1 static char help[] = "One-Shot Multigrid for Parameter Estimation Problem for the Poisson Equation.\n\ 2 Using the Interior Point Method.\n\n\n"; 3 4 /*F 5 We are solving the parameter estimation problem for the Laplacian. We will ask to minimize a Lagrangian 6 function over $y$ and $u$, given by 7 \begin{align} 8 L(u, a, \lambda) = \frac{1}{2} || Qu - d_A ||^2 || Qu - d_B ||^2 + \frac{\beta}{2} || L (a - a_r) ||^2 + \lambda F(u; a) 9 \end{align} 10 where $Q$ is a sampling operator, $L$ is a regularization operator, $F$ defines the PDE. 11 12 Currently, we have perfect information, meaning $Q = I$, and then we need no regularization, $L = I$. We 13 also give the null vector for the reference control $a_r$. Right now $\beta = 1$. 14 15 The PDE will be the Laplace equation with homogeneous boundary conditions 16 \begin{align} 17 -Delta u = a 18 \end{align} 19 20 F*/ 21 22 #include <petsc.h> 23 #include <petscfe.h> 24 25 typedef enum {RUN_FULL, RUN_TEST} RunType; 26 27 typedef struct { 28 RunType runType; /* Whether to run tests, or solve the full problem */ 29 PetscBool useDualPenalty; /* Penalize deviation from both goals */ 30 PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx); 31 } AppCtx; 32 33 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 34 { 35 const char *runTypes[2] = {"full", "test"}; 36 PetscInt run; 37 PetscErrorCode ierr; 38 39 PetscFunctionBeginUser; 40 options->runType = RUN_FULL; 41 options->useDualPenalty = PETSC_FALSE; 42 43 ierr = PetscOptionsBegin(comm, "", "Inverse Problem Options", "DMPLEX");CHKERRQ(ierr); 44 run = options->runType; 45 ierr = PetscOptionsEList("-run_type", "The run type", "ex2.c", runTypes, 2, runTypes[options->runType], &run, NULL);CHKERRQ(ierr); 46 options->runType = (RunType) run; 47 ierr = PetscOptionsBool("-use_dual_penalty", "Penalize deviation from both goals", "ex2.c", options->useDualPenalty, &options->useDualPenalty, NULL);CHKERRQ(ierr); 48 ierr = PetscOptionsEnd();CHKERRQ(ierr); 49 PetscFunctionReturn(0); 50 } 51 52 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) 53 { 54 DM distributedMesh = NULL; 55 PetscErrorCode ierr; 56 57 PetscFunctionBeginUser; 58 ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr); 59 ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr); 60 ierr = DMPlexDistribute(*dm, 0, NULL, &distributedMesh);CHKERRQ(ierr); 61 if (distributedMesh) { 62 ierr = DMDestroy(dm);CHKERRQ(ierr); 63 *dm = distributedMesh; 64 } 65 ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); 66 ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr); 67 PetscFunctionReturn(0); 68 } 69 70 void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 71 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 72 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 73 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 74 { 75 f0[0] = (u[0] - (x[0]*x[0] + x[1]*x[1])); 76 } 77 void f0_u_full(PetscInt dim, PetscInt Nf, PetscInt NfAux, 78 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 79 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 80 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 81 { 82 f0[0] = (u[0] - (x[0]*x[0] + x[1]*x[1]))*PetscSqr(u[0] - (sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1]))) + 83 PetscSqr(u[0] - (x[0]*x[0] + x[1]*x[1]))*(u[0] - (sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1]))); 84 } 85 void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 86 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 87 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 88 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 89 { 90 PetscInt d; 91 for (d = 0; d < dim; ++d) f1[d] = u_x[dim*2+d]; 92 } 93 void g0_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 94 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 95 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 96 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 97 { 98 g0[0] = 1.0; 99 } 100 void g0_uu_full(PetscInt dim, PetscInt Nf, PetscInt NfAux, 101 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 102 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 103 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 104 { 105 g0[0] = PetscSqr(u[0] - sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1])) 106 + PetscSqr(u[0] - (x[0]*x[0] + x[1]*x[1])) 107 - 2.0*((x[0]*x[0] + x[1]*x[1]) + (sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1])))*u[0] 108 + 4.0*(x[0]*x[0] + x[1]*x[1])*(sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1])); 109 } 110 void g3_ul(PetscInt dim, PetscInt Nf, PetscInt NfAux, 111 