PC1=_PC1A; _PC2=_PC2A; _PC3=_PC3A; _PC4=_PC4A; Z=ZA; } /****************************************************************************************/ /****************************************************************************************/ t1 = nz * nz; t2 = t1 * t1; t3 = t2 * nz; t4 = x * t3; t5 = 0.3141592654e1 * 0.3141592654e1; t6 = t5 * 0.3141592654e1; t11 = _PC3 * t6; t12 = x * nz; t13 = nx * nx; t14 = t13 * t13; t15 = t12 * t14; t19 = PetscExpReal(t12 * 0.3141592654e1); t20 = t19 * t19; t21 = t4 * t20; t24 = _PC1 * t5; t25 = Z * t20; t29 = _PC1 * t6; t30 = t29 * Z; t31 = t1 * nz; t32 = x * t31; t33 = t32 * t13; t36 = t11 * x; t41 = nz * t20; t45 = t6 * _PC4; t49 = t20 * t1; t51 = _PC2 * Z; 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; t58 = t32 * t6; t59 = _PC4 * t20; t63 = t20 * t13; t67 = t12 * t6; t68 = t20 * t14; t87 = t49 * t13; 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; t106 = _PC3 * t5; 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; t129 = PetscSinReal(nx * 0.3141592654e1 * x); 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; t158 = t5 * Z; u1 = (t55 + t90 + t120 + t155) / (0.4e1 * t158 * t19 * t2 + 0.8e1 * t158 * t19 * t1 * t13 + 0.4e1 * t158 * t19 * t14); /****************************************************************************************/ /****************************************************************************************/ t1 = nz * nz; t2 = t1 * nz; t3 = x * t2; t4 = 0.3141592654e1 * 0.3141592654e1; t5 = t4 * 0.3141592654e1; t6 = t3 * t5; t7 = _PC2 * Z; t8 = nx * nx; t12 = t1 * t1; t13 = t12 * nz; t14 = x * t13; t15 = t5 * _PC4; t16 = x * nz; t18 = PetscExpReal(t16 * 0.3141592654e1); t19 = t18 * t18; t23 = t16 * t5; t24 = t8 * t8; t28 = _PC3 * t5; t29 = t14 * t19; t32 = _PC1 * t5; t33 = t32 * Z; t34 = t16 * t24; t37 = _PC4 * t19; t45 = _PC2 * t4; t53 = t19 * t8; t58 = _PC4 * t4; t60 = t1 * t19 * t8; t63 = t19 * t24; t67 = t3 * t8; t73 = nz * t19; t86 = t28 * x; 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; t94 = Z * t12; 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; t146 = PetscCosReal(nx * 0.3141592654e1 * x); 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; t159 = t4 * Z; 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); /****************************************************************************************/ /****************************************************************************************/ t1 = 0.3141592654e1 * 0.3141592654e1; t2 = t1 * 0.3141592654e1; t3 = _PC1 * t2; t4 = t3 * Z; t5 = nz * nz; t6 = t5 * t5; t7 = t6 * nz; t8 = x * t7; t9 = x * nz; t11 = PetscExpReal(t9 * 0.3141592654e1); t12 = t11 * t11; t13 = t8 * t12; t16 = t5 * nz; t17 = x * t16; t18 = t17 * t2; t19 = _PC4 * t12; t20 = nx * nx; t24 = t2 * _PC4; t28 = _PC3 * t2; t29 = t28 * x; t30 = t12 * nz; t31 = t20 * t20; t40 = _PC2 * Z; t44 = t9 * t2; t48 = t12 * t20; t52 = t17 * t20; 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; t58 = t9 * t31; t61 = _PC3 * t1; t62 = t12 * t31; t73 = t5 * t20; t78 = _PC1 * t1; t90 = Z * t12; 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; t101 = PetscCosReal(nx * 0.3141592654e1 * x); t102 = t11 * t101; t109 = t12 * t5; t110 = t109 * t20; 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; 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; t159 = t1 * t11; u3 = (t57 + t94 + t128 + t156) / (0.4e1 * t159 * t6 + 0.8e1 * t159 * t73 + 0.4e1 * t159 * t31); /****************************************************************************************/ /****************************************************************************************/ t1 = _PC2 * Z; t2 = 0.3141592654e1 * 0.3141592654e1; t3 = t2 * 0.3141592654e1; t4 = nz * nz; t5 = t4 * t4; t6 = t5 * t4; t8 = t3 * t6 * x; t11 = x * t4; t12 = t11 * t3; t15 = PetscExpReal(x * nz * 0.3141592654e1); t16 = t15 * t15; t17 = _PC3 * t16; t18 = nx * nx; t19 = t18 * t18; t23 = t5 * nz; t24 = t2 * t23; t28 = t1 * t3; t29 = t6 * x; t30 = t29 * t16; t33 = _PC4 * t3; t34 = t5 * x; t35 = t34 * t18; t41 = PetscSinReal(nx * 0.3141592654e1 * x); t47 = t11 * t19; t54 = t3 * _PC3; 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; t58 = 0.3141592654e1 * t16; t60 = t2 * _PC4; t69 = t4 * nz; t73 = t1 * t2; t75 = t69 * t16 * t18; t79 = x * t16; t83 = nz * t16; t84 = t83 * t19; 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; t97 = t34 * t3; t101 = Z * _PC1; t102 = t16 * t19; t106 = t16 * t18; t127 = t2 * t69; t131 = t2 * nz; 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; 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; u4 = (t57 + t95 + t135 + t164) / (0.4e1 * t24 * t15 + 0.8e1 * t127 * t15 * t18 + 0.4e1 * t131 * t15 * t19); /****************************************************************************************/ /****************************************************************************************/ u5 = (PetscReal)(-2*Z*nz*PETSC_PI*u2-u3*2*nz*PETSC_PI)*PetscCosReal(nz*PETSC_PI*z); /* pressure */ u6 = (PetscReal)(u3*2*nz*PETSC_PI + 4*Z*nz*PETSC_PI*u2)*PetscCosReal(nz*PETSC_PI*z); /* zz stress */ sum5 +=u5; sum6 +=u6; u1 *= PetscCosReal(nz*PETSC_PI*z); /* x velocity */ sum1 += u1; u2 *= PetscSinReal(nz*PETSC_PI*z); /* z velocity */ sum2 += u2; u3 *= 2*nz*PETSC_PI*PetscCosReal(nz*PETSC_PI*z); /* xx stress */ sum3 += u3; u4 *= 2*nz*PETSC_PI*PetscSinReal(nz*PETSC_PI*z); /* zx stress */ sum4 += u4; /* Output */ if (mu) { *mu = Z; } if (vel) { vel[0] = sum1; vel[1] = sum2; } if (p) { (*p) = sum5; } if (s) { s[0] = sum3; s[1] = sum4; s[2] = sum6; } if (gamma) { /* sigma = tau - p, tau = sigma + p, tau[] = 2*eta*gamma[] */ gamma[0] = (sum3+sum5)/(2.0*Z); gamma[1] = (sum4)/(2.0*Z); gamma[2] = (sum6+sum5)/(2.0*Z); } PetscFunctionReturn(0); } static PetscErrorCode SolCxSolutionVelocity(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar v[], void *ctx) { Parameter *s = (Parameter *) ctx; PetscErrorCode ierr; PetscFunctionBegin; ierr = SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, v, NULL, NULL, NULL, NULL);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode SolCxSolutionPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar p[], void *ctx) { Parameter *s = (Parameter *) ctx; PetscErrorCode ierr; PetscFunctionBegin; ierr = SolCxSolution(x, s->m, s->n, s->xc, s->etaA, s->etaB, NULL, p, NULL, NULL, NULL);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) { PetscInt sol; PetscErrorCode ierr; PetscFunctionBeginUser; options->debug = 0; options->dim = 2; options->serRef = 0; options->simplex = PETSC_TRUE; options->showSolution = PETSC_FALSE; options->showError = PETSC_FALSE; options->solType = SOLKX; ierr = PetscOptionsBegin(comm, "", "Variable-Viscosity Stokes Problem Options", "DMPLEX");CHKERRQ(ierr); ierr = PetscOptionsInt("-debug", "The debugging level", "ex69.c", options->debug, &options->debug, NULL);CHKERRQ(ierr); ierr = PetscOptionsInt("-dim", "The topological mesh dimension", "ex69.c", options->dim, &options->dim, NULL);CHKERRQ(ierr); ierr = PetscOptionsBool("-simplex", "Use simplices or tensor product cells", "ex69.c", options->simplex, &options->simplex, NULL);CHKERRQ(ierr); ierr = PetscOptionsInt("-serial_refinements", "Number of serial uniform refinements steps", "ex69.c", options->serRef, &options->serRef, NULL);CHKERRQ(ierr); ierr = PetscOptionsBool("-show_solution", "Output the solution for verification", "ex69.c", options->showSolution, &options->showSolution, NULL);CHKERRQ(ierr); ierr = PetscOptionsBool("-show_error", "Output the error for verification", "ex69.c", options->showError, &options->showError, NULL);CHKERRQ(ierr); sol = options->solType; ierr = PetscOptionsEList("-sol_type", "Type of exact solution", "ex69.