1 static char help[] = "Poiseuille flow problem. Viscous, laminar flow in a 2D channel with parabolic velocity\n\ 2 profile and linear pressure drop, exact solution of the 2D Stokes\n"; 3 4 /*---------------------------------------------------------------------------- */ 5 /* M A R I T I M E R E S E A R C H I N S T I T U T E N E T H E R L A N D S */ 6 /*---------------------------------------------------------------------------- */ 7 /* author : Christiaan M. Klaij */ 8 /*---------------------------------------------------------------------------- */ 9 /* */ 10 /* Poiseuille flow problem. */ 11 /* */ 12 /* Viscous, laminar flow in a 2D channel with parabolic velocity */ 13 /* profile and linear pressure drop, exact solution of the 2D Stokes */ 14 /* equations. */ 15 /* */ 16 /* Discretized with the cell-centered finite-volume method on a */ 17 /* Cartesian grid with co-located variables. Variables ordered as */ 18 /* [u1...uN v1...vN p1...pN]^T. Matrix [A00 A01; A10, A11] solved with */ 19 /* PCFIELDSPLIT. Lower factorization is used to mimick the Semi-Implicit */ 20 /* Method for Pressure Linked Equations (SIMPLE) used as preconditioner */ 21 /* instead of solver. */ 22 /* */ 23 /* Disclaimer: does not contain the pressure-weighed interpolation */ 24 /* method needed to suppress spurious pressure modes in real-life */ 25 /* problems. */ 26 /* */ 27 /* Usage: */ 28 /* */ 29 /* mpiexec -n 2 ./ex70 -nx 32 -ny 48 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -fieldsplit_1_pc_type none */ 30 /* */ 31 /* Runs with PCFIELDSPLIT on 32x48 grid, no PC for the Schur */ 32 /* complement because A11 is zero. FGMRES is needed because */ 33 /* PCFIELDSPLIT is a variable preconditioner. */ 34 /* */ 35 /* mpiexec -n 2 ./ex70 -nx 32 -ny 48 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -user_pc */ 36 /* */ 37 /* Same as above but with user defined PC for the true Schur */ 38 /* complement. PC based on the SIMPLE-type approximation (inverse of */ 39 /* A00 approximated by inverse of its diagonal). */ 40 /* */ 41 /* mpiexec -n 2 ./ex70 -nx 32 -ny 48 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -user_ksp */ 42 /* */ 43 /* Replace the true Schur complement with a user defined Schur */ 44 /* complement based on the SIMPLE-type approximation. Same matrix is */ 45 /* used as PC. */ 46 /* */ 47 /* mpiexec -n 2 ./ex70 -nx 32 -ny 48 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type bjacobi -fieldsplit_1_pc_type jacobi -fieldsplit_1_inner_ksp_type preonly -fieldsplit_1_inner_pc_type jacobi -fieldsplit_1_upper_ksp_type preonly -fieldsplit_1_upper_pc_type jacobi */ 48 /* */ 49 /* Out-of-the-box SIMPLE-type preconditioning. The major advantage */ 50 /* is that the user neither needs to provide the approximation of */ 51 /* the Schur complement, nor the corresponding preconditioner. */ 52 /* */ 53 /*---------------------------------------------------------------------------- */ 54 55 #include <petscksp.h> 56 57 typedef struct { 58 PetscBool userPC, userKSP, matsymmetric; /* user defined preconditioner and matrix for the Schur complement */ 59 PetscInt nx, ny; /* nb of cells in x- and y-direction */ 60 PetscReal hx, hy; /* mesh size in x- and y-direction */ 61 Mat A; /* block matrix */ 62 Mat subA[4]; /* the four blocks */ 63 Mat myS; /* the approximation of the Schur complement */ 64 Vec x, b, y; /* solution, rhs and temporary vector */ 65 IS isg[2]; /* index sets of split "0" and "1" */ 66 } Stokes; 67 68 PetscErrorCode StokesSetupMatBlock00(Stokes*); /* setup the block Q */ 69 PetscErrorCode StokesSetupMatBlock01(Stokes*); /* setup the block G */ 70 PetscErrorCode StokesSetupMatBlock10(Stokes*); /* setup