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 112 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 113 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 114 { 115 PetscInt d; 116 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 117 } 118 119 void f0_a(PetscInt dim, PetscInt Nf, PetscInt NfAux, 120 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 121 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 122 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 123 { 124 f0[0] = u[1] - 4.0 /* 0.0 */ + u[2]; 125 } 126 void g0_aa(PetscInt dim, PetscInt Nf, PetscInt NfAux, 127 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 128 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 129 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 130 { 131 g0[0] = 1.0; 132 } 133 void g0_al(PetscInt dim, PetscInt Nf, PetscInt NfAux, 134 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 135 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 136 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 137 { 138 g0[0] = 1.0; 139 } 140 141 void f0_l(PetscInt dim, PetscInt Nf, PetscInt NfAux, 142 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 143 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 144 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 145 { 146 f0[0] = u[1]; 147 } 148 void f1_l(PetscInt dim, PetscInt Nf, PetscInt NfAux, 149 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 150 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 151 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 152 { 153 PetscInt d; 154 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 155 } 156 void g0_la(PetscInt dim, PetscInt Nf, PetscInt NfAux, 157 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 158 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 159 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 160 { 161 g0[0] = 1.0; 162 } 163 void g3_lu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 164 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 165 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 166 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 167 { 168 PetscInt d; 169 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 170 } 171 172 /* 173 In 2D for Dirichlet conditions with a variable coefficient, we use exact solution: 174 175 u = x^2 + y^2 176 a = 4 177 d_A = 4 178 d_B = sin(2*pi*x[0]) * sin(2*pi*x[1]) 179 180 so that 181 182 -\Delta u + a = -4 + 4 = 0 183 */ 184 PetscErrorCode quadratic_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) 185 { 186 *u = x[0]*x[0] + x[1]*x[1]; 187 return 0; 188 } 189 PetscErrorCode constant_a_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *a, void *ctx) 190 { 191 *a = 4; 192 return 0; 193 } 194 PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *l, void *ctx) 195 { 196 *l = 0.0; 197 return 0; 198 } 199 200 PetscErrorCode SetupProblem(DM dm, AppCtx *user) 201 { 202 PetscDS prob; 203 const PetscInt id = 1; 204 PetscErrorCode ierr; 205 206 PetscFunctionBeginUser; 207 ierr = DMGetDS(dm, &prob);CHKERRQ(ierr); 208 ierr = PetscDSSetResidual(prob, 0, user->useDualPenalty == PETSC_TRUE ? f0_u_full : f0_u, f1_u);CHKERRQ(ierr); 209 ierr = PetscDSSetResidual(prob, 1, f0_a, NULL);CHKERRQ(ierr); 210 ierr = PetscDSSetResidual(prob, 2, f0_l, f1_l);CHKERRQ(ierr); 211 ierr = PetscDSSetJacobian(prob, 0, 0, user->useDualPenalty == PETSC_TRUE ? g0_uu_full : g0_uu, NULL, NULL, NULL);CHKERRQ(ierr); 212 ierr = PetscDSSetJacobian(prob, 0, 2, NULL, NULL, NULL, g3_ul);CHKERRQ(ierr); 213 ierr = PetscDSSetJacobian(prob, 1, 1, g0_aa, NULL, NULL, NULL);CHKERRQ(ierr); 214 ierr = PetscDSSetJacobian(prob, 1, 2, g0_al, NULL, NULL, NULL);CHKERRQ(ierr); 215 ierr = PetscDSSetJacobian(prob, 2, 1, g0_la, NULL, NULL, NULL);CHKERRQ(ierr); 216 ierr = PetscDSSetJacobian(prob, 2, 0, NULL, NULL, NULL, g3_lu);CHKERRQ(ierr); 217 218 user->exactFuncs[0] = quadratic_u_2d; 219 user->exactFuncs[1] = constant_a_2d; 220 user->exactFuncs[2] = zero; 221 ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "wall", "marker", 0, 0, NULL, (void (*)()) user->exactFuncs[0], 1, &id, user);CHKERRQ(ierr); 222 ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "wall", "marker", 1, 0, NULL, (void (*)()) user->exactFuncs[1], 1, &id, user);CHKERRQ(ierr); 223 ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "wall", "marker", 2, 0, NULL, (void (*)()) user->exactFuncs[2], 1, &id, user);CHKERRQ(ierr); 224 PetscFunctionReturn(0); 225 } 226 227 PetscErrorCode SetupDiscretization(DM dm, AppCtx *user) 228 { 229 DM cdm = dm; 230 const PetscInt dim = 2; 231 PetscFE fe[3]; 232 