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 { 16 u[0] = x[0]*x[0] + x[1]*x[1]; 17 return 0; 18 } 19 20 static PetscErrorCode quad_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 21 { 22 u[0] = 2.0; 23 return 0; 24 } 25 26 static void f0_quad_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 27 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 28 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 29 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 30 { 31 PetscInt d; 32 for (d = 0; d < dim; ++d) f0[0] += 2.0; 33 } 34 35 static void f0_quad_p(PetscInt dim, PetscInt Nf, PetscInt NfAux, 36 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 37 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 38 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 39 { 40 f0[0] = u[uOff[1]] - 2.0; 41 } 42 43 static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 44 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 45 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 46 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 47 { 48 PetscInt d; 49 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 50 } 51 52 static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 53 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 54 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 55 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 56 { 57 PetscInt d; 58 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 59 } 60 61 static void g0_pp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 62 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 63 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 64 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 65 { 66 g0[0] = 1.0; 67 } 68 69 static PetscErrorCode DivideDomain(DM dm, AppCtx *user) 70 { 71 DMLabel top, bottom; 72 PetscReal low[3], high[3], midy; 73 PetscInt cStart, cEnd, c; 74 75 PetscFunctionBeginUser; 76 PetscCall(DMCreateLabel(dm, "top")); 77 PetscCall(DMCreateLabel(dm, "bottom")); 78 PetscCall(DMGetLabel(dm, "top", &top)); 79 PetscCall(DMGetLabel(dm, "bottom", &bottom)); 80 PetscCall(DMGetCoordinatesLocalSetUp(dm)); 81 PetscCall(DMGetBoundingBox(dm, low, high)); 82 midy = 0.5*(high[1] - low[1]); 83 PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd)); 84 for (c = cStart; c < cEnd; ++c) { 85 PetscReal centroid[3]; 86 87 PetscCall(DMPlexComputeCellGeometryFVM(dm, c, NULL, centroid, NULL)); 88 if (centroid[1] > midy) PetscCall(DMLabelSetValue(top, c, 1)); 89 else PetscCall(DMLabelSetValue(bottom, c, 1)); 90 } 91 PetscCall(DMPlexLabelComplete(dm, top)); 92 PetscFunctionReturn(0); 93 } 94 95 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) 96 { 97 PetscFunctionBeginUser; 98 PetscCall(DMCreate(comm, dm)); 99 PetscCall(DMSetType(*dm, DMPLEX)); 100 PetscCall(DMSetFromOptions(*dm)); 101 PetscCall(DivideDomain(*dm, user)); 102 PetscCall(DMSetApplicationContext(*dm, user)); 103 PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view")); 104 PetscFunctionReturn(0); 105 } 106 107 static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user) 108 { 109 PetscDS ds; 110 PetscWeakForm wf; 111 DMLabel label; 112 const PetscInt id = 1; 113 114 PetscFunctionBeginUser; 115 PetscCall(DMGetRegionNumDS(dm, 0, &label, NULL, &ds)); 116 PetscCall(PetscDSGetWeakForm(ds, &wf)); 117 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u)); 118 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu)); 119 PetscCall(PetscDSSetExactSolution(ds, 0, quad_u, user)); 120 PetscCall(DMGetRegionNumDS(dm, 1, &label, NULL, &ds)); 121 PetscCall(PetscDSGetWeakForm(ds, &wf)); 122 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u)); 123 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu)); 124 PetscCall(PetscWeakFormSetIndexResidual(wf, label, 1, 1, 0, 0, f0_quad_p, 0, NULL)); 125 PetscCall(PetscWeakFormSetIndexJacobian(wf, label, 1, 1, 1, 0, 0, g0_pp, 0, NULL, 0, NULL, 0, NULL)); 126 PetscCall(PetscDSSetExactSolution(ds, 0, quad_u, user)); 127 PetscCall(PetscDSSetExactSolution(ds, 1, quad_p, user)); 128 PetscCall(DMGetLabel(dm, "marker", &label)); 129 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) quad_u, NULL, user, NULL)); 130 PetscFunctionReturn(0); 131 } 132 133 static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user) 134 { 135 DM cdm = dm; 136 DMLabel top; 137 PetscFE fe, feTop; 138 PetscQuadrature q; 139 PetscInt dim; 140 PetscBool simplex; 141 const char *nameTop = "pressure"; 142 char prefix[PETSC_MAX_PATH_LEN]; 143 144 PetscFunctionBeginUser; 145 PetscCall(DMGetDimension(dm, &dim)); 146 PetscCall(DMPlexIsSimplex(dm, &simplex)); 147 PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name)); 148 PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, simplex, name ? prefix : NULL, -1, &fe)); 149 PetscCall(PetscObjectSetName((PetscObject) fe, name)); 150 PetscCall(DMSetField(dm, 0, NULL, (PetscObject) fe)); 151 PetscCall(PetscFEGetQuadrature(fe, &q)); 152 PetscCall(PetscFEDestroy(&fe)); 153 PetscCall(DMGetLabel(dm, "top", &top)); 154 PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_top_", nameTop)); 155 PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, simplex, name ? prefix : NULL, -1, &feTop)); 156 PetscCall(PetscObjectSetName((PetscObject) feTop, nameTop)); 157 PetscCall(PetscFESetQuadrature(feTop, q)); 158 PetscCall(DMSetField(dm, 1, top, (PetscObject) feTop)); 159 PetscCall(PetscFEDestroy(&feTop)); 160 PetscCall(DMCreateDS(dm)); 161 PetscCall((*setup)(dm, user)); 162 while (cdm) { 163 PetscCall(DMCopyDisc(dm,cdm)); 164 PetscCall(DMGetCoarseDM(cdm, &cdm)); 165 } 166 PetscFunctionReturn(0); 167 } 168 169 int main(int argc, char **argv) 170 { 171 DM dm; /* Problem specification */ 172 SNES snes; /* Nonlinear solver */ 173 Vec u; /* Solutions */ 174 AppCtx user; /* User-defined work context */ 175 176 PetscFunctionBeginUser; 177 PetscCall(PetscInitialize(&argc, &argv, NULL,help)); 178 /* Primal system */ 179 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 180 PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm)); 181 PetscCall(SNESSetDM(snes, dm)); 182 PetscCall(SetupDiscretization(dm, "potential", SetupPrimalProblem, &user)); 183 PetscCall(DMCreateGlobalVector(dm, &u)); 184 PetscCall(VecSet(u, 0.0)); 185 PetscCall(PetscObjectSetName((PetscObject) u, "solution")); 186 PetscCall(DMPlexSetSNESLocalFEM(dm, &user, &user, &user)); 187 PetscCall(SNESSetFromOptions(snes)); 188 PetscCall(DMSNESCheckFromOptions(snes, u)); 189 PetscCall(SNESSolve(snes, NULL, u)); 190 PetscCall(SNESGetSolution(snes, &u)); 191 PetscCall(VecViewFromOptions(u, NULL, "-sol_view")); 192 /* Cleanup */ 193 PetscCall(VecDestroy(&u)); 194 PetscCall(SNESDestroy(&snes)); 195 PetscCall(DMDestroy(&dm)); 196 PetscCall(PetscFinalize()); 197 return 0; 198 } 199 200 /*TEST 201 202 test: 203 suffix: 2d_p1_0 204 requires: triangle 205 args: -potential_petscspace_degree 2 -pressure_top_petscspace_degree 0 -dm_refine 0 -dmsnes_check 206 207 test: 208 suffix: 2d_p1_1 209 requires: triangle 210 args: -potential_petscspace_degree 1 -pressure_top_petscspace_degree 0 -dm_refine 0 -convest_num_refine 3 -snes_convergence_estimate 211 212 TEST*/ 213