the block D (equal to the transpose of G) */ 71 PetscErrorCode StokesSetupMatBlock11(Stokes*); /* setup the block C (equal to zero) */ 72 73 PetscErrorCode StokesGetPosition(Stokes*, PetscInt, PetscInt*, PetscInt*); /* row number j*nx+i corresponds to position (i,j) in grid */ 74 75 PetscErrorCode StokesStencilLaplacian(Stokes*, PetscInt, PetscInt, PetscInt*, PetscInt*, PetscScalar*); /* stencil of the Laplacian operator */ 76 PetscErrorCode StokesStencilGradientX(Stokes*, PetscInt, PetscInt, PetscInt*, PetscInt*, PetscScalar*); /* stencil of the Gradient operator (x-component) */ 77 PetscErrorCode StokesStencilGradientY(Stokes*, PetscInt, PetscInt, PetscInt*, PetscInt*, PetscScalar*); /* stencil of the Gradient operator (y-component) */ 78 79 PetscErrorCode StokesRhs(Stokes*); /* rhs vector */ 80 PetscErrorCode StokesRhsMomX(Stokes*, PetscInt, PetscInt, PetscScalar*); /* right hand side of velocity (x-component) */ 81 PetscErrorCode StokesRhsMomY(Stokes*, PetscInt, PetscInt, PetscScalar*); /* right hand side of velocity (y-component) */ 82 PetscErrorCode StokesRhsMass(Stokes*, PetscInt, PetscInt, PetscScalar*); /* right hand side of pressure */ 83 84 PetscErrorCode StokesSetupApproxSchur(Stokes*); /* approximation of the Schur complement */ 85 86 PetscErrorCode StokesExactSolution(Stokes*); /* exact solution vector */ 87 PetscErrorCode StokesWriteSolution(Stokes*); /* write solution to file */ 88 89 /* exact solution for the velocity (x-component, y-component is zero) */ 90 PetscScalar StokesExactVelocityX(const PetscScalar y) 91 { 92 return 4.0*y*(1.0-y); 93 } 94 95 /* exact solution for the pressure */ 96 PetscScalar StokesExactPressure(const PetscScalar x) 97 { 98 return 8.0*(2.0-x); 99 } 100 101 PetscErrorCode StokesSetupPC(Stokes *s, KSP ksp) 102 { 103 KSP *subksp; 104 PC pc; 105 PetscInt n = 1; 106 PetscErrorCode ierr; 107 108 PetscFunctionBeginUser; 109 ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr); 110 ierr = PCFieldSplitSetIS(pc, "0", s->isg[0]);CHKERRQ(ierr); 111 ierr = PCFieldSplitSetIS(pc, "1", s->isg[1]);CHKERRQ(ierr); 112 if (s->userPC) { 113 ierr = PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_USER, s->myS);CHKERRQ(ierr); 114 } 115 if (s->userKSP) { 116 ierr = PCSetUp(pc);CHKERRQ(ierr); 117 ierr = PCFieldSplitGetSubKSP(pc, &n, &subksp);CHKERRQ(ierr); 118 ierr = KSPSetOperators(subksp[1], s->myS, s->myS);CHKERRQ(ierr); 119 ierr = PetscFree(subksp);CHKERRQ(ierr); 120 } 121 PetscFunctionReturn(0); 122 } 123 124 PetscErrorCode StokesWriteSolution(Stokes *s) 125 { 126 PetscMPIInt size; 127 PetscInt n,i,j; 128 const PetscScalar *array; 129 PetscErrorCode ierr; 130 131 PetscFunctionBeginUser; 132 /* write data (*warning* only works sequential) */ 133 ierr = MPI_Comm_size(MPI_COMM_WORLD,&size);CHKERRMPI(ierr); 134 /*ierr = PetscPrintf(PETSC_COMM_WORLD," number of processors = %D\n",size);CHKERRQ(ierr);*/ 135 if (size == 1) { 136 PetscViewer viewer; 137 ierr = VecGetArrayRead(s->x, &array);CHKERRQ(ierr); 138 ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD, "solution.dat", &viewer);CHKERRQ(ierr); 139 ierr = PetscViewerASCIIPrintf(viewer, "# x, y, u, v, p\n");CHKERRQ(ierr); 140 for (j = 0; j < s->ny; j++) { 141 for (i = 0; i < s->nx; i++) { 142 n = j*s->nx+i; 143 ierr = PetscViewerASCIIPrintf(viewer, "%.12g %.12g %.12g %.12g %.12g\n", (double)(i*s->hx+s->hx/2),(double)(j*s->hy+s->hy/2), (double)PetscRealPart(array[n]), (double)PetscRealPart(array[n+s->nx*s->ny]),(double)PetscRealPart(array[n+2*s->nx*s->ny]));CHKERRQ(ierr); 144 } 145 } 146 ierr = VecRestoreArrayRead(s->x, &array);CHKERRQ(ierr); 147 ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr); 148 } 149 