PetscInt f; 233 MPI_Comm comm; 234 PetscErrorCode ierr; 235 236 PetscFunctionBeginUser; 237 /* Create finite element */ 238 ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr); 239 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "potential_", -1, &fe[0]);CHKERRQ(ierr); 240 ierr = PetscObjectSetName((PetscObject) fe[0], "potential");CHKERRQ(ierr); 241 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "charge_", -1, &fe[1]);CHKERRQ(ierr); 242 ierr = PetscObjectSetName((PetscObject) fe[1], "charge");CHKERRQ(ierr); 243 ierr = PetscFECopyQuadrature(fe[0], fe[1]);CHKERRQ(ierr); 244 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "multiplier_", -1, &fe[2]);CHKERRQ(ierr); 245 ierr = PetscObjectSetName((PetscObject) fe[2], "multiplier");CHKERRQ(ierr); 246 ierr = PetscFECopyQuadrature(fe[0], fe[2]);CHKERRQ(ierr); 247 /* Set discretization and boundary conditions for each mesh */ 248 for (f = 0; f < 3; ++f) {ierr = DMSetField(dm, f, NULL, (PetscObject) fe[f]);CHKERRQ(ierr);} 249 ierr = DMCreateDS(cdm);CHKERRQ(ierr); 250 ierr = SetupProblem(dm, user);CHKERRQ(ierr); 251 while (cdm) { 252 ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr); 253 ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); 254 } 255 for (f = 0; f < 3; ++f) {ierr = PetscFEDestroy(&fe[f]);CHKERRQ(ierr);} 256 PetscFunctionReturn(0); 257 } 258 259 int main(int argc, char **argv) 260 { 261 DM dm; 262 SNES snes; 263 Vec u, r; 264 AppCtx user; 265 PetscErrorCode ierr; 266 267 ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr; 268 ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr); 269 ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr); 270 ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr); 271 ierr = SNESSetDM(snes, dm);CHKERRQ(ierr); 272 273 ierr = PetscMalloc(3 * sizeof(void (*)()), &user.exactFuncs);CHKERRQ(ierr); 274 ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr); 275 276 ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr); 277 ierr = PetscObjectSetName((PetscObject) u, "solution");CHKERRQ(ierr); 278 ierr = VecDuplicate(u, &r);CHKERRQ(ierr); 279 ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr); 280 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 281 282 ierr = DMProjectFunction(dm, 0.0, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);CHKERRQ(ierr); 283 ierr = DMSNESCheckFromOptions(snes, u, user.exactFuncs, NULL);CHKERRQ(ierr); 284 if (user.runType == RUN_FULL) { 285 PetscErrorCode (*initialGuess[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx); 286 PetscReal error; 287 288 initialGuess[0] = zero; 289 initialGuess[1] = zero; 290 initialGuess[2] = zero; 291 ierr = DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr); 292 ierr = VecViewFromOptions(u, NULL, "-initial_vec_view");CHKERRQ(ierr); 293 ierr = DMComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr); 294 if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);} 295 else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: %g\n", error);CHKERRQ(ierr);} 296 ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr); 297 ierr = DMComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr); 298 if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);} 299 else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: %g\n", error);CHKERRQ(ierr);} 300 } 301 ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr); 302 303 ierr = VecDestroy(&u);CHKERRQ(ierr); 304 ierr = VecDestroy(&r);CHKERRQ(ierr); 305 ierr = SNESDestroy(&snes);CHKERRQ(ierr); 306 ierr = DMDestroy(&dm);CHKERRQ(ierr); 307 ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr); 308 ierr = PetscFinalize(); 309 return ierr; 310 } 311 312 /*TEST 313 314 build: 315 requires: !complex triangle 316 317 test: 318 suffix: 0 319 args: -run_type test -dmsnes_check -potential_petscspace_degree 2 -charge_petscspace_degree 1 -multiplier_petscspace_degree 1 320 321 test: 322 suffix: 1 323 args: -potential_petscspace_degree 2 -charge_petscspace_degree 1 -multiplier_petscspace_degree 1 -snes_monitor -snes_converged_reason -pc_type fieldsplit -pc_fieldsplit_0_fields 0,1 -pc_fieldsplit_1_fields 2 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition selfp -fieldsplit_0_pc_type lu -sol_vec_view 324 325 test: 326 suffix: 2 327 args: -potential_petscspace_degree 2 -charge_petscspace_degree 1 -multiplier_petscspace_degree 1 -snes_monitor -snes_converged_reason -snes_fd -pc_type fieldsplit -pc_fieldsplit_0_fields 0,1 -pc_fieldsplit_1_fields 2 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_schur_precondition selfp -fieldsplit_0_pc_type lu -sol_vec_view 328 329 TEST*/ 330