1 static const char help[] = "Tests for determining whether a new finite element works"; 2 3 /* 4 Use -interpolation_view and -l2_projection_view to look at the interpolants. 5 */ 6 7 #include <petscdmplex.h> 8 #include <petscfe.h> 9 #include <petscds.h> 10 #include <petscsnes.h> 11 12 static void constant(PetscInt dim, PetscInt Nf, PetscInt NfAux, 13 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 14 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 15 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 16 { 17 const PetscInt Nc = uOff[1] - uOff[0]; 18 for (PetscInt c = 0; c < Nc; ++c) f0[c] += 5.; 19 } 20 21 static void linear(PetscInt dim, PetscInt Nf, PetscInt NfAux, 22 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 23 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 24 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 25 { 26 const PetscInt Nc = uOff[1] - uOff[0]; 27 for (PetscInt c = 0; c < Nc; ++c) f0[c] += 5.*x[c]; 28 } 29 30 static void quadratic(PetscInt dim, PetscInt Nf, PetscInt NfAux, 31 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 32 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 33 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 34 { 35 const PetscInt Nc = uOff[1] - uOff[0]; 36 for (PetscInt c = 0; c < Nc; ++c) f0[c] += 5.*x[c]*x[c]; 37 } 38 39 static void trig(PetscInt dim, PetscInt Nf, PetscInt NfAux, 40 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 41 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 42 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 43 { 44 const PetscInt Nc = uOff[1] - uOff[0]; 45 for (PetscInt c = 0; c < Nc; ++c) f0[c] += PetscCosReal(2.*PETSC_PI*x[c]); 46 } 47 48 /* 49 The prime basis for the Wheeler-Yotov-Xue prism. 50 */ 51 static void prime(PetscInt dim, PetscInt Nf, PetscInt NfAux, 52 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 53 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 54 PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 55 { 56 PetscReal x = X[0], y = X[1], z = X[2], b = 1 + x + y + z; 57 f0[0] += b + 2.0*x*z + 2.0*y*z + x*y + x*x; 58 f0[1] += b + 2.0*x*z + 2.0*y*z + x*y + y*y; 59 f0[2] += b - 3.0*x*z - 3.0*y*z - 2.0*z*z; 60 } 61 62 static const char *names[] = {"constant", "linear", "quadratic", "trig", "prime"}; 63 static PetscPointFunc functions[] = { constant, linear, quadratic, trig, prime }; 64 65 typedef struct { 66 PetscPointFunc exactSol; 67 PetscReal shear,flatten; 68 } AppCtx; 69 70 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 71 { 72 char name[PETSC_MAX_PATH_LEN] = "constant"; 73 PetscInt Nfunc = sizeof(names)/sizeof(char *), i; 74 PetscErrorCode ierr; 75 76 PetscFunctionBeginUser; 77 options->exactSol = NULL; 78 options->shear = 0.; 79 options->flatten = 1.; 80 81 ierr = PetscOptionsBegin(comm, "", "FE Test Options", "PETSCFE");PetscCall(ierr); 82 PetscCall(PetscOptionsString("-func", "Function to project into space", "", name, name, PETSC_MAX_PATH_LEN, NULL)); 83 PetscCall(PetscOptionsReal("-shear", "Factor by which to shear along the x-direction", "", options->shear, &(options->shear), NULL)); 84 PetscCall(PetscOptionsReal("-flatten", "Factor by which to flatten", "", options->flatten, &(options->flatten), NULL)); 85 ierr = PetscOptionsEnd();PetscCall(ierr); 86 87 for (i = 0; i < Nfunc; ++i) { 88 PetscBool flg; 89 90 PetscCall(PetscStrcmp(name, names[i], &flg)); 91 if (flg) {options->exactSol = functions[i]; break;} 92 } 93 PetscCheck(options->exactSol, comm, PETSC_ERR_ARG_WRONG, "Invalid test function %s", name); 94 PetscFunctionReturn(0); 95 } 96 97 /* The exact solution is the negative of the f0 contribution */ 98 static PetscErrorCode exactSolution(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 99 { 100 AppCtx *user = (AppCtx *) ctx; 101 PetscInt uOff[2] = {0, Nc}; 102 103 user->exactSol(dim, 1, 