Actual source code: ex58.c
1: #include <petscsnes.h>
2: #include <petscdm.h>
3: #include <petscdmda.h>
5: static const char help[] = "Parallel version of the minimum surface area problem in 2D using DMDA.\n\
6: It solves a system of nonlinear equations in mixed\n\
7: complementarity form.This example is based on a\n\
8: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and\n\
9: boundary values along the edges of the domain, the objective is to find the\n\
10: surface with the minimal area that satisfies the boundary conditions.\n\
11: This application solves this problem using complimentarity -- We are actually\n\
12: solving the system (grad f)_i >= 0, if x_i == l_i \n\
13: (grad f)_i = 0, if l_i < x_i < u_i \n\
14: (grad f)_i <= 0, if x_i == u_i \n\
15: where f is the function to be minimized. \n\
16: \n\
17: The command line options are:\n\
18: -da_grid_x <nx>, where <nx> = number of grid points in the 1st coordinate direction\n\
19: -da_grid_y <ny>, where <ny> = number of grid points in the 2nd coordinate direction\n\
20: -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise\n\
21: -lb <value>, lower bound on the variables\n\
22: -ub <value>, upper bound on the variables\n\n";
24: /*
25: User-defined application context - contains data needed by the
26: application-provided call-back routines, FormJacobian() and
27: FormFunction().
28: */
30: /*
31: This is a new version of the ../tests/ex8.c code
33: Run, for example, with the options ./ex58 -snes_vi_monitor -ksp_monitor -mg_levels_ksp_monitor -pc_type mg -pc_mg_levels 2 -pc_mg_galerkin pmat -ksp_type fgmres
35: Or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
36: multigrid levels, it will be determined automatically based on the number of refinements done)
38: ./ex58 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
39: -mg_levels_ksp_monitor -snes_vi_monitor -mg_levels_pc_type sor -pc_mg_type full
41: */
43: typedef struct {
44: PetscScalar *bottom, *top, *left, *right;
45: PetscScalar lb, ub;
46: } AppCtx;
48: /* -------- User-defined Routines --------- */
50: extern PetscErrorCode FormBoundaryConditions(SNES, AppCtx **);
51: extern PetscErrorCode DestroyBoundaryConditions(AppCtx **);
52: extern PetscErrorCode ComputeInitialGuess(SNES, Vec, void *);
53: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void *);
54: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
55: extern PetscErrorCode FormBounds(SNES, Vec, Vec);
57: int main(int argc, char **argv)
58: {
59: Vec x, r; /* solution and residual vectors */
60: SNES snes; /* nonlinear solver context */
61: Mat J; /* Jacobian matrix */
62: DM da;
64: PetscFunctionBeginUser;
65: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
67: /* Create distributed array to manage the 2d grid */
68: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da));
69: PetscCall(DMSetFromOptions(da));
70: PetscCall(DMSetUp(da));
72: /* Extract global vectors from DMDA; */
73: PetscCall(DMCreateGlobalVector(da, &x));
74: PetscCall(VecDuplicate(x, &r));
76: PetscCall(DMSetMatType(da, MATAIJ));
77: PetscCall(DMCreateMatrix(da, &J));
79: /* Create nonlinear solver context */
80: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
81: PetscCall(SNESSetDM(snes, da));
83: /* Set function evaluation and Jacobian evaluation routines */
84: PetscCall(SNESSetFunction(snes, r, FormGradient, NULL));
85: PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL));
87: PetscCall(SNESSetComputeApplicationContext(snes, (PetscErrorCode(*)(SNES, void **))FormBoundaryConditions, (PetscErrorCode(*)(void **))DestroyBoundaryConditions));
89: PetscCall(SNESSetComputeInitialGuess(snes, ComputeInitialGuess, NULL));
91: PetscCall(SNESVISetComputeVariableBounds(snes, FormBounds));
93: PetscCall(SNESSetFromOptions(snes));
95: /* Solve the application */
96: PetscCall(SNESSolve(snes, NULL, x));
98: /* Free memory */
99: PetscCall(VecDestroy(&x));
100: PetscCall(VecDestroy(&r));
101: PetscCall(MatDestroy(&J));
102: PetscCall(SNESDestroy(&snes));
104: /* Free user-created data structures */
105: PetscCall(DMDestroy(&da));
107: PetscCall(PetscFinalize());
108: return 0;
109: }
111: /* -------------------------------------------------------------------- */
113: /* FormBounds - sets the upper and lower bounds
115: Input Parameters:
116: . snes - the SNES context
118: Output Parameters:
119: . xl - lower bounds
120: . xu - upper bounds
121: */
122: PetscErrorCode FormBounds(SNES snes, Vec xl, Vec xu)
123: {
124: AppCtx *ctx;
126: PetscFunctionBeginUser;
127: PetscCall(SNESGetApplicationContext(snes, &ctx));
128: PetscCall(VecSet(xl, ctx->lb));
129: PetscCall(VecSet(xu, ctx->ub));
130: PetscFunctionReturn(PETSC_SUCCESS);
131: }
133: /* -------------------------------------------------------------------- */
135: /* FormGradient - Evaluates gradient of f.
