Actual source code: ex70.c
petsc-3.8.4 2018-03-24
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";
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: /*---------------------------------------------------------------------------- */
55: #include <petscksp.h>
57: typedef struct {
58: PetscBool userPC, userKSP; /* 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;
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) */
73: PetscErrorCode StokesGetPosition(Stokes*, PetscInt, PetscInt*, PetscInt*); /* row number j*nx+i corresponds to position (i,j) in grid */
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) */
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 */
84: PetscErrorCode StokesSetupApproxSchur(Stokes*); /* approximation of the Schur complement */
86: PetscErrorCode StokesExactSolution(Stokes*); /* exact solution vector */
87: PetscErrorCode StokesWriteSolution(Stokes*); /* write solution to file */
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: }
95: /* exact solution for the pressure */
96: PetscScalar StokesExactPressure(const PetscScalar x)
97: {
98: return 8.0*(2.0-x);
99: }
101: PetscErrorCode StokesSetupPC(Stokes *s, KSP ksp)
102: {
103: KSP *subksp;
104: PC pc;
105: PetscInt n = 1;
109: KSPGetPC(ksp, &pc);
110: PCFieldSplitSetIS(pc, "0", s->isg[0]);
111: PCFieldSplitSetIS(pc, "1", s->isg[1]);
112: if (s->userPC) {
113: PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_USER, s->myS);
114: }
115: if (s->userKSP) {
116: PCSetUp(pc);
117: PCFieldSplitGetSubKSP(pc, &n, &subksp);
118: KSPSetOperators(subksp[1], s->myS, s->myS);
119: PetscFree(subksp);
120: }
121: return(0);
122: }
124: PetscErrorCode StokesWriteSolution(Stokes *s)
125: {
126: PetscMPIInt size;
127: PetscInt n,i,j;
128: const PetscScalar *array;
129: PetscErrorCode ierr;
132: /* write data (*warning* only works sequential) */
133: MPI_Comm_size(MPI_COMM_WORLD,&size);
134: /*PetscPrintf(PETSC_COMM_WORLD," number of processors = %D\n",size);*/
135: if (size == 1) {
136: PetscViewer viewer;
137: VecGetArrayRead(s->x, &array);
138: PetscViewerASCIIOpen(PETSC_COMM_WORLD, "solution.dat", &viewer);
139: PetscViewerASCIIPrintf(viewer, "# x, y, u, v, p\n");
140: for (j = 0; j < s->ny; j++) {
141: for (i = 0; i < s->nx; i++) {
142: n = j*s->nx+i;
143: 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]));
144: }
145: }
146: VecRestoreArrayRead(s->x, &array);
147: PetscViewerDestroy(&viewer);
148: }
149: return(0);
150: }
152: PetscErrorCode StokesSetupIndexSets(Stokes *s)
153: {
157: /* the two index sets */
158: MatNestGetISs(s->A, s->isg, NULL);
159: /* ISView(isg[0],PETSC_VIEWER_STDOUT_WORLD); */
160: /* ISView(isg[1],PETSC_VIEWER_STDOUT_WORLD); */
161: return(0);
162: }
164: PetscErrorCode StokesSetupVectors(Stokes *s)
165: {
169: /* solution vector x */
170: VecCreate(PETSC_COMM_WORLD, &s->x);
171: VecSetSizes(s->x, PETSC_DECIDE, 3*s->nx*s->ny);
172: VecSetType(s->x, VECMPI);
173: /* VecSetRandom(s->x, NULL); */
174: /* VecView(s->x, (PetscViewer) PETSC_VIEWER_DEFAULT); */