PetscFunctionReturn(0); 150 } 151 152 PetscErrorCode StokesSetupIndexSets(Stokes *s) 153 { 154 PetscErrorCode ierr; 155 156 PetscFunctionBeginUser; 157 /* the two index sets */ 158 ierr = MatNestGetISs(s->A, s->isg, NULL);CHKERRQ(ierr); 159 /* ISView(isg[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */ 160 /* ISView(isg[1],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */ 161 PetscFunctionReturn(0); 162 } 163 164 PetscErrorCode StokesSetupVectors(Stokes *s) 165 { 166 PetscErrorCode ierr; 167 168 PetscFunctionBeginUser; 169 /* solution vector x */ 170 ierr = VecCreate(PETSC_COMM_WORLD, &s->x);CHKERRQ(ierr); 171 ierr = VecSetSizes(s->x, PETSC_DECIDE, 3*s->nx*s->ny);CHKERRQ(ierr); 172 ierr = VecSetType(s->x, VECMPI);CHKERRQ(ierr); 173 /* ierr = VecSetRandom(s->x, NULL);CHKERRQ(ierr); */ 174 /* ierr = VecView(s->x, (PetscViewer) PETSC_VIEWER_DEFAULT);CHKERRQ(ierr); */ 175 176 /* exact solution y */ 177 ierr = VecDuplicate(s->x, &s->y);CHKERRQ(ierr); 178 ierr = StokesExactSolution(s);CHKERRQ(ierr); 179 /* ierr = VecView(s->y, (PetscViewer) PETSC_VIEWER_DEFAULT);CHKERRQ(ierr); */ 180 181 /* rhs vector b */ 182 ierr = VecDuplicate(s->x, &s->b);CHKERRQ(ierr); 183 ierr = StokesRhs(s);CHKERRQ(ierr); 184 /*ierr = VecView(s->b, (PetscViewer) PETSC_VIEWER_DEFAULT);CHKERRQ(ierr);*/ 185 PetscFunctionReturn(0); 186 } 187 188 PetscErrorCode StokesGetPosition(Stokes *s, PetscInt row, PetscInt *i, PetscInt *j) 189 { 190 PetscInt n; 191 192 PetscFunctionBeginUser; 193 /* cell number n=j*nx+i has position (i,j) in grid */ 194 n = row%(s->nx*s->ny); 195 *i = n%s->nx; 196 *j = (n-(*i))/s->nx; 197 PetscFunctionReturn(0); 198 } 199 200 PetscErrorCode StokesExactSolution(Stokes *s) 201 { 202 PetscInt row, start, end, i, j; 203 PetscScalar val; 204 Vec y0,y1; 205 PetscErrorCode ierr; 206 207 PetscFunctionBeginUser; 208 /* velocity part */ 209 ierr = VecGetSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr); 210 ierr = VecGetOwnershipRange(y0, &start, &end);CHKERRQ(ierr); 211 for (row = start; row < end; row++) { 212 ierr = StokesGetPosition(s, row,&i,&j);CHKERRQ(ierr); 213 if (row < s->nx*s->ny) { 214 val = StokesExactVelocityX(j*s->hy+s->hy/2); 215 } else { 216 val = 0; 217 } 218 ierr = VecSetValue(y0, row, val, INSERT_VALUES);CHKERRQ(ierr); 219 } 220 ierr = VecRestoreSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr); 221 222 /* pressure part */ 223 ierr = VecGetSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr); 224 ierr = VecGetOwnershipRange(y1, &start, &end);CHKERRQ(ierr); 225 for (row = start; row < end; row++) { 226 ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr); 227 val = StokesExactPressure(i*s->hx+s->hx/2); 228 ierr = VecSetValue(y1, row, val, INSERT_VALUES);CHKERRQ(ierr); 229 } 230 ierr = VecRestoreSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr); 231 PetscFunctionReturn(0); 232 } 233 234 PetscErrorCode StokesRhs(Stokes *s) 235 { 236 PetscInt row, start, end, i, j; 237 PetscScalar val; 238 Vec b0,b1; 239 PetscErrorCode ierr; 240 241 PetscFunctionBeginUser; 242 /* velocity part */ 243 ierr = VecGetSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr); 244 ierr = VecGetOwnershipRange(b0, &start, &end);CHKERRQ(ierr); 245 for (row = start; row < end; row++) { 246 ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr); 247 if (row < s->nx*s->ny) { 248 ierr = StokesRhsMomX(s, i, j, &val);CHKERRQ(ierr); 249 } else { 250 ierr = StokesRhsMomY(s, i, j, &val);CHKERRQ(ierr); 251 } 252 ierr = VecSetValue(b0, row, val, INSERT_VALUES);CHKERRQ(ierr); 253 } 254 ierr = VecRestoreSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr); 255 256 /* pressure part */ 257 ierr = VecGetSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr); 258 ierr = VecGetOwnershipRange(b1, &start, &end);CHKERRQ(ierr); 259 for (row = start; row < end; row++) { 260 ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr); 261 ierr = StokesRhsMass(s, i, j, &val);CHKERRQ(ierr); 262 if (s->matsymmetric) { 263 val = -1.0*val; 264 } 265 ierr = VecSetValue(b1, row, val, INSERT_VALUES);CHKERRQ(ierr); 266 } 267 ierr = VecRestoreSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr); 268 PetscFunctionReturn(0); 269 } 270 271 PetscErrorCode StokesSetupMatBlock00(Stokes *s) 272 { 273 PetscInt row, start, end, sz, i, j; 274 PetscInt cols[5]; 275 PetscScalar vals[5]; 276 PetscErrorCode ierr; 277 278 PetscFunctionBeginUser; 279 /* A[0] is 2N-by-2N */ 280 ierr = MatCreate(PETSC_COMM_WORLD,&s->subA[0]);CHKERRQ(ierr); 281 ierr = MatSetOptionsPrefix(s->subA[0],"a00_");CHKERRQ(ierr); 282 ierr = MatSetSizes(s->subA[0],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,2*s->nx*s->ny);CHKERRQ(ierr); 283 ierr = MatSetType(s->subA[0],MATMPIAIJ);CHKERRQ(ierr); 284 ierr = MatMPIAIJSetPreallocation(s->subA[0],5,NULL,5,NULL);CHKERRQ(ierr); 285 ierr = MatGetOwnershipRange(s->subA[0], &start, &end);CHKERRQ(ierr); 286 287 for (row = start; row < end; row++) { 288 ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr); 289 /* first part: rows 0 to (nx*ny-1) */ 290 ierr = StokesStencilLaplacian(s, i, j, &sz, cols, vals);CHKERRQ(ierr); 291 /* second part: rows (nx*ny) to (2*nx*ny-1) */ 292 if (row >= s->nx*s->ny) { 293 for (i = 0; i < sz; i++) cols[i] += s->nx*s->ny; 294 } 295 for (i = 0; i < sz; i++) vals[i] = -1.0*vals[i]; /* dynamic viscosity coef mu=-1 */ 296 ierr = MatSetValues(s->subA[0], 1, &row, sz, cols, vals, INSERT_VALUES);CHKERRQ(ierr); 297 } 298 ierr = MatAssemblyBegin(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 299 ierr = MatAssemblyEnd(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 300 PetscFunctionReturn(0); 301 } 302 303 PetscErrorCode StokesSetupMatBlock01(Stokes *s) 304 { 305 PetscInt row, start, end, sz, i, j; 306 PetscInt cols[5]; 307 PetscScalar vals[5]; 308 PetscErrorCode ierr; 309 310 PetscFunctionBeginUser; 311 /* A[1] is 2N-by-N */ 312 ierr = MatCreate(PETSC_COMM_WORLD, &s->subA[1]);CHKERRQ(ierr); 313 ierr = MatSetOptionsPrefix(s->subA[1],"a01_");CHKERRQ(ierr); 314 ierr = MatSetSizes(s->subA[1],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,s->nx*s->ny);CHKERRQ(ierr); 315 ierr = MatSetType(s->subA[1],MATMPIAIJ);CHKERRQ(ierr); 316 ierr = MatMPIAIJSetPreallocation(s->subA[1],5,NULL,5,NULL);CHKERRQ(ierr); 317 ierr = MatGetOwnershipRange(s->subA[1],&start,&end);CHKERRQ(ierr); 318 319 ierr = MatSetOption(s->subA[1],MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr); 320 321 for (row = start; row < end; row++) { 322 ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr); 323 /* first part: rows 0 to (nx*ny-1) */ 324 if (row < s->nx*s->ny) { 325 ierr = StokesStencilGradientX(s, i, j, &sz, cols, vals);CHKERRQ(ierr); 326 } else { /* second part: rows (nx*ny) to (2*nx*ny-1) */ 327 ierr = StokesStencilGradientY(s, i, j, &sz, cols, vals);CHKERRQ(ierr); 328 } 329 ierr = MatSetValues(s->subA[1], 1, &row, sz, cols, vals, INSERT_VALUES);CHKERRQ(ierr); 330 } 331 ierr = MatAssemblyBegin(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 332 ierr = MatAssemblyEnd(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 333 PetscFunctionReturn(0); 334 } 335 336 PetscErrorCode StokesSetupMatBlock10(Stokes *s) 337 { 338 PetscErrorCode ierr; 339 340 PetscFunctionBeginUser; 341 /* A[2] is minus transpose of A[1] */ 342 ierr = MatTranspose(s->subA[1], MAT_INITIAL_MATRIX, &s->subA[2]);CHKERRQ(ierr); 343 if (!s->matsymmetric) { 344 ierr = MatScale(s->subA[2], -1.0);CHKERRQ(ierr); 345 } 346 ierr = MatSetOptionsPrefix(s->subA[2], "a10_");CHKERRQ(ierr); 347 PetscFunctionReturn(0); 348 } 349 350 PetscErrorCode StokesSetupMatBlock11(Stokes *s) 351 { 352 PetscErrorCode ierr; 353 354 PetscFunctionBeginUser; 355 /* A[3] is N-by-N null matrix */ 356 ierr = MatCreate(PETSC_COMM_WORLD, &s->subA[3]);CHKERRQ(ierr); 357 ierr = MatSetOptionsPrefix(s->subA[3], "a11_");CHKERRQ(ierr); 358 ierr = MatSetSizes(s->subA[3], PETSC_DECIDE, PETSC_DECIDE, s->nx*s->ny, s->nx*s->ny);CHKERRQ(ierr); 359 ierr = MatSetType(s->subA[3], MATMPIAIJ);CHKERRQ(ierr); 360 ierr = MatMPIAIJSetPreallocation(s->subA[3], 0, NULL, 0, NULL);CHKERRQ(ierr); 361 ierr = MatAssemblyBegin(s->subA[3], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 362 ierr = MatAssemblyEnd(s->subA[3], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 363 PetscFunctionReturn(0); 364 } 365 366 PetscErrorCode StokesSetupApproxSchur(Stokes *s) 367 { 368 Vec diag; 369 PetscErrorCode ierr; 370 371 PetscFunctionBeginUser; 372 /* Schur complement approximation: myS = A11 - A10 diag(A00)^(-1) A01 */ 373 /* note: A11 is zero */ 374 /* note: in real life this matrix would be build directly, */ 375 /* i.e. without MatMatMult */ 376 377 /* inverse of diagonal of A00 */ 378 ierr = VecCreate(PETSC_COMM_WORLD,&diag);CHKERRQ(ierr); 379 ierr = VecSetSizes(diag,PETSC_DECIDE,2*s->nx*s->ny);CHKERRQ(ierr); 380 ierr = VecSetType(diag,VECMPI);CHKERRQ(ierr); 381 ierr = MatGetDiagonal(s->subA[0],diag);CHKERRQ(ierr); 382 ierr = VecReciprocal(diag);CHKERRQ(ierr); 383 384 /* compute: - A10 diag(A00)^(-1) A01 */ 385 ierr = MatDiagonalScale(s->subA[1],diag,NULL);CHKERRQ(ierr); /* (*warning* overwrites subA[1]) */ 386 ierr = MatMatMult(s->subA[2],s->subA[1],MAT_INITIAL_MATRIX,PETSC_DEFAULT,&s->myS);CHKERRQ(ierr); 387 ierr = MatScale(s->myS,-1.0);CHKERRQ(ierr); 388 389 /* restore A10 */ 390 ierr = MatGetDiagonal(s->subA[0],diag);CHKERRQ(ierr); 391 ierr = MatDiagonalScale(s->subA[1],diag,NULL);CHKERRQ(ierr); 392 ierr = VecDestroy(&diag);CHKERRQ(ierr); 393 PetscFunctionReturn(0); 394 } 395 396 PetscErrorCode StokesSetupMatrix(Stokes *s) 397 { 398 PetscErrorCode ierr; 399 400 PetscFunctionBeginUser; 401 ierr = StokesSetupMatBlock00(s);CHKERRQ(ierr); 402 ierr = StokesSetupMatBlock01(s);CHKERRQ(ierr); 403 ierr = StokesSetupMatBlock10(s);CHKERRQ(ierr); 404 ierr = StokesSetupMatBlock11(s);CHKERRQ(ierr); 405 ierr = MatCreateNest(PETSC_COMM_WORLD, 2, NULL, 2, NULL, s->subA, &s->A);CHKERRQ(ierr); 406 ierr = StokesSetupApproxSchur(s);CHKERRQ(ierr); 407 PetscFunctionReturn(0); 408 } 409 410 PetscErrorCode StokesStencilLaplacian(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals) 411 { 412 PetscInt p =j*s->nx+i, w=p-1, e=p+1, s2=p-s->nx, n=p+s->nx; 413 PetscScalar ae=s->hy/s->hx, aeb=0; 414 PetscScalar aw=s->hy/s->hx, awb=s->hy/(s->hx/2); 415 PetscScalar as=s->hx/s->hy, asb=s->hx/(s->hy/2); 416 PetscScalar an=s->hx/s->hy, anb=s->hx/(s->hy/2); 417 418 PetscFunctionBeginUser; 419 if (i==0 && j==0) { /* south-west corner */ 420 *sz =3; 421 cols[0]=p; vals[0]=-(ae+awb+asb+an); 422 cols[1]=e; vals[1]=ae; 423 cols[2]=n; vals[2]=an; 424 } else if (i==0 && j==s->ny-1) { /* north-west corner */ 425 *sz =3; 426 cols[0]=s2; vals[0]=as; 427 cols[1]=p; vals[1]=-(ae+awb+as+anb); 428 cols[2]=e; vals[2]=ae; 429 } else if (i==s->nx-1 && j==0) { /* south-east corner */ 430 *sz =3; 431 cols[0]=w; vals[0]=aw; 432 cols[1]=p; vals[1]=-(aeb+aw+asb+an); 433 cols[2]=n; vals[2]=an; 434 } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */ 435 *sz =3; 436 cols[0]=s2; vals[0]=as; 437 cols[1]=w; vals[1]=aw; 438 cols[2]=p; vals[2]=-(aeb+aw+as+anb); 439 } else if (i==0) { /* west boundary */ 440 *sz =4; 441 cols[0]=s2; vals[0]=as; 442 cols[1]=p; vals[1]=-(ae+awb+as+an); 443 cols[2]=e; vals[2]=ae; 444 cols[3]=n; vals[3]=an; 445 } else if (i==s->nx-1) { /* east boundary */ 446 *sz =4; 447 cols[0]=s2; vals[0]=as; 448 cols[1]=w; vals[1]=aw; 449 cols[2]=p; vals[2]=-(aeb+aw+as+an); 450 cols[3]=n; vals[3]=an; 451 } else if (j==0) { /* south boundary */ 452 *sz =4; 453 cols[0]=w; vals[0]=aw; 454 cols[1]=p; vals[1]=-(ae+aw+asb+an); 455 cols[2]=e; vals[2]=ae; 456 cols[3]=n; vals[3]=an; 457 } else if (j==s->ny-1) { /* north boundary */ 458 *sz =4; 459 cols[0]=s2; vals[0]=as; 460 cols[1]=w; vals[1]=aw; 461 cols[2]=p; vals[2]=-(ae+aw+as+anb); 462 cols[3]=e; vals[3]=ae; 463 } else { /* interior */ 464 *sz =5; 465 cols[0]=s2; vals[0]=as; 466 cols[1]=w; vals[1]=aw; 467 cols[2]=p; vals[2]=-(ae+aw+as+an); 468 cols[3]=e; vals[3]=ae; 469 cols[4]=n; vals[4]=an; 470 } 471 PetscFunctionReturn(0); 472 } 473 474 PetscErrorCode StokesStencilGradientX(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals) 475 { 476 PetscInt p =j*s->nx+i, w=p-1, e=p+1; 477 PetscScalar ae= s->hy/2, aeb=s->hy; 478 PetscScalar aw=-s->hy/2, awb=0; 479 480 PetscFunctionBeginUser; 481 if (i==0 && j==0) { /* south-west corner */ 482 *sz =2; 483 cols[0]=p; vals[0]=-(ae+awb); 484 cols[1]=e; vals[1]=ae; 485 } else if (i==0 && j==s->ny-1) { /* north-west corner */ 486 *sz =2; 487 cols[0]=p; vals[0]=-(ae+awb); 488 cols[1]=e; vals[1]=ae; 489 } else if (i==s->nx-1 && j==0) { /* south-east corner */ 490 *sz =2; 491 cols[0]=w; vals[0]=aw; 492 cols[1]=p; vals[1]=-(aeb+aw); 493 } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */ 494 *sz =2; 495 cols[0]=w; vals[0]=aw; 496 cols[1]=p; vals[1]=-(aeb+aw); 497 } else if (i==0) { /* west boundary */ 498 *sz =2; 499 cols[0]=p; vals[0]=-(ae+awb); 500 cols[1]=e; vals[1]=ae; 501 } else if (i==s->nx-1) { /* east boundary */ 502 *sz =2; 503 cols[0]=w; vals[0]=aw; 504 cols[1]=p; vals[1]=-(aeb+aw); 505 } else if (j==0) { /* south boundary */ 506 *sz =3; 507 cols[0]=w; vals[0]=aw; 508 cols[1]=p; vals[1]=-(ae+aw); 509 cols[2]=e; vals[2]=ae; 510 } else if (j==s->ny-1) { /* north boundary */ 511 *sz =3; 512 cols[0]=w; vals[0]=aw; 513 cols[1]=p; vals[1]=-(ae+aw); 514 cols[2]=e; vals[2]=ae; 515 } else { /* interior */ 516 *sz =3; 517 cols[0]=w; vals[0]=aw; 518 cols[1]=p; vals[1]=-(ae+aw); 519 cols[2]=e; vals[2]=ae; 520 } 521 PetscFunctionReturn(0); 522 } 523 524 PetscErrorCode StokesStencilGradientY(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals) 525 { 526 PetscInt p =j*s->nx+i, s2=p-s->nx, n=p+s->nx; 527 PetscScalar as=-s->hx/2, asb=0; 528 PetscScalar an= s->hx/2, anb=0; 529 530 PetscFunctionBeginUser; 531 if (i==0 && j==0) { /* south-west corner */ 532 *sz =2; 533 cols[0]=p; vals[0]=-(asb+an); 534 cols[1]=n; vals[1]=an; 535 } else if (i==0 && j==s->ny-1) { /* north-west corner */ 536 *sz =2; 537 cols[0]=s2; vals[0]=as; 538 cols[1]=p; vals[1]=-(as+anb); 539 } else if (i==s->nx-1 && j==0) { /* south-east corner */ 540 *sz =2; 541 cols[0]=p; vals[0]=-(asb+an); 542 cols[1]=n; vals[1]=an; 543 } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */ 544 *sz =2; 545 cols[0]=s2; vals[0]=as; 546 cols[1]=p; vals[1]=-(as+anb); 547 } else if (i==0) { /* west boundary */ 548 *sz =3; 549 cols[0]=s2; vals[0]=as; 550 cols[1]=p; vals[1]=-(as+an); 551 cols[2]=n; vals[2]=an; 552 } else if (i==s->nx-1) { /* east boundary */ 553 *sz =3; 554 cols[0]=s2; vals[0]=as; 555 cols[1]=p; vals[1]=-(as+an); 556 cols[2]=n; vals[2]=an; 557 } else if (j==0) { /* south boundary */ 558 *sz =2; 559 cols[0]=p; vals[0]=-(asb+an); 560 cols[1]=n; vals[1]=an; 561 } else if (j==s->ny-1) { /* north boundary */ 562 *sz =2; 563 cols[0]=s2; vals[0]=as; 564 cols[1]=p; vals[1]=-(as+anb); 565 } else { /* interior */ 566 *sz =3; 567 cols[0]=s2; vals[0]=as; 568 cols[1]=p; vals[1]=-(as+an); 569 cols[2]=n; vals[2]=an; 570 } 571 PetscFunctionReturn(0); 572 } 573 574 PetscErrorCode StokesRhsMomX(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val) 575 { 576 PetscScalar y = j*s->hy+s->hy/2; 577 PetscScalar awb = s->hy/(s->hx/2); 578 579 PetscFunctionBeginUser; 580 if (i == 0) { /* west boundary */ 581 *val = awb*StokesExactVelocityX(y); 582 } else { 583 *val = 0.0; 584 } 585 PetscFunctionReturn(0); 586 } 587 588 PetscErrorCode StokesRhsMomY(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val) 589 { 590 PetscFunctionBeginUser; 591 *val = 0.0; 592 PetscFunctionReturn(0); 593 } 594 595 PetscErrorCode StokesRhsMass(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val) 596 { 597 PetscScalar y = j*s->hy+s->hy/2; 598 PetscScalar aeb = s->hy; 599 600 PetscFunctionBeginUser; 601 if (i == 0) { /* west boundary */ 602 *val = aeb*StokesExactVelocityX(y); 603 } else { 604 *val = 0.0; 605 } 606 PetscFunctionReturn(0); 607 } 608 609 PetscErrorCode StokesCalcResidual(Stokes *s) 610 { 611 PetscReal val; 612 Vec b0, b1; 613 PetscErrorCode ierr; 614 615 PetscFunctionBeginUser; 616 /* residual Ax-b (*warning* overwrites b) */ 617 ierr = VecScale(s->b, -1.0);CHKERRQ(ierr); 618 ierr = MatMultAdd(s->A, s->x, s->b, s->b);CHKERRQ(ierr); 619 /* ierr = VecView(s->b, (PetscViewer)PETSC_VIEWER_DEFAULT);CHKERRQ(ierr); */ 620 621 /* residual velocity */ 622 ierr = VecGetSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr); 623 ierr = VecNorm(b0, NORM_2, &val);CHKERRQ(ierr); 624 ierr = PetscPrintf(PETSC_COMM_WORLD," residual u = %g\n",(double)val);CHKERRQ(ierr); 625 ierr = VecRestoreSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr); 626 627 /* residual pressure */ 628 ierr = VecGetSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr); 629 ierr = VecNorm(b1, NORM_2, &val);CHKERRQ(ierr); 630 ierr = PetscPrintf(PETSC_COMM_WORLD," residual p = %g\n",(double)val);CHKERRQ(ierr); 631 ierr = VecRestoreSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr); 632 633 /* total residual */ 634 ierr = VecNorm(s->b, NORM_2, &val);CHKERRQ(ierr); 635 ierr = PetscPrintf(PETSC_COMM_WORLD," residual [u,p] = %g\n", (double)val);CHKERRQ(ierr); 636 PetscFunctionReturn(0); 637 } 638 639 PetscErrorCode StokesCalcError(Stokes *s) 640 { 641 PetscScalar scale = PetscSqrtReal((double)s->nx*s->ny); 642 PetscReal val; 643 Vec y0, y1; 644 PetscErrorCode ierr; 645 646 PetscFunctionBeginUser; 647 /* error y-x */ 648 ierr = VecAXPY(s->y, -1.0, s->x);CHKERRQ(ierr); 649 /* ierr = VecView(s->y, (PetscViewer)PETSC_VIEWER_DEFAULT);CHKERRQ(ierr); */ 650 651 /* error in velocity */ 652 ierr = VecGetSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr); 653 ierr = VecNorm(y0, NORM_2, &val);CHKERRQ(ierr); 654 ierr = PetscPrintf(PETSC_COMM_WORLD," discretization error u = %g\n",(double)(PetscRealPart(val/scale)));CHKERRQ(ierr); 655 ierr = VecRestoreSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr); 656 657 /* error in pressure */ 658 ierr = VecGetSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr); 659 ierr = VecNorm(y1, NORM_2, &val);CHKERRQ(ierr); 660 ierr = PetscPrintf(PETSC_COMM_WORLD," discretization error p = %g\n",(double)(PetscRealPart(val/scale)));CHKERRQ(ierr); 661 ierr = VecRestoreSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr); 662 663 /* total error */ 664 ierr = VecNorm(s->y, NORM_2, &val);CHKERRQ(ierr); 665 ierr = PetscPrintf(PETSC_COMM_WORLD," discretization error [u,p] = %g\n", (double)PetscRealPart((val/scale)));CHKERRQ(ierr); 666 PetscFunctionReturn(0); 667 } 668 669 int main(int argc, char **argv) 670 { 671 Stokes s; 672 KSP ksp; 673 PetscErrorCode ierr; 674 675 ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr; 676 s.nx = 4; 677 s.ny = 6; 678 ierr = PetscOptionsGetInt(NULL,NULL, "-nx", &s.nx, NULL);CHKERRQ(ierr); 679 ierr = PetscOptionsGetInt(NULL,NULL, "-ny", &s.ny, NULL);CHKERRQ(ierr); 680 s.hx = 2.0/s.nx; 681 s.hy = 1.0/s.ny; 682 s.matsymmetric = PETSC_FALSE; 683 ierr = PetscOptionsGetBool(NULL,NULL, "-mat_set_symmetric", &s.matsymmetric,NULL);CHKERRQ(ierr); 684 s.userPC = s.userKSP = PETSC_FALSE; 685 ierr = PetscOptionsHasName(NULL,NULL, "-user_pc", &s.userPC);CHKERRQ(ierr); 686 ierr = PetscOptionsHasName(NULL,NULL, "-user_ksp", &s.userKSP);CHKERRQ(ierr); 687 688 ierr = StokesSetupMatrix(&s);CHKERRQ(ierr); 689 ierr = StokesSetupIndexSets(&s);CHKERRQ(ierr); 690 ierr = StokesSetupVectors(&s);CHKERRQ(ierr); 691 692 ierr = KSPCreate(PETSC_COMM_WORLD, &ksp);CHKERRQ(ierr); 693 ierr = KSPSetOperators(ksp, s.A, s.A);CHKERRQ(ierr); 694 ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr); 695 ierr = StokesSetupPC(&s, ksp);CHKERRQ(ierr); 696 ierr = KSPSolve(ksp, s.b, s.x);CHKERRQ(ierr); 697 698 /* don't trust, verify! */ 699 ierr = StokesCalcResidual(&s);CHKERRQ(ierr); 700 ierr = StokesCalcError(&s);CHKERRQ(ierr); 701 ierr = StokesWriteSolution(&s);CHKERRQ(ierr); 702 703 ierr = KSPDestroy(&ksp);CHKERRQ(ierr); 704 ierr = MatDestroy(&s.subA[0]);CHKERRQ(ierr); 705 ierr = MatDestroy(&s.subA[1]);CHKERRQ(ierr); 706 ierr = MatDestroy(&s.subA[2]);CHKERRQ(ierr); 707 ierr = MatDestroy(&s.subA[3]);CHKERRQ(ierr); 708 ierr = MatDestroy(&s.A);CHKERRQ(ierr); 709 ierr = VecDestroy(&s.x);CHKERRQ(ierr); 710 ierr = VecDestroy(&s.b);CHKERRQ(ierr); 711 ierr = VecDestroy(&s.y);CHKERRQ(ierr); 712 ierr = MatDestroy(&s.myS);CHKERRQ(ierr); 713 ierr = PetscFinalize(); 714 return ierr; 715 } 716 717 /*TEST 718 719 test: 720 nsize: 2 721 args: -nx 16 -ny 24 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -fieldsplit_1_pc_type none 722 723 test: 724 suffix: 2 725 nsize: 2 726 args: -nx 16 -ny 24 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -user_pc 727 728 test: 729 suffix: 3 730 nsize: 2 731 args: -nx 16 -ny 24 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -user_pc 732 733 test: 734 suffix: 4 735 nsize: 2 736 args: -nx 16 -ny 24 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type bjacobi -fieldsplit_1_pc_type jacobi -fieldsplit_1_inner_ksp_type preonly -fieldsplit_1_inner_pc_type jacobi -fieldsplit_1_upper_ksp_type preonly -fieldsplit_1_upper_pc_type jacobi 737 738 test: 739 suffix: 4_pcksp 740 nsize: 2 741 args: -nx 16 -ny 24 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type bjacobi -fieldsplit_1_pc_type jacobi -fieldsplit_1_inner_ksp_type preonly -fieldsplit_1_upper_ksp_type preonly -fieldsplit_1_upper_pc_type jacobi 742 743 test: 744 suffix: 5 745 nsize: 2 746 args: -nx 4 -ny 8 -mat_set_symmetric -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type gkb -fieldsplit_0_ksp_type cg -fieldsplit_0_pc_type jacobi -fieldsplit_0_ksp_rtol 1e-10 747 748 test: 749 suffix: 6 750 nsize: 2 751 args: -nx 4 -ny 8 -mat_set_symmetric -ksp_type preonly -pc_type fieldsplit -pc_fieldsplit_type gkb -fieldsplit_0_ksp_type cg -fieldsplit_0_pc_type jacobi -fieldsplit_0_ksp_rtol 1e-10 752 753 test: 754 suffix: 7 755 nsize: 2 756 args: -nx 4 -ny 8 -mat_set_symmetric -ksp_type preonly -pc_type fieldsplit -pc_fieldsplit_type gkb -pc_fieldsplit_gkb_tol 1e-4 -pc_fieldsplit_gkb_nu 5 -fieldsplit_0_ksp_type cg -fieldsplit_0_pc_type jacobi -fieldsplit_0_ksp_rtol 1e-6 757 758 TEST*/ 759