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 } AppCtx; 31 32 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 33 { 34 const char *runTypes[2] = {"full", "test"}; 35 PetscInt run; 36 PetscErrorCode ierr; 37 38 PetscFunctionBeginUser; 39 options->runType = RUN_FULL; 40 options->useDualPenalty = PETSC_FALSE; 41 42 ierr = PetscOptionsBegin(comm, "", "Inverse Problem Options", "DMPLEX");CHKERRQ(ierr); 43 run = options->runType; 44 ierr = PetscOptionsEList("-run_type", "The run type", "ex2.c", runTypes, 2, runTypes[options->runType], &run, NULL);CHKERRQ(ierr); 45 options->runType = (RunType) run; 46 ierr = PetscOptionsBool("-use_dual_penalty", "Penalize deviation from both goals", "ex2.c", options->useDualPenalty, &options->useDualPenalty, NULL);CHKERRQ(ierr); 47 ierr = PetscOptionsEnd();CHKERRQ(ierr); 48 PetscFunctionReturn(0); 49 } 50 51 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm) 52 { 53 DM distributedMesh = NULL; 54 PetscErrorCode ierr; 55 56 PetscFunctionBeginUser; 57 ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr); 58 ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr); 59 ierr = DMPlexDistribute(*dm, 0, NULL, &distributedMesh);CHKERRQ(ierr); 60 if (distributedMesh) { 61 ierr = DMDestroy(dm);CHKERRQ(ierr); 62 *dm = distributedMesh; 63 } 64 ierr = DMSetFromOptions(*dm);CHKERRQ(ierr); 65 ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr); 66 PetscFunctionReturn(0); 67 } 68 69 void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 70 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 71 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 72 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 73 { 74 f0[0] = (u[0] - (x[0]*x[0] + x[1]*x[1])); 75 } 76 void f0_u_full(PetscInt dim, PetscInt Nf, PetscInt NfAux, 77 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 78 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 79 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 80 { 81 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]))) + 82 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]))); 83 } 84 void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, 85 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 86 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 87 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 88 { 89 PetscInt d; 90 for (d = 0; d < dim; ++d) f1[d] = u_x[dim*2+d]; 91 } 92 void g0_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 93 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 94 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 95 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 96 { 97 g0[0] = 1.0; 98 } 99 void g0_uu_full(PetscInt dim, PetscInt Nf, PetscInt NfAux, 100 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 101 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 102 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 103 { 104 g0[0] = PetscSqr(u[0] - sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1])) 105 + PetscSqr(u[0] - (x[0]*x[0] + x[1]*x[1])) 106 - 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] 107 + 4.0*(x[0]*x[0] + x[1]*x[1])*(sin(2.0*PETSC_PI*x[0]) * sin(2.0*PETSC_PI*x[1])); 108 } 109 void g3_ul(PetscInt dim, PetscInt Nf, PetscInt NfAux, 110 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 111 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 112 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 113 { 114 PetscInt d; 115 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 116 } 117 118 void f0_a(PetscInt dim, PetscInt Nf, PetscInt NfAux, 119 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 120 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 121 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 122 { 123 f0[0] = u[1] - 4.0 /* 0.0 */ + u[2]; 124 } 125 void g0_aa(PetscInt dim, PetscInt Nf, PetscInt NfAux, 126 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 127 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 128 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 129 { 130 g0[0] = 