0, uOff, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, time, x, 0, NULL, u); 104 for (PetscInt c = 0; c < Nc; ++c) u[c] *= -1.; 105 return 0; 106 } 107 108 static void f0(PetscInt dim, PetscInt Nf, PetscInt NfAux, 109 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 110 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 111 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 112 { 113 const PetscInt Nc = uOff[1] - uOff[0]; 114 for (PetscInt c = 0; c < Nc; ++c) f0[c] += u[c]; 115 } 116 117 static void g0(PetscInt dim, PetscInt Nf, PetscInt NfAux, 118 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 119 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 120 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 121 { 122 const PetscInt Nc = uOff[1] - uOff[0]; 123 for (PetscInt c = 0; c < Nc; ++c) g0[c*Nc+c] = 1.0; 124 } 125 126 static PetscErrorCode SetupProblem(DM dm, AppCtx *user) 127 { 128 PetscDS ds; 129 PetscWeakForm wf; 130 131 PetscFunctionBeginUser; 132 PetscCall(DMGetDS(dm, &ds)); 133 PetscCall(PetscDSGetWeakForm(ds, &wf)); 134 PetscCall(PetscWeakFormSetIndexResidual(wf, NULL, 0, 0, 0, 0, f0, 0, NULL)); 135 PetscCall(PetscWeakFormSetIndexResidual(wf, NULL, 0, 0, 0, 1, user->exactSol, 0, NULL)); 136 PetscCall(PetscWeakFormSetIndexJacobian(wf, NULL, 0, 0, 0, 0, 0, g0, 0, NULL, 0, NULL, 0, NULL)); 137 PetscCall(PetscDSSetExactSolution(ds, 0, exactSolution, user)); 138 PetscFunctionReturn(0); 139 } 140 141 static PetscErrorCode SetupDiscretization(DM dm, const char name[], AppCtx *user) 142 { 143 DM cdm = dm; 144 PetscFE fe; 145 char prefix[PETSC_MAX_PATH_LEN]; 146 147 PetscFunctionBeginUser; 148 PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name)); 149 PetscCall(DMCreateFEDefault(dm, 1, name ? prefix : NULL, -1, &fe)); 150 PetscCall(PetscObjectSetName((PetscObject) fe, name ? name : "Solution")); 151 /* Set discretization and boundary conditions for each mesh */ 152 PetscCall(DMSetField(dm, 0, NULL, (PetscObject) fe)); 153 PetscCall(DMCreateDS(dm)); 154 PetscCall(SetupProblem(dm, user)); 155 while (cdm) { 156 PetscCall(DMCopyDisc(dm, cdm)); 157 PetscCall(DMGetCoarseDM(cdm, &cdm)); 158 } 159 PetscCall(PetscFEDestroy(&fe)); 160 PetscFunctionReturn(0); 161 } 162 163 /* This test tells us whether the given function is contained in the approximation space */ 164 static PetscErrorCode CheckInterpolation(DM dm, AppCtx *user) 165 { 166 PetscSimplePointFunc exactSol[1]; 167 void *exactCtx[1]; 168 PetscDS ds; 169 Vec u; 170 PetscReal error, tol = PETSC_SMALL; 171 MPI_Comm comm; 172 173 PetscFunctionBeginUser; 174 PetscCall(PetscObjectGetComm((PetscObject) dm, &comm)); 175 PetscCall(DMGetDS(dm, &ds)); 176 PetscCall(DMGetGlobalVector(dm, &u)); 177 PetscCall(PetscDSGetExactSolution(ds, 0, &exactSol[0], &exactCtx[0])); 178 PetscCall(DMProjectFunction(dm, 0.0, exactSol, exactCtx, INSERT_ALL_VALUES, u)); 179 PetscCall(VecViewFromOptions(u, NULL, "-interpolation_view")); 180 PetscCall(DMComputeL2Diff(dm, 0.0, exactSol, exactCtx, u, &error)); 181 PetscCall(DMRestoreGlobalVector(dm, &u)); 182 if (error > tol) PetscCall(PetscPrintf(comm, "Interpolation tests FAIL at tolerance %g error %g\n", (double) tol, (double) error)); 183 else PetscCall(PetscPrintf(comm, "Interpolation tests pass at tolerance %g\n", (double) tol)); 184 PetscFunctionReturn(0); 185 } 186 187 /* This test tells us whether the element is unisolvent (the mass matrix has full rank), and what rate of convergence we achieve */ 188 static PetscErrorCode CheckL2Projection(DM dm, AppCtx *user) 189 { 190 PetscSimplePointFunc exactSol[1]; 191 void *exactCtx[1]; 192 SNES snes; 193 PetscDS ds; 194 Vec u; 195 PetscReal error, tol = PETSC_SMALL; 196 MPI_Comm comm; 197 198 PetscFunctionBeginUser; 199 PetscCall(PetscObjectGetComm((PetscObject) dm, &comm)); 200 PetscCall(DMGetDS(dm, &ds)); 201 PetscCall(DMGetGlobalVector(dm, &u)); 