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL);CHKERRQ(ierr); options->solType = (SolutionType) sol; ierr = PetscOptionsEnd(); PetscFunctionReturn(0); } static PetscErrorCode SetUpParameters(AppCtx *user) { PetscBag bag; Parameter *p; PetscErrorCode ierr; PetscFunctionBeginUser; /* setup PETSc parameter bag */ ierr = PetscBagGetData(user->bag, (void **) &p);CHKERRQ(ierr); ierr = PetscBagSetName(user->bag, "par", "Problem parameters");CHKERRQ(ierr); bag = user->bag; switch (user->solType) { case SOLKX: ierr = PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation");CHKERRQ(ierr); ierr = PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation");CHKERRQ(ierr); ierr = PetscBagRegisterReal(bag, &p->B, 1.0, "B", "Exponential scale for viscosity variation");CHKERRQ(ierr); break; case SOLCX: ierr = PetscBagRegisterInt(bag, &p->n, 1, "n", "x-wavelength for forcing variation");CHKERRQ(ierr); ierr = PetscBagRegisterInt(bag, &p->m, 1, "m", "z-wavelength for forcing variation");CHKERRQ(ierr); ierr = PetscBagRegisterReal(bag, &p->etaA, 1.0, "etaA", "Viscosity for x < xc");CHKERRQ(ierr); ierr = PetscBagRegisterReal(bag, &p->etaB, 1.0, "etaB", "Viscosity for x > xc");CHKERRQ(ierr); ierr = PetscBagRegisterReal(bag, &p->xc, 0.5, "xc", "x-coordinate of the viscosity jump");CHKERRQ(ierr); break; default: SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]); } PetscFunctionReturn(0); } static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) { DM dmDist = NULL; PetscPartitioner part; PetscInt dim = user->dim; PetscInt cells[3]; PetscErrorCode ierr; PetscFunctionBeginUser; if (dim > 3) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"dim %D is too big, must be <= 3",dim); cells[0] = cells[1] = cells[2] = user->simplex ? dim : 3; ierr = DMPlexCreateBoxMesh(comm, dim, user->simplex, cells, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr); /* Make split labels so that we can have corners in multiple labels */ { const char *names[4] = {"markerBottom", "markerRight", "markerTop", "markerLeft"}; PetscInt ids[4] = {1, 2, 3, 4}; DMLabel label; IS is; PetscInt f; for (f = 0; f < 4; ++f) { ierr = DMGetStratumIS(*dm, "marker", ids[f], &is);CHKERRQ(ierr); if (!is) continue; ierr = DMCreateLabel(*dm, names[f]);CHKERRQ(ierr); ierr = DMGetLabel(*dm, names[f], &label);CHKERRQ(ierr); if (is) { ierr = DMLabelInsertIS(label, is, 1);CHKERRQ(ierr); } ierr = ISDestroy(&is);CHKERRQ(ierr); } } ierr = PetscObjectSetName((PetscObject)(*dm),"Mesh");CHKERRQ(ierr); { PetscInt r; for (r = 0; r < user->serRef; ++r) { DM dmRefined; ierr = DMPlexSetRefinementUniform(*dm, PETSC_TRUE);CHKERRQ(ierr); ierr = DMRefine(*dm, PetscObjectComm((PetscObject)*dm), &dmRefined);CHKERRQ(ierr); if (dmRefined) { ierr = DMDestroy(dm);CHKERRQ(ierr); *dm = dmRefined; } } } /* Distribute mesh over processes */ ierr = DMPlexGetPartitioner(*dm, &part);CHKERRQ(ierr); ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr); ierr = DMPlexDistribute(*dm, 0, NULL, &dmDist);CHKERRQ(ierr); if (dmDist) { ierr = PetscObjectSetName((PetscObject)dmDist,"Distributed Mesh");CHKERRQ(ierr); ierr = DMDestroy(dm);CHKERRQ(ierr); *dm = dmDist; } ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode SetupProblem(DM dm, AppCtx *user) { PetscErrorCode (*exactFunc)(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx); PetscDS prob; const PetscInt id = 1; PetscInt comp; Parameter *ctx; void *data; PetscErrorCode ierr; PetscFunctionBeginUser; ierr = DMGetDS(dm, &prob);CHKERRQ(ierr); switch (user->solType) { case SOLKX: ierr = PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_kx);CHKERRQ(ierr); ierr = PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_kx, NULL, NULL, NULL);CHKERRQ(ierr); break; case SOLCX: ierr = PetscDSSetResidual(prob, 0, f0_u, stokes_momentum_cx);CHKERRQ(ierr); ierr = PetscDSSetResidual(prob, 1, stokes_mass, f1_zero);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_cx);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobian(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 0, 0, NULL, NULL, NULL, stokes_momentum_vel_J_kx);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 0, 1, NULL, NULL, stokes_momentum_pres_J, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 1, 0, NULL, stokes_mass_J, NULL, NULL);CHKERRQ(ierr); ierr = PetscDSSetJacobianPreconditioner(prob, 1, 1, stokes_identity_J_cx, NULL, NULL, NULL);CHKERRQ(ierr); break; default: SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]); } ierr = PetscBagGetData(user->bag, &data);CHKERRQ(ierr); switch (user->dim) { case 2: switch (user->solType) { case SOLKX: ierr = PetscDSSetExactSolution(prob, 0, SolKxSolutionVelocity, data);CHKERRQ(ierr); ierr = PetscDSSetExactSolution(prob, 1, SolKxSolutionPressure, data);CHKERRQ(ierr); break; case SOLCX: ierr = PetscDSSetExactSolution(prob, 0, SolCxSolutionVelocity, data);CHKERRQ(ierr); ierr = PetscDSSetExactSolution(prob, 1, SolCxSolutionPressure, data);CHKERRQ(ierr); break; default: SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid solution type %d (%s)", (PetscInt) user->solType, solTypes[PetscMin(user->solType, NUM_SOL_TYPES)]); } break; default: SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %D", user->dim); } /* Setup constants */ { Parameter *param; ierr = PetscBagGetData(user->bag, (void **) ¶m);CHKERRQ(ierr); switch (user->solType) { case SOLKX: { PetscScalar constants[3]; constants[0] = param->m; constants[1] = param->n; constants[2] = param->B; ierr = PetscDSSetConstants(prob, 3, constants);CHKERRQ(ierr); } break; case SOLCX: { PetscScalar constants[5]; constants[0] = param->m; constants[1] = param->n; constants[2] = param->etaA; constants[3] = param->etaB; constants[4] = param->xc; ierr = PetscDSSetConstants(prob, 5, constants);CHKERRQ(ierr); } break; default: SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP, "No parameter information for solution type %d", user->solType); } } /* Setup Boundary Conditions */ ierr = PetscDSGetExactSolution(prob, 0, &exactFunc, (void **) &ctx);CHKERRQ(ierr); comp = 1; ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallB", "markerBottom", 0, 1, &comp, (void (*)(void)) exactFunc, NULL, 1, &id, ctx);CHKERRQ(ierr); comp = 0; ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallR", "markerRight", 0, 1, &comp, (void (*)(void)) exactFunc, NULL, 1, &id, ctx);CHKERRQ(ierr); comp = 1; ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallT", "markerTop", 0, 1, &comp, (void (*)(void)) exactFunc, NULL, 1, &id, ctx);CHKERRQ(ierr); comp = 0; ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wallL", "markerLeft", 0, 1, &comp, (void (*)(void)) exactFunc, NULL, 1, &id, ctx);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user) { DM cdm = dm; const PetscInt dim = user->dim; PetscFE fe[2]; MPI_Comm comm; PetscErrorCode ierr; PetscFunctionBeginUser; /* Create discretization of solution fields */ ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr); ierr = PetscFECreateDefault(comm, dim, dim, user->simplex, "vel_", PETSC_DEFAULT, &fe[0]);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) fe[0], "velocity");CHKERRQ(ierr); ierr = PetscFECreateDefault(comm, dim, 1, user->simplex, "pres_", PETSC_DEFAULT, &fe[1]);CHKERRQ(ierr); ierr = PetscFECopyQuadrature(fe[0], fe[1]);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) fe[1], "pressure");CHKERRQ(ierr); /* Set discretization and boundary conditions for each mesh */ ierr = DMSetField(dm, 0, NULL, (PetscObject) fe[0]);CHKERRQ(ierr); ierr = DMSetField(dm, 1, NULL, (PetscObject) fe[1]);CHKERRQ(ierr); ierr = DMCreateDS(dm);CHKERRQ(ierr); ierr = SetupProblem(dm, user);CHKERRQ(ierr); while (cdm) { ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr); ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); } ierr = PetscFEDestroy(&fe[0]);CHKERRQ(ierr); ierr = PetscFEDestroy(&fe[1]);CHKERRQ(ierr); { PetscObject pressure; MatNullSpace nullSpacePres; ierr = DMGetField(dm, 1, NULL, &pressure);CHKERRQ(ierr); ierr = MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres);CHKERRQ(ierr); ierr = PetscObjectCompose(pressure, "nullspace", (PetscObject) nullSpacePres);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullSpacePres);CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode CreatePressureNullSpace(DM dm, AppCtx *user, Vec *v, MatNullSpace *nullSpace) { Vec vec; PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero_vector, one_scalar}; PetscErrorCode ierr; PetscFunctionBeginUser; ierr = DMCreateGlobalVector(dm, &vec);CHKERRQ(ierr); ierr = DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);CHKERRQ(ierr); ierr = VecNormalize(vec, NULL);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) vec, "Pressure Null Space");CHKERRQ(ierr); ierr = VecViewFromOptions(vec, NULL, "-null_space_vec_view");CHKERRQ(ierr); ierr = MatNullSpaceCreate(PetscObjectComm((PetscObject) dm), PETSC_FALSE, 1, &vec, nullSpace);CHKERRQ(ierr); if (v) {*v = vec;} else {ierr = VecDestroy(&vec);CHKERRQ(ierr);} PetscFunctionReturn(0); } int main(int argc, char **argv) { SNES snes; /* nonlinear solver */ DM dm; /* problem definition */ Vec u,r; /* solution, residual vectors */ Mat J, M; /* Jacobian matrix */ MatNullSpace nullSpace; /* May be necessary for pressure */ Vec nullVec; PetscScalar pint; AppCtx user; /* user-defined work context */ PetscInt its; /* iterations for convergence */ PetscReal error = 0.0; /* L_2 error in the solution */ PetscReal ferrors[2]; PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero_vector, zero_scalar}; PetscErrorCode ierr; ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr; ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr); ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr); ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr); ierr = SNESSetDM(snes, dm);CHKERRQ(ierr); ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr); /* Setup problem parameters */ ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);CHKERRQ(ierr); ierr = SetUpParameters(&user);CHKERRQ(ierr); /* Setup problem */ ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr); ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr); ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr); ierr = VecDuplicate(u, &r);CHKERRQ(ierr); ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr); ierr = CreatePressureNullSpace(dm, &user, &nullVec, &nullSpace);CHKERRQ(ierr); { /* set tolerances */ KSP ksp; ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr); ierr = KSPSetTolerances(ksp,1.e-2*PETSC_SMALL,PETSC_SMALL,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr); } ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); /* There should be a way to express this using the DM */ ierr = SNESSetUp(snes);CHKERRQ(ierr); ierr = SNESGetJacobian(snes, &J, &M, NULL, NULL);CHKERRQ(ierr); ierr = MatSetNullSpace(J, nullSpace);CHKERRQ(ierr); { PetscErrorCode (*exacts[2])(PetscInt dim, PetscReal t, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx); void *ectxs[2]; PetscDS ds; ierr = DMGetDS(dm, &ds);CHKERRQ(ierr); ierr = PetscDSGetExactSolution(ds, 0, &exacts[0], &ectxs[0]);CHKERRQ(ierr); ierr = PetscDSGetExactSolution(ds, 1, &exacts[1], &ectxs[1]);CHKERRQ(ierr); ierr = DMProjectFunction(dm, 0.0, exacts, ectxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) u, "Exact Solution");CHKERRQ(ierr); ierr = VecViewFromOptions(u, NULL, "-exact_vec_view");CHKERRQ(ierr); ierr = VecDot(nullVec, u, &pint);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD, "Integral of pressure: %g\n",(double) (PetscAbsScalar(pint) < 1.0e-14 ? 0.0 : PetscRealPart(pint)));CHKERRQ(ierr); ierr = DMSNESCheckFromOptions(snes, u);CHKERRQ(ierr); ierr = DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) u, "Initial Solution");CHKERRQ(ierr); ierr = VecViewFromOptions(u, NULL, "-initial_vec_view");CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) u, "Solution");CHKERRQ(ierr); ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr); ierr = SNESGetIterationNumber(snes, &its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);CHKERRQ(ierr); ierr = DMComputeL2Diff(dm, 0.0, exacts, ectxs, u, &error);CHKERRQ(ierr); ierr = DMComputeL2FieldDiff(dm, 0.0, exacts, ectxs, u, ferrors);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %.3g [%.3g, %.3g]\n", (double)error, (double)ferrors[0], (double)ferrors[1]);CHKERRQ(ierr); ierr = VecDot(nullVec, u, &pint);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD, "Integral of pressure: %g\n", (double) (PetscAbsScalar(pint) < 1.0e-14 ? 0.0 : PetscRealPart(pint)));CHKERRQ(ierr); if (user.showError) { Vec r; ierr = DMGetGlobalVector(dm, &r);CHKERRQ(ierr); ierr = DMProjectFunction(dm, 0.0, exacts, ectxs, INSERT_ALL_VALUES, r);CHKERRQ(ierr); ierr = VecAXPY(r, -1.0, u);CHKERRQ(ierr); ierr = PetscObjectSetName((PetscObject) r, "Solution Error");CHKERRQ(ierr); ierr = VecViewFromOptions(r, NULL, "-error_vec_view");CHKERRQ(ierr); ierr = DMRestoreGlobalVector(dm, &r);CHKERRQ(ierr); } } if (user.showSolution) { ierr = PetscPrintf(PETSC_COMM_WORLD, "Solution\n");CHKERRQ(ierr); ierr = VecChop(u, 3.0e-9);CHKERRQ(ierr); ierr = VecView(u, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); } ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr); ierr = VecDestroy(&nullVec);CHKERRQ(ierr); ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&r);CHKERRQ(ierr); ierr = SNESDestroy(&snes);CHKERRQ(ierr); ierr = DMDestroy(&dm);CHKERRQ(ierr); ierr = PetscBagDestroy(&user.bag);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; } /*TEST # 2D serial P2/P1 tests 0-2 test: suffix: 0 requires: triangle filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type svd -snes_error_if_not_converged -ksp_error_if_not_converged -snes_view -dm_view -dmsnes_check .001 -show_solution test: suffix: 1 requires: triangle filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type svd -snes_error_if_not_converged -ksp_error_if_not_converged -snes_view -dm_view -dmsnes_check .001 -show_solution test: suffix: 2 requires: triangle filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_use_amat -ksp_rtol 1.0e-9 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-9 -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -ksp_error_if_not_converged -snes_view -dm_view -dmsnes_check .001 -show_solution # 2D serial discretization tests test: suffix: p2p1 requires: triangle filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: p2p1ref requires: triangle filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q2q1 requires: filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q2q1ref requires: !single filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q1p0 requires: filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q1p0ref requires: filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -dm_refine 2 -vel_petscspace_degree 1 -pres_petscspace_degree 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q2p1 requires: filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu -fieldsplit_pressure_pc_factor_shift_type -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view test: suffix: q2p1ref requires: !single filter: sed -e "s/SNES iterations *= *[123]/SNES iterations=4/g" -e "s/solver iterations *= *[123]/solver iterations=4/g" -e "s/evaluations=2/evaluations=3/g" args: -dm_plex_separate_marker -simplex 0 -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pc_fieldsplit_diag_use_amat -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition a11 -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type lu -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view # FETI-DP tests testset: output_file: output/ex69_q2p1fetidp.out suffix: q2p1fetidp requires: !single nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" | sed -e "s/type: seqaijviennacl/type: seqaij/g" -e "s/type: seqaijcusparse/type: seqaij/g" args: -petscpartitioner_type simple -dm_plex_separate_marker -simplex 0 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -pres_petscdualspace_lagrange_node_endpoints 0 -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd test: suffix: aij args: -matis_localmat_type aij test: requires: viennacl suffix: aijviennacl args: -matis_localmat_type aijviennacl test: requires: cuda suffix: aijcusparse args: -matis_localmat_type aijcusparse testset: suffix: q2p1fetidp_deluxe output_file: output/ex69_q2p1fetidp_deluxe.out requires: mumps double nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" | sed -e "s/type: seqaijviennacl/type: seqaij/g" -e "s/type: seqaijcusparse/type: seqaij/g" args: -petscpartitioner_type simple -dm_plex_separate_marker -simplex 0 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -snes_error_if_not_converged -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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 -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 test: suffix: aij args: -matis_localmat_type aij test: suffix: aij_seqdense args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense test: requires: viennacl suffix: aijviennacl args: -matis_localmat_type aijviennacl test: requires: cuda suffix: aijcusparse args: -matis_localmat_type aijcusparse testset: suffix: q2p1fetidp_deluxe_adaptive output_file: output/ex69_q2p1fetidp_deluxe_adaptive.out requires: mumps double nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" | sed -e "s/type: seqaijviennacl/type: seqaij/g" -e "s/type: seqaijcusparse/type: seqaij/g" args: -petscpartitioner_type simple -dm_plex_separate_marker -simplex 0 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -pres_petscspace_poly_tensor 0 -pres_petscdualspace_lagrange_continuity 0 -snes_error_if_not_converged -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_sub_schurs_mat_solver_type mumps -fetidp_bddc_pc_bddc_adaptive_threshold 1.3 -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd test: suffix: aij args: -matis_localmat_type aij test: suffix: aij_seqdense args: -matis_localmat_type aij -fetidp_bddc_sub_schurs_schur_mat_type seqdense test: requires: viennacl suffix: aijviennacl args: -matis_localmat_type aijviennacl test: requires: cuda suffix: aijcusparse args: -matis_localmat_type aijcusparse test: suffix: p2p1fetidp requires: triangle nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly test: suffix: p2p1fetidp_allp requires: triangle nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type svd -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly -ksp_fetidp_pressure_all test: suffix: p2p1fetidp_discharm requires: triangle nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly -fetidp_pc_discrete_harmonic -fetidp_harmonic_pc_type cholesky test: suffix: p2p1fetidp_lumped requires: triangle nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -snes_view -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly -fetidp_pc_lumped test: suffix: p2p1fetidp_deluxe requires: triangle mumps nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0 test: suffix: p2p1fetidp_deluxe_discharm requires: triangle mumps nsize: 5 filter: grep -v "variant HERMITIAN" | grep -v "SNES iterations" | grep -v "solver iterations" | grep -v "evaluations=" args: -petscpartitioner_type simple -dm_plex_separate_marker -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -snes_error_if_not_converged -ksp_error_if_not_converged -dm_view -dm_mat_type is -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_pc_fieldsplit_schur_fact_type diag -fetidp_fieldsplit_p_pc_type jacobi -fetidp_fieldsplit_lag_ksp_type preonly -fetidp_fieldsplit_p_ksp_type preonly -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat -fetidp_bddc_sub_schurs_mat_mumps_icntl_14 500 -fetidp_bddc_sub_schurs_posdef 0 -fetidp_bddc_sub_schurs_discrete_harmonic testset: nsize: 3 requires: triangle output_file: output/ex69_p2p1fetidp_olof.out args: -dm_view -dm_mat_type is -dm_refine 1 -dm_plex_separate_marker -vel_petscspace_degree 2 -pres_petscspace_degree 1 -petscpartitioner_type simple -snes_error_if_not_converged -ksp_error_if_not_converged -ksp_type fetidp -ksp_fetidp_saddlepoint -ksp_fetidp_saddlepoint_flip -fetidp_ksp_type cg -fetidp_ksp_norm_type natural -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_dirichlet_pc_type none -fetidp_bddc_pc_bddc_neumann_pc_type svd -fetidp_bddc_pc_bddc_coarse_redundant_pc_type cholesky -fetidp_pc_discrete_harmonic 1 -fetidp_harmonic_pc_type cholesky -fetidp_fieldsplit_lag_ksp_error_if_not_converged 0 -fetidp_fieldsplit_lag_ksp_type chebyshev -fetidp_fieldsplit_lag_ksp_max_it 2 -ksp_fetidp_pressure_schur -fetidp_fieldsplit_p_ksp_type preonly -fetidp_fieldsplit_p_pc_type bddc -fetidp_fieldsplit_p_pc_bddc_dirichlet_pc_type none test: suffix: p2p1fetidp_olof_full args: -fetidp_pc_fieldsplit_schur_fact_type full test: suffix: p2p1fetidp_olof_diag args: -fetidp_pc_fieldsplit_schur_fact_type diag test: suffix: p2p1fetidp_olof_additive args: -fetidp_pc_fieldsplit_type additive TEST*/