1.0; 131 } 132 void g0_al(PetscInt dim, PetscInt Nf, PetscInt NfAux, 133 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 134 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 135 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 136 { 137 g0[0] = 1.0; 138 } 139 140 void f0_l(PetscInt dim, PetscInt Nf, PetscInt NfAux, 141 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 142 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 143 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 144 { 145 f0[0] = u[1]; 146 } 147 void f1_l(PetscInt dim, PetscInt Nf, PetscInt NfAux, 148 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 149 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 150 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 151 { 152 PetscInt d; 153 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 154 } 155 void g0_la(PetscInt dim, PetscInt Nf, PetscInt NfAux, 156 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 157 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 158 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 159 { 160 g0[0] = 1.0; 161 } 162 void g3_lu(PetscInt dim, PetscInt Nf, PetscInt NfAux, 163 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 164 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 165 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 166 { 167 PetscInt d; 168 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 169 } 170 171 /* 172 In 2D for Dirichlet conditions with a variable coefficient, we use exact solution: 173 174 u = x^2 + y^2 175 a = 4 176 d_A = 4 177 d_B = sin(2*pi*x[0]) * sin(2*pi*x[1]) 178 179 so that 180 181 -\Delta u + a = -4 + 4 = 0 182 */ 183 PetscErrorCode quadratic_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx) 184 { 185 *u = x[0]*x[0] + x[1]*x[1]; 186 return 0; 187 } 188 PetscErrorCode constant_a_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *a, void *ctx) 189 { 190 *a = 4; 191 return 0; 192 } 193 PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *l, void *ctx) 194 { 195 *l = 0.0; 196 return 0; 197 } 198 199 PetscErrorCode SetupProblem(DM dm, AppCtx *user) 200 { 201 PetscDS prob; 202 const PetscInt id = 1; 203 PetscErrorCode ierr; 204 205 PetscFunctionBeginUser; 206 ierr = DMGetDS(dm, &prob);CHKERRQ(ierr); 207 ierr = PetscDSSetResidual(prob, 0, user->useDualPenalty == PETSC_TRUE ? f0_u_full : f0_u, f1_u);CHKERRQ(ierr); 208 ierr = PetscDSSetResidual(prob, 1, f0_a, NULL);CHKERRQ(ierr); 209 ierr = PetscDSSetResidual(prob, 2, f0_l, f1_l);CHKERRQ(ierr); 210 ierr = PetscDSSetJacobian(prob, 0, 0, user->useDualPenalty == PETSC_TRUE ? g0_uu_full : g0_uu, NULL, NULL, NULL);CHKERRQ(ierr); 211 ierr = PetscDSSetJacobian(prob, 0, 2, NULL, NULL, NULL, g3_ul);CHKERRQ(ierr); 212 ierr = PetscDSSetJacobian(prob, 1, 1, g0_aa, NULL, NULL, NULL);CHKERRQ(ierr); 213 ierr = PetscDSSetJacobian(prob, 1, 2, g0_al, NULL, NULL, NULL);CHKERRQ(ierr); 214 ierr = PetscDSSetJacobian(prob, 2, 1, g0_la, NULL, NULL, NULL);CHKERRQ(ierr); 215 ierr = PetscDSSetJacobian(prob, 2, 0, NULL, NULL, NULL, g3_lu);CHKERRQ(ierr); 216 217 ierr = PetscDSSetExactSolution(prob, 0, quadratic_u_2d, NULL);CHKERRQ(ierr); 218 ierr = PetscDSSetExactSolution(prob, 1, constant_a_2d, NULL);CHKERRQ(ierr); 219 ierr = PetscDSSetExactSolution(prob, 2, zero, NULL);CHKERRQ(ierr); 220 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "marker", 0, 0, NULL, (void (*)()) quadratic_u_2d, NULL, 1, &id, user);CHKERRQ(ierr); 221 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "marker", 1, 0, NULL, (void (*)()) constant_a_2d, NULL, 1, &id, user);CHKERRQ(ierr); 222 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "marker", 2, 0, NULL, (void (*)()) zero, NULL, 1, &id, user);CHKERRQ(ierr); 223 PetscFunctionReturn(0); 224 } 225 226 PetscErrorCode SetupDiscretization(DM dm, AppCtx *user) 227 { 228 DM cdm = dm; 229 const PetscInt dim = 2; 230 PetscFE fe[3]; 231 PetscInt f; 232 MPI_Comm comm; 233 PetscErrorCode ierr; 234 235 PetscFunctionBeginUser; 236 /* Create finite element */ 237 ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr); 