137: Input Parameters:
138: . snes - the SNES context
139: . X - input vector
140: . ptr - optional user-defined context, as set by SNESSetFunction()
142: Output Parameters:
143: . G - vector containing the newly evaluated gradient
144: */
145: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
146: {
147: AppCtx *user;
148: PetscInt i, j;
149: PetscInt mx, my;
150: PetscScalar hx, hy, hydhx, hxdhy;
151: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
152: PetscScalar df1dxc, df2dxc, df3dxc, df4dxc, df5dxc, df6dxc;
153: PetscScalar **g, **x;
154: PetscInt xs, xm, ys, ym;
155: Vec localX;
156: DM da;
158: PetscFunctionBeginUser;
159: PetscCall(SNESGetDM(snes, &da));
160: PetscCall(SNESGetApplicationContext(snes, &user));
161: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &mx, &my, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
162: hx = 1.0 / (mx + 1);
163: hy = 1.0 / (my + 1);
164: hydhx = hy / hx;
165: hxdhy = hx / hy;
167: PetscCall(VecSet(G, 0.0));
169: /* Get local vector */
170: PetscCall(DMGetLocalVector(da, &localX));
171: /* Get ghost points */
172: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
173: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
174: /* Get pointer to local vector data */
175: PetscCall(DMDAVecGetArray(da, localX, &x));
176: PetscCall(DMDAVecGetArray(da, G, &g));
178: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
179: /* Compute function over the locally owned part of the mesh */
180: for (j = ys; j < ys + ym; j++) {
181: for (i = xs; i < xs + xm; i++) {
182: xc = x[j][i];
183: xlt = xrb = xl = xr = xb = xt = xc;
185: if (i == 0) { /* left side */
186: xl = user->left[j + 1];
187: xlt = user->left[j + 2];
188: } else xl = x[j][i - 1];
190: if (j == 0) { /* bottom side */
191: xb = user->bottom[i + 1];
192: xrb = user->bottom[i + 2];
193: } else xb = x[j - 1][i];
195: if (i + 1 == mx) { /* right side */
196: xr = user->right[j + 1];
197: xrb = user->right[j];
198: } else xr = x[j][i + 1];
200: if (j + 1 == 0 + my) { /* top side */
201: xt = user->top[i + 1];
202: xlt = user->top[i];
203: } else xt = x[j + 1][i];
205: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1]; /* left top side */
206: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1]; /* right bottom */
208: d1 = (xc - xl);
209: d2 = (xc - xr);
210: d3 = (xc - xt);
211: d4 = (xc - xb);
212: d5 = (xr - xrb);
213: d6 = (xrb - xb);
214: d7 = (xlt - xl);
215: d8 = (xt - xlt);
217: df1dxc = d1 * hydhx;
218: df2dxc = (d1 * hydhx + d4 * hxdhy);
219: df3dxc = d3 * hxdhy;
220: df4dxc = (d2 * hydhx + d3 * hxdhy);
221: df5dxc = d2 * hydhx;
222: df6dxc = d4 * hxdhy;
224: d1 /= hx;
225: d2 /= hx;
226: d3 /= hy;
227: d4 /= hy;
228: d5 /= hy;
229: d6 /= hx;
230: d7 /= hy;
231: d8 /= hx;
233: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
234: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
235: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
236: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
237: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
238: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
240: df1dxc /= f1;
241: df2dxc /= f2;
242: df3dxc /= f3;
243: df4dxc /= f4;
244: df5dxc /= f5;
245: df6dxc /= f6;
247: g[j][i] = (df1dxc + df2dxc + df3dxc + df4dxc + df5dxc + df6dxc) / 2.0;
248: }
249: }
251: /* Restore vectors */
252: PetscCall(DMDAVecRestoreArray(da, localX, &x));
253: PetscCall(DMDAVecRestoreArray(da, G, &g));
254: PetscCall(DMRestoreLocalVector(da, &localX));
255: PetscCall(PetscLogFlops(67.0 * mx * my));
256: PetscFunctionReturn(PETSC_SUCCESS);
257: }
259: /* ------------------------------------------------------------------- */
260: /*
261: FormJacobian - Evaluates Jacobian matrix.