202 PetscCall(PetscDSGetExactSolution(ds, 0, &exactSol[0], &exactCtx[0])); 203 PetscCall(SNESCreate(comm, &snes)); 204 PetscCall(SNESSetDM(snes, dm)); 205 PetscCall(VecSet(u, 0.0)); 206 PetscCall(PetscObjectSetName((PetscObject) u, "solution")); 207 PetscCall(DMPlexSetSNESLocalFEM(dm, user, user, user)); 208 PetscCall(SNESSetFromOptions(snes)); 209 PetscCall(DMSNESCheckFromOptions(snes, u)); 210 PetscCall(SNESSolve(snes, NULL, u)); 211 PetscCall(SNESDestroy(&snes)); 212 PetscCall(VecViewFromOptions(u, NULL, "-l2_projection_view")); 213 PetscCall(DMComputeL2Diff(dm, 0.0, exactSol, exactCtx, u, &error)); 214 PetscCall(DMRestoreGlobalVector(dm, &u)); 215 if (error > tol) PetscCall(PetscPrintf(comm, "L2 projection tests FAIL at tolerance %g error %g\n", (double) tol, (double) error)); 216 else PetscCall(PetscPrintf(comm, "L2 projection tests pass at tolerance %g\n", (double) tol)); 217 PetscFunctionReturn(0); 218 } 219 220 /* Distorts the mesh by shearing in the x-direction and flattening, factors provided in the options. */ 221 static PetscErrorCode DistortMesh(DM dm, AppCtx *user) 222 { 223 Vec coordinates; 224 PetscScalar *ca; 225 PetscInt dE, n, i; 226 227 PetscFunctionBeginUser; 228 PetscCall(DMGetCoordinateDim(dm, &dE)); 229 PetscCall(DMGetCoordinates(dm, &coordinates)); 230 PetscCall(VecGetLocalSize(coordinates, &n)); 231 PetscCall(VecGetArray(coordinates, &ca)); 232 for (i = 0; i < (n/dE); ++i) { 233 ca[i*dE+0] += user->shear*ca[i*dE+0]; 234 ca[i*dE+1] *= user->flatten; 235 } 236 PetscCall(VecRestoreArray(coordinates, &ca)); 237 PetscFunctionReturn(0); 238 } 239 240 int main(int argc, char **argv) 241 { 242 DM dm; 243 AppCtx user; 244 PetscMPIInt size; 245 246 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 247 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 248 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_SUP, "This is a uniprocessor example only."); 249 PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user)); 250 PetscCall(DMCreate(PETSC_COMM_WORLD, &dm)); 251 PetscCall(DMSetType(dm, DMPLEX)); 252 PetscCall(DMSetFromOptions(dm)); 253 PetscCall(DistortMesh(dm,&user)); 254 PetscCall(DMViewFromOptions(dm, NULL, "-dm_view")); 255 PetscCall(SetupDiscretization(dm, NULL, &user)); 256 257 PetscCall(CheckInterpolation(dm, &user)); 258 PetscCall(CheckL2Projection(dm, &user)); 259 260 PetscCall(DMDestroy(&dm)); 261 PetscCall(PetscFinalize()); 262 return 0; 263 } 264 265 /*TEST 266 267 testset: 268 args: -dm_plex_reference_cell_domain -dm_plex_cell triangle -petscspace_degree 1\ 269 -snes_error_if_not_converged -ksp_error_if_not_converged -pc_type lu 270 271 test: 272 suffix: p1_0 273 args: -func {{constant linear}} 274 275 # Using -dm_refine 2 -convest_num_refine 4 gives convergence rate 2.0 276 test: 277 suffix: p1_1 278 args: -func {{quadratic trig}} \ 279 -snes_convergence_estimate -convest_num_refine 2 280 281 testset: 282 requires: !complex double 283 args: -dm_plex_reference_cell_domain -dm_plex_cell triangular_prism \ 284 -petscspace_type sum \ 285 -petscspace_variables 3 \ 286 -petscspace_components 3 \ 287 -petscspace_sum_spaces 2 \ 288 -petscspace_sum_concatenate false \ 289 -sumcomp_0_petscspace_variables 3 \ 290 -sumcomp_0_petscspace_components 3 \ 291 -sumcomp_0_petscspace_degree 1 \ 292 -sumcomp_1_petscspace_variables 3 \ 293 -sumcomp_1_petscspace_components 3 \ 294 -sumcomp_1_petscspace_type wxy \ 295 -petscdualspace_form_degree 0 \ 296 -petscdualspace_order 1 \ 297 -petscdualspace_components 3 \ 298 -snes_error_if_not_converged -ksp_error_if_not_converged -pc_type lu 299 300 test: 301 suffix: wxy_0 302 args: -func constant 303 304 test: 305 suffix: wxy_1 306 args: -func linear 307 308 test: 309 suffix: wxy_2 310 args: -func prime 311 312 test: 313 suffix: wxy_3 314 args: -func linear -shear 1 -flatten 1e-5 315 316 TEST*/ 317