238 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "potential_", -1, &fe[0]);CHKERRQ(ierr); 239 ierr = PetscObjectSetName((PetscObject) fe[0], "potential");CHKERRQ(ierr); 240 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "charge_", -1, &fe[1]);CHKERRQ(ierr); 241 ierr = PetscObjectSetName((PetscObject) fe[1], "charge");CHKERRQ(ierr); 242 ierr = PetscFECopyQuadrature(fe[0], fe[1]);CHKERRQ(ierr); 243 ierr = PetscFECreateDefault(comm, dim, 1, PETSC_TRUE, "multiplier_", -1, &fe[2]);CHKERRQ(ierr); 244 ierr = PetscObjectSetName((PetscObject) fe[2], "multiplier");CHKERRQ(ierr); 245 ierr = PetscFECopyQuadrature(fe[0], fe[2]);CHKERRQ(ierr); 246 /* Set discretization and boundary conditions for each mesh */ 247 for (f = 0; f < 3; ++f) {ierr = DMSetField(dm, f, NULL, (PetscObject) fe[f]);CHKERRQ(ierr);} 248 ierr = DMCreateDS(cdm);CHKERRQ(ierr); 249 ierr = SetupProblem(dm, user);CHKERRQ(ierr); 250 while (cdm) { 251 ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr); 252 ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); 253 } 254 for (f = 0; f < 3; ++f) {ierr = PetscFEDestroy(&fe[f]);CHKERRQ(ierr);} 255 PetscFunctionReturn(0); 256 } 257 258 int main(int argc, char **argv) 259 { 260 DM dm; 261 SNES snes; 262 Vec u, r; 263 AppCtx user; 264 PetscErrorCode ierr; 265 266 ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr; 267 ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr); 268 ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr); 269 ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr); 270 ierr = SNESSetDM(snes, dm);CHKERRQ(ierr); 271 ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr); 272 273 ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr); 274 ierr = PetscObjectSetName((PetscObject) u, "solution");CHKERRQ(ierr); 275 ierr = VecDuplicate(u, &r);CHKERRQ(ierr); 276 ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr); 277 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 278 279 ierr = DMSNESCheckFromOptions(snes, u);CHKERRQ(ierr); 280 if (user.runType == RUN_FULL) { 281 PetscDS ds; 282 PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx); 283 PetscErrorCode (*initialGuess[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx); 284 PetscReal error; 285 286 ierr = DMGetDS(dm, &ds);CHKERRQ(ierr); 287 ierr = PetscDSGetExactSolution(ds, 0, &exactFuncs[0], NULL);CHKERRQ(ierr); 288 ierr = PetscDSGetExactSolution(ds, 1, &exactFuncs[1], NULL);CHKERRQ(ierr); 289 ierr = PetscDSGetExactSolution(ds, 2, &exactFuncs[2], NULL);CHKERRQ(ierr); 290 initialGuess[0] = zero; 291 initialGuess[1] = zero; 292 initialGuess[2] = zero; 293 ierr = DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr); 294 ierr = VecViewFromOptions(u, NULL, "-initial_vec_view");CHKERRQ(ierr); 295 ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, NULL, u, &error);CHKERRQ(ierr); 296 if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);} 297 else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Initial L_2 Error: %g\n", error);CHKERRQ(ierr);} 298 ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr); 299 ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, NULL, u, &error);CHKERRQ(ierr); 300 if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);} 301 else {ierr = PetscPrintf(PETSC_COMM_WORLD, "Final L_2 Error: %g\n", error);CHKERRQ(ierr);} 302 } 303 ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr); 304 305 ierr = VecDestroy(&u);CHKERRQ(ierr); 306 ierr = VecDestroy(&r);CHKERRQ(ierr); 307 ierr = SNESDestroy(&snes);CHKERRQ(ierr); 308 ierr = DMDestroy(&dm);CHKERRQ(ierr); 309 ierr = PetscFinalize(); 310 return ierr; 311 } 312 313 /*TEST 314 315 build: 316 requires: !complex triangle 317 318 test: 319 suffix: 0 320 args: -run_type test -dmsnes_check -potential_petscspace_degree 2 -charge_petscspace_degree 1 -multiplier_petscspace_degree 1 321 322 test: 323 suffix: 1 324 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 325 326 test: 327 suffix: 2 328 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 329 330 TEST*/ 331