176: /* exact solution y */
177: VecDuplicate(s->x, &s->y);
178: StokesExactSolution(s);
179: /* VecView(s->y, (PetscViewer) PETSC_VIEWER_DEFAULT); */
181: /* rhs vector b */
182: VecDuplicate(s->x, &s->b);
183: StokesRhs(s);
184: /*VecView(s->b, (PetscViewer) PETSC_VIEWER_DEFAULT);*/
185: return(0);
186: }
188: PetscErrorCode StokesGetPosition(Stokes *s, PetscInt row, PetscInt *i, PetscInt *j)
189: {
190: PetscInt n;
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: return(0);
198: }
200: PetscErrorCode StokesExactSolution(Stokes *s)
201: {
202: PetscInt row, start, end, i, j;
203: PetscScalar val;
204: Vec y0,y1;
208: /* velocity part */
209: VecGetSubVector(s->y, s->isg[0], &y0);
210: VecGetOwnershipRange(y0, &start, &end);
211: for (row = start; row < end; row++) {
212: StokesGetPosition(s, row,&i,&j);
213: if (row < s->nx*s->ny) {
214: val = StokesExactVelocityX(j*s->hy+s->hy/2);
215: } else {
216: val = 0;
217: }
218: VecSetValue(y0, row, val, INSERT_VALUES);
219: }
220: VecRestoreSubVector(s->y, s->isg[0], &y0);
222: /* pressure part */
223: VecGetSubVector(s->y, s->isg[1], &y1);
224: VecGetOwnershipRange(y1, &start, &end);
225: for (row = start; row < end; row++) {
226: StokesGetPosition(s, row, &i, &j);
227: val = StokesExactPressure(i*s->hx+s->hx/2);
228: VecSetValue(y1, row, val, INSERT_VALUES);
229: }
230: VecRestoreSubVector(s->y, s->isg[1], &y1);
231: return(0);
232: }
234: PetscErrorCode StokesRhs(Stokes *s)
235: {
236: PetscInt row, start, end, i, j;
237: PetscScalar val;
238: Vec b0,b1;
242: /* velocity part */
243: VecGetSubVector(s->b, s->isg[0], &b0);
244: VecGetOwnershipRange(b0, &start, &end);
245: for (row = start; row < end; row++) {
246: StokesGetPosition(s, row, &i, &j);
247: if (row < s->nx*s->ny) {
248: StokesRhsMomX(s, i, j, &val);
249: } else {
250: StokesRhsMomY(s, i, j, &val);
251: }
252: VecSetValue(b0, row, val, INSERT_VALUES);
253: }
254: VecRestoreSubVector(s->b, s->isg[0], &b0);
256: /* pressure part */
257: VecGetSubVector(s->b, s->isg[1], &b1);
258: VecGetOwnershipRange(b1, &start, &end);
259: for (row = start; row < end; row++) {
260: StokesGetPosition(s, row, &i, &j);
261: StokesRhsMass(s, i, j, &val);
262: VecSetValue(b1, row, val, INSERT_VALUES);
263: }
264: VecRestoreSubVector(s->b, s->isg[1], &b1);
265: return(0);
266: }
268: PetscErrorCode StokesSetupMatBlock00(Stokes *s)
269: {
270: PetscInt row, start, end, sz, i, j;
271: PetscInt cols[5];
272: PetscScalar vals[5];
276: /* A[0] is 2N-by-2N */
277: MatCreate(PETSC_COMM_WORLD,&s->subA[0]);
278: MatSetOptionsPrefix(s->subA[0],"a00_");
279: MatSetSizes(s->subA[0],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,2*s->nx*s->ny);
280: MatSetType(s->subA[0],MATMPIAIJ);
281: MatMPIAIJSetPreallocation(s->subA[0],5,NULL,5,NULL);
282: MatGetOwnershipRange(s->subA[0], &start, &end);
284: for (row = start; row < end; row++) {
285: StokesGetPosition(s, row, &i, &j);
286: /* first part: rows 0 to (nx*ny-1) */
287: StokesStencilLaplacian(s, i, j, &sz, cols, vals);
288: /* second part: rows (nx*ny) to (2*nx*ny-1) */
289: if (row >= s->nx*s->ny) {
290: for (i = 0; i < sz; i++) cols[i] += s->nx*s->ny;
291: }
292: for (i = 0; i < sz; i++) vals[i] = -1.0*vals[i]; /* dynamic viscosity coef mu=-1 */
293: MatSetValues(s->subA[0], 1, &row, sz, cols, vals, INSERT_VALUES);
294: }
295: MatAssemblyBegin(s->subA[0], MAT_FINAL_ASSEMBLY);
296: MatAssemblyEnd(s->subA[0], MAT_FINAL_ASSEMBLY);
297: return(0);
298: }
300: PetscErrorCode StokesSetupMatBlock01(Stokes *s)
301: {
302: PetscInt row, start, end, sz, i, j;
303: PetscInt cols[5];
304: PetscScalar vals[5];
308: /* A[1] is 2N-by-N */
309: MatCreate(PETSC_COMM_WORLD, &s->subA[1]);
310: MatSetOptionsPrefix(s->subA[1],"a01_");
311: MatSetSizes(s->subA[1],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,s->nx*s->ny);
312: MatSetType(s->subA[1],MATMPIAIJ);
313: MatMPIAIJSetPreallocation(s->subA[1],5,NULL,5,NULL);
314: MatGetOwnershipRange(s->subA[1],&start,&end);
316: MatSetOption(s->subA[1],MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
318: for (row = start; row < end; row++) {
319: StokesGetPosition(s, row, &i, &j);
320: /* first part: rows 0 to (nx*ny-1) */
321: if (row < s->nx*s->ny) {
322: StokesStencilGradientX(s, i, j, &sz, cols, vals);
323: } else { /* second part: rows (nx*ny) to (2*nx*ny-1) */
324: StokesStencilGradientY(s, i, j, &sz, cols, vals);
325: }
326: MatSetValues(s->subA[1], 1, &row, sz, cols, vals, INSERT_VALUES);
327: }
328: MatAssemblyBegin(s->subA[1], MAT_FINAL_ASSEMBLY);
329: MatAssemblyEnd(s->subA[1], MAT_FINAL_ASSEMBLY);
330: return(0);
331: }
333: PetscErrorCode StokesSetupMatBlock10(Stokes *s)
334: {
338: /* A[2] is minus transpose of A[1] */
339: MatTranspose(s->subA[1], MAT_INITIAL_MATRIX, &s->subA[2]);
340: MatScale(s->subA[2], -1.0);
341: MatSetOptionsPrefix(s->subA[2], "a10_");
342: return(0);
343: }
345: PetscErrorCode StokesSetupMatBlock11(Stokes *s)
346: {
350: /* A[3] is N-by-N null matrix */
351: MatCreate(PETSC_COMM_WORLD, &s->subA[3]);
352: MatSetOptionsPrefix(s->subA[3], "a11_");
353: MatSetSizes(s->subA[3], PETSC_DECIDE, PETSC_DECIDE, s->nx*s->ny, s->nx*s->ny);
354: MatSetType(s->subA[3], MATMPIAIJ);
355: MatMPIAIJSetPreallocation(s->subA[3], 0, NULL, 0, NULL);
356: MatAssemblyBegin(s->subA[3], MAT_FINAL_ASSEMBLY);
357: MatAssemblyEnd(s->subA[3], MAT_FINAL_ASSEMBLY);
358: return(0);
359: }
361: PetscErrorCode StokesSetupApproxSchur(Stokes *s)
362: {
363: Vec diag;
367: /* Schur complement approximation: myS = A11 - A10 diag(A00)^(-1) A01 */
368: /* note: A11 is zero */
369: /* note: in real life this matrix would be build directly, */
370: /* i.e. without MatMatMult */
372: /* inverse of diagonal of A00 */
373: VecCreate(PETSC_COMM_WORLD,&diag);
374: VecSetSizes(diag,PETSC_DECIDE,2*s->nx*s->ny);
375: VecSetType(diag,VECMPI);
376: MatGetDiagonal(s->subA[0],diag);
377: VecReciprocal(diag);
379: /* compute: - A10 diag(A00)^(-1) A01 */
380: MatDiagonalScale(s->subA[1],diag,NULL); /* (*warning* overwrites subA[1]) */
381: MatMatMult(s->subA[2],s->subA[1],MAT_INITIAL_MATRIX,PETSC_DEFAULT,&s->myS);
382: MatScale(s->myS,-1.0);
384: /* restore A10 */
385: MatGetDiagonal(s->subA[0],diag);
386: MatDiagonalScale(s->subA[1],diag,NULL);
387: VecDestroy(&diag);
388: return(0);
389: }
391: PetscErrorCode StokesSetupMatrix(Stokes *s)
392: {
396: StokesSetupMatBlock00(s);
397: StokesSetupMatBlock01(s);
398: StokesSetupMatBlock10(s);
399: StokesSetupMatBlock11(s);
400: MatCreateNest(PETSC_COMM_WORLD, 2, NULL, 2, NULL, s->subA, &s->A);
401: StokesSetupApproxSchur(s);
402: return(0);
403: }
405: PetscErrorCode StokesStencilLaplacian(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals)
406: {
407: PetscInt p =j*s->nx+i, w=p-1, e=p+1, s2=p-s->nx, n=p+s->nx;
408: PetscScalar ae=s->hy/s->hx, aeb=0;
409: PetscScalar aw=s->hy/s->hx, awb=s->hy/(s->hx/2);
410: PetscScalar as=s->hx/s->hy, asb=s->hx/(s->hy/2);
411: PetscScalar an=s->hx/s->hy, anb=s->hx/(s->hy/2);
414: if (i==0 && j==0) { /* south-west corner */
415: *sz =3;
416: cols[0]=p; vals[0]=-(ae+awb+asb+an);
417: cols[1]=e; vals[1]=ae;
418: cols[2]=n; vals[2]=an;
419: } else if (i==0 && j==s->ny-1) { /* north-west corner */
420: *sz =3;
421: cols[0]=s2; vals[0]=as;
422: cols[1]=p; vals[1]=-(ae+awb+as+anb);
423: cols[2]=e; vals[2]=ae;
424: } else if (i==s->nx-1 && j==0) { /* south-east corner */
425: *sz =3;
426: cols[0]=w; vals[0]=aw;
427: cols[1]=p; vals[1]=-(aeb+aw+asb+an);
428: cols[2]=n; vals[2]=an;
429: } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */
430: *sz =3;
431: cols[0]=s2; vals[0]=as;
432: cols[1]=w; vals[1]=aw;
433: cols[2]=p; vals[2]=-(aeb+aw+as+anb);
434: } else if (i==0) { /* west boundary */
435: *sz =4;
436: cols[0]=s2; vals[0]=as;
437: cols[1]=p; vals[1]=-(ae+awb+as+an);
438: cols[2]=e; vals[2]=ae;
439: cols[3]=n; vals[3]=an;
440: } else if (i==s->nx-1) { /* east boundary */
441: *sz =4;
442: cols[0]=s2; vals[0]=as;
443: cols[1]=w; vals[1]=aw;
444: cols[2]=p; vals[2]=-(aeb+aw+as+an);
445: cols[3]=n; vals[3]=an;
446: } else if (j==0) { /* south boundary */
447: *sz =4;
448: cols[0]=w; vals[0]=aw;
449: cols[1]=p; vals[1]=-(ae+aw+asb+an);
450: cols[2]=e; vals[2]=ae;
451: cols[3]=n; vals[3]=an;
452: } else if (j==s->ny-1) { /* north boundary */
453: *sz =4;
454: cols[0]=s2; vals[0]=as;
455: cols[1]=w; vals[1]=aw;
456: cols[2]=p; vals[2]=-(ae+aw+as+anb);
457: cols[3]=e; vals[3]=ae;
458: } else { /* interior */
459: *sz =5;
460: cols[0]=s2; vals[0]=as;
461: cols[1]=w; vals[1]=aw;
462: cols[2]=p; vals[2]=-(ae+aw+as+an);
463: cols[3]=e; vals[3]=ae;
464: cols[4]=n; vals[4]=an;
465: }
466: return(0);
467: }
469: PetscErrorCode StokesStencilGradientX(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals)
470: {
471: PetscInt p =j*s->nx+i, w=p-1, e=p+1;
472: PetscScalar ae= s->hy/2, aeb=s->hy;
473: PetscScalar aw=-s->hy/2, awb=0;
476: if (i==0 && j==0) { /* south-west corner */
477: *sz =2;
478: cols[0]=p; vals[0]=-(ae+awb);
479: cols[1]=e; vals[1]=ae;
480: } else if (i==0 && j==s->ny-1) { /* north-west corner */
481: *sz =2;
482: cols[0]=p; vals[0]=-(ae+awb);
483: cols[1]=e; vals[1]=ae;
484: } else if (i==s->nx-1 && j==0) { /* south-east corner */
485: *sz =2;
486: cols[0]=w; vals[0]=aw;
487: cols[1]=p; vals[1]=-(aeb+aw);
488: } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */
489: *sz =2;
490: cols[0]=w; vals[0]=aw;
491: cols[1]=p; vals[1]=-(aeb+aw);
492: } else if (i==0) { /* west boundary */
493: *sz =2;
494: cols[0]=p; vals[0]=-(ae+awb);
495: cols[1]=e; vals[1]=ae;
496: } else if (i==s->nx-1) { /* east boundary */
497: *sz =2;
498: cols[0]=w; vals[0]=aw;
499: cols[1]=p; vals[1]=-(aeb+aw);
500: } else if (j==0) { /* south boundary */
501: *sz =3;
502: cols[0]=w; vals[0]=aw;
503: cols[1]=p; vals[1]=-(ae+aw);
504: cols[2]=e; vals[2]=ae;
505: } else if (j==s->ny-1) { /* north 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 { /* interior */
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: }
516: return(0);
517: }
519: PetscErrorCode StokesStencilGradientY(Stokes *s, PetscInt i, PetscInt j, PetscInt *sz, PetscInt *cols, PetscScalar *vals)
520: {
521: PetscInt p =j*s->nx+i, s2=p-s->nx, n=p+s->nx;
522: PetscScalar as=-s->hx/2, asb=0;
523: PetscScalar an= s->hx/2, anb=0;
526: if (i==0 && j==0) { /* south-west corner */
527: *sz =2;
528: cols[0]=p; vals[0]=-(asb+an);
529: cols[1]=n; vals[1]=an;
530: } else if (i==0 && j==s->ny-1) { /* north-west corner */
531: *sz =2;
532: cols[0]=s2; vals[0]=as;
533: cols[1]=p; vals[1]=-(as+anb);
534: } else if (i==s->nx-1 && j==0) { /* south-east corner */
535: *sz =2;
536: cols[0]=p; vals[0]=-(asb+an);
537: cols[1]=n; vals[1]=an;
538: } else if (i==s->nx-1 && j==s->ny-1) { /* north-east corner */
539: *sz =2;
540: cols[0]=s2; vals[0]=as;
541: cols[1]=p; vals[1]=-(as+anb);
542: } else if (i==0) { /* west boundary */
543: *sz =3;
544: cols[0]=s2; vals[0]=as;
545: cols[1]=p; vals[1]=-(as+an);
546: cols[2]=n; vals[2]=an;
547: } else if (i==s->nx-1) { /* east 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 (j==0) { /* south boundary */
553: *sz =2;
554: cols[0]=p; vals[0]=-(asb+an);
555: cols[1]=n; vals[1]=an;
556: } else if (j==s->ny-1) { /* north boundary */
557: *sz =2;
558: cols[0]=s2; vals[0]=as;
559: cols[1]=p; vals[1]=-(as+anb);
560: } else { /* interior */
561: *sz =3;
562: cols[0]=s2; vals[0]=as;
563: cols[1]=p; vals[1]=-(as+an);
564: cols[2]=n; vals[2]=an;
565: }
566: return(0);
567: }
569: PetscErrorCode StokesRhsMomX(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val)
570: {
571: PetscScalar y = j*s->hy+s->hy/2;
572: PetscScalar awb = s->hy/(s->hx/2);
575: if (i == 0) { /* west boundary */
576: *val = awb*StokesExactVelocityX(y);
577: } else {
578: *val = 0.0;
579: }
580: return(0);
581: }
583: PetscErrorCode StokesRhsMomY(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val)
584: {
586: *val = 0.0;
587: return(0);
588: }
590: PetscErrorCode StokesRhsMass(Stokes *s, PetscInt i, PetscInt j, PetscScalar *val)
591: {
592: PetscScalar y = j*s->hy+s->hy/2;
593: PetscScalar aeb = s->hy;
596: if (i == 0) { /* west boundary */
597: *val = aeb*StokesExactVelocityX(y);
598: } else {
599: *val = 0.0;
600: }
601: return(0);
602: }
604: PetscErrorCode StokesCalcResidual(Stokes *s)
605: {
606: PetscReal val;
607: Vec b0, b1;
611: /* residual Ax-b (*warning* overwrites b) */
612: VecScale(s->b, -1.0);
613: MatMultAdd(s->A, s->x, s->b, s->b);
614: /* VecView(s->b, (PetscViewer)PETSC_VIEWER_DEFAULT); */
616: /* residual velocity */
617: VecGetSubVector(s->b, s->isg[0], &b0);
618: VecNorm(b0, NORM_2, &val);
619: PetscPrintf(PETSC_COMM_WORLD," residual u = %g\n",(double)val);
620: VecRestoreSubVector(s->b, s->isg[0], &b0);
622: /* residual pressure */
623: VecGetSubVector(s->b, s->isg[1], &b1);
624: VecNorm(b1, NORM_2, &val);
625: PetscPrintf(PETSC_COMM_WORLD," residual p = %g\n",(double)val);
626: VecRestoreSubVector(s->b, s->isg[1], &b1);
628: /* total residual */
629: VecNorm(s->b, NORM_2, &val);
630: PetscPrintf(PETSC_COMM_WORLD," residual [u,p] = %g\n", (double)val);
631: return(0);
632: }
634: PetscErrorCode StokesCalcError(Stokes *s)
635: {
636: PetscScalar scale = PetscSqrtReal((double)s->nx*s->ny);
637: PetscReal val;
638: Vec y0, y1;
642: /* error y-x */
643: VecAXPY(s->y, -1.0, s->x);
644: /* VecView(s->y, (PetscViewer)PETSC_VIEWER_DEFAULT); */
646: /* error in velocity */
647: VecGetSubVector(s->y, s->isg[0], &y0);
648: VecNorm(y0, NORM_2, &val);
649: PetscPrintf(PETSC_COMM_WORLD," discretization error u = %g\n",(double)(PetscRealPart(val/scale)));
650: VecRestoreSubVector(s->y, s->isg[0], &y0);
652: /* error in pressure */
653: VecGetSubVector(s->y, s->isg[1], &y1);
654: VecNorm(y1, NORM_2, &val);
655: PetscPrintf(PETSC_COMM_WORLD," discretization error p = %g\n",(double)(PetscRealPart(val/scale)));
656: VecRestoreSubVector(s->y, s->isg[1], &y1);
658: /* total error */
659: VecNorm(s->y, NORM_2, &val);
660: PetscPrintf(PETSC_COMM_WORLD," discretization error [u,p] = %g\n", (double)PetscRealPart((val/scale)));
661: return(0);
662: }
664: int main(int argc, char **argv)
665: {
666: Stokes s;
667: KSP ksp;
670: PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
671: s.nx = 4;
672: s.ny = 6;
673: PetscOptionsGetInt(NULL,NULL, "-nx", &s.nx, NULL);
674: PetscOptionsGetInt(NULL,NULL, "-ny", &s.ny, NULL);
675: s.hx = 2.0/s.nx;
676: s.hy = 1.0/s.ny;
677: s.userPC = s.userKSP = PETSC_FALSE;
678: PetscOptionsHasName(NULL,NULL, "-user_pc", &s.userPC);
679: PetscOptionsHasName(NULL,NULL, "-user_ksp", &s.userKSP);
681: StokesSetupMatrix(&s);
682: StokesSetupIndexSets(&s);
683: StokesSetupVectors(&s);
685: KSPCreate(PETSC_COMM_WORLD, &ksp);
686: KSPSetOperators(ksp, s.A, s.A);
687: KSPSetFromOptions(ksp);
688: StokesSetupPC(&s, ksp);
689: KSPSolve(ksp, s.b, s.x);
691: /* don't trust, verify! */
692: StokesCalcResidual(&s);
693: StokesCalcError(&s);
694: StokesWriteSolution(&s);
696: KSPDestroy(&ksp);
697: MatDestroy(&s.subA[0]);
698: MatDestroy(&s.subA[1]);
699: MatDestroy(&s.subA[2]);
700: MatDestroy(&s.subA[3]);
701: MatDestroy(&s.A);
702: VecDestroy(&s.x);
703: VecDestroy(&s.b);
704: VecDestroy(&s.y);
705: MatDestroy(&s.myS);
706: PetscFinalize();
707: return ierr;
708: }