263: Input Parameters:
264: . snes - SNES context
265: . X - input vector
266: . ptr - optional user-defined context, as set by SNESSetJacobian()
268: Output Parameters:
269: . tH - Jacobian matrix
271: */
272: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
273: {
274: AppCtx *user;
275: PetscInt i, j, k;
276: PetscInt mx, my;
277: MatStencil row, col[7];
278: PetscScalar hx, hy, hydhx, hxdhy;
279: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
280: PetscScalar hl, hr, ht, hb, hc, htl, hbr;
281: PetscScalar **x, v[7];
282: PetscBool assembled;
283: PetscInt xs, xm, ys, ym;
284: Vec localX;
285: DM da;
287: PetscFunctionBeginUser;
288: PetscCall(SNESGetDM(snes, &da));
289: PetscCall(SNESGetApplicationContext(snes, &user));
290: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &mx, &my, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
291: hx = 1.0 / (mx + 1);
292: hy = 1.0 / (my + 1);
293: hydhx = hy / hx;
294: hxdhy = hx / hy;
296: /* Set various matrix options */
297: PetscCall(MatAssembled(H, &assembled));
298: if (assembled) PetscCall(MatZeroEntries(H));
300: /* Get local vector */
301: PetscCall(DMGetLocalVector(da, &localX));
302: /* Get ghost points */
303: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
304: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
306: /* Get pointers to vector data */
307: PetscCall(DMDAVecGetArray(da, localX, &x));
309: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
310: /* Compute Jacobian over the locally owned part of the mesh */
311: for (j = ys; j < ys + ym; j++) {
312: for (i = xs; i < xs + xm; i++) {
313: xc = x[j][i];
314: xlt = xrb = xl = xr = xb = xt = xc;
316: /* Left */
317: if (i == 0) {
318: xl = user->left[j + 1];
319: xlt = user->left[j + 2];
320: } else xl = x[j][i - 1];
322: /* Bottom */
323: if (j == 0) {
324: xb = user->bottom[i + 1];
325: xrb = user->bottom[i + 2];
326: } else xb = x[j - 1][i];
328: /* Right */
329: if (i + 1 == mx) {
330: xr = user->right[j + 1];
331: xrb = user->right[j];
332: } else xr = x[j][i + 1];
334: /* Top */
335: if (j + 1 == my) {
336: xt = user->top[i + 1];
337: xlt = user->top[i];
338: } else xt = x[j + 1][i];
340: /* Top left */
341: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1];
343: /* Bottom right */
344: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1];
346: d1 = (xc - xl) / hx;
347: d2 = (xc - xr) / hx;
348: d3 = (xc - xt) / hy;
349: d4 = (xc - xb) / hy;
350: d5 = (xrb - xr) / hy;
351: d6 = (xrb - xb) / hx;
352: d7 = (xlt - xl) / hy;
353: d8 = (xlt - xt) / hx;
355: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
356: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
357: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
358: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
359: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
360: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
362: hl = (-hydhx * (1.0 + d7 * d7) + d1 * d7) / (f1 * f1 * f1) + (-hydhx * (1.0 + