1 static char help[] = "Poisson Problem with a split domain.\n\ 2 We solve the Poisson problem in two halves of a domain.\n\ 3 In one half, we include an additional field.\n\n\n"; 4 5 #include <petscdmplex.h> 6 #include <petscsnes.h> 7 #include <petscds.h> 8 #include <petscconvest.h> 9 10 typedef struct { 11 PetscInt dummy; 12 } AppCtx; 13 14 static PetscErrorCode quad_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) { 15 u[0] = x[0] * x[0] + x[1] * x[1]; 16 return 0; 17 } 18 19 static PetscErrorCode quad_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) { 20 u[0] = 2.0; 21 return 0; 22 } 23 24 static void f0_quad_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[]) { 25 PetscInt d; 26 for (d = 0; d < dim; ++d) f0[0] += 2.0; 27 } 28 29 static void f0_quad_p(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[]) { 30 f0[0] = u[uOff[1]] - 2.0; 31 } 32 33 static void f1_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 f1[]) { 34 PetscInt d; 35 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 36 } 37 38 static void g3_uu(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[]) { 39 PetscInt d; 40 for (d = 0; d < dim; ++d) g3[d * dim + d] = 1.0; 41 } 42 43 static void g0_pp(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[]) { 44 g0[0] = 1.0; 45 } 46 47 static PetscErrorCode DivideDomain(DM dm, AppCtx *user) { 48 DMLabel top, bottom; 49 PetscReal low[3], high[3], midy; 50 PetscInt cStart, cEnd, c; 51 52 PetscFunctionBeginUser; 53 PetscCall(DMCreateLabel(dm, "top")); 54 PetscCall(DMCreateLabel(dm, "bottom")); 55 PetscCall(DMGetLabel(dm, "top", &top)); 56 PetscCall(DMGetLabel(dm, "bottom", &bottom)); 57 PetscCall(DMGetCoordinatesLocalSetUp(dm)); 58 PetscCall(DMGetBoundingBox(dm, low, high)); 59 midy = 0.5 * (high[1] - low[1]); 60 PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd)); 61 for (c = cStart; c < cEnd; ++c) { 62 PetscReal centroid[3]; 63 64 PetscCall(DMPlexComputeCellGeometryFVM(dm, c, NULL, centroid, NULL)); 65 if (centroid[1] > midy) PetscCall(DMLabelSetValue(top, c, 1)); 66 else PetscCall(DMLabelSetValue(bottom, c, 1)); 67 } 68 PetscCall(DMPlexLabelComplete(dm, top)); 69 PetscFunctionReturn(0); 70 } 71 72 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) { 73 PetscFunctionBeginUser; 74 PetscCall(DMCreate(comm, dm)); 75 PetscCall(DMSetType(*dm, DMPLEX)); 76 PetscCall(DMSetFromOptions(*dm)); 77 PetscCall(DivideDomain(*dm, user)); 78 PetscCall(DMSetApplicationContext(*dm, user)); 79 PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view")); 80 PetscFunctionReturn(0); 81 } 82 83 static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user) { 84 PetscDS ds; 85 PetscWeakForm wf; 86 DMLabel label; 87 const PetscInt id = 1; 88 89 PetscFunctionBeginUser; 90 PetscCall(DMGetRegionNumDS(dm, 0, &label, NULL, &ds)); 91 PetscCall(PetscDSGetWeakForm(ds, &wf)); 92 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u)); 93 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu)); 94 PetscCall(PetscDSSetExactSolution(ds, 0, quad_u, user)); 95 PetscCall(DMGetRegionNumDS(dm, 1, &label, NULL, &ds)); 96 PetscCall(PetscDSGetWeakForm(ds, &wf)); 97 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u)); 98 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu)); 99 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 1, 0, 0, f0_quad_p, 0, NULL)); 100 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 1, 1, 0, 0, g0_pp, 0, NULL, 0, NULL, 0, NULL)); 101 PetscCall(PetscDSSetExactSolution(ds, 0, quad_u, user)); 102 PetscCall(PetscDSSetExactSolution(ds, 1, quad_p, user)); 103 PetscCall(DMGetLabel(dm, "marker", &label)); 104 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void))quad_u, NULL, user, NULL)); 105 PetscFunctionReturn(0); 106 } 107 108 static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user) { 109 DM cdm = dm; 110 DMLabel top; 111 PetscFE fe, feTop; 112 PetscQuadrature q; 113 PetscInt dim; 114 PetscBool simplex; 115 const char *nameTop = "pressure"; 116 char prefix[PETSC_MAX_PATH_LEN]; 117 118 PetscFunctionBeginUser; 119 PetscCall(DMGetDimension(dm, &dim)); 120 PetscCall(DMPlexIsSimplex(dm, &simplex)); 121 PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name)); 122 PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)dm), dim, 1, simplex, name ? prefix : NULL, -1, &fe)); 123 PetscCall(PetscObjectSetName((PetscObject)fe, name)); 124 PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe)); 125 PetscCall(PetscFEGetQuadrature(fe, &q)); 126 PetscCall(PetscFEDestroy(&fe)); 127 PetscCall(DMGetLabel(dm, "top", &top)); 128 PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_top_", nameTop)); 129 PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)dm), dim, 1, simplex, name ? prefix : NULL, -1, &feTop)); 130 PetscCall(PetscObjectSetName((PetscObject)feTop, nameTop)); 131 PetscCall(PetscFESetQuadrature(feTop, q)); 132 PetscCall(DMSetField(dm, 1, top, (PetscObject)feTop)); 133 PetscCall(PetscFEDestroy(&feTop)); 134 PetscCall(DMCreateDS(dm)); 135 PetscCall((*setup)(dm, user)); 136 while (cdm) { 137 PetscCall(DMCopyDisc(dm, cdm)); 138 PetscCall(DMGetCoarseDM(cdm, &cdm)); 139 } 140 PetscFunctionReturn(0); 141 } 142 143 int main(int argc, char **argv) { 144 DM dm; /* Problem specification */ 145 SNES snes; /* Nonlinear solver */ 146 Vec u; /* Solutions */ 147 AppCtx user; /* User-defined work context */ 148 149 PetscFunctionBeginUser; 150 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 151 /* Primal system */ 152 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 153 PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm)); 154 PetscCall(SNESSetDM(snes, dm)); 155 PetscCall(SetupDiscretization(dm, "potential", SetupPrimalProblem, &user)); 156 PetscCall(DMCreateGlobalVector(dm, &u)); 157 PetscCall(VecSet(u, 0.0)); 158 PetscCall(PetscObjectSetName((PetscObject)u, "solution")); 159 PetscCall(DMPlexSetSNESLocalFEM(dm, &user, &user, &user)); 160 PetscCall(SNESSetFromOptions(snes)); 161 PetscCall(DMSNESCheckFromOptions(snes, u)); 162 PetscCall(SNESSolve(snes, NULL, u)); 163 PetscCall(SNESGetSolution(snes, &u)); 164 PetscCall(VecViewFromOptions(u, NULL, "-sol_view")); 165 /* Cleanup */ 166 PetscCall(VecDestroy(&u)); 167 PetscCall(SNESDestroy(&snes)); 168 PetscCall(DMDestroy(&dm)); 169 PetscCall(PetscFinalize()); 170 return 0; 171 } 172 173 /*TEST 174 175 test: 176 suffix: 2d_p1_0 177 requires: triangle 178 args: -potential_petscspace_degree 2 -pressure_top_petscspace_degree 0 -dm_refine 0 -dmsnes_check 179 180 test: 181 suffix: 2d_p1_1 182 requires: triangle 183 args: -potential_petscspace_degree 1 -pressure_top_petscspace_degree 0 -dm_refine 0 -convest_num_refine 3 -snes_convergence_estimate 184 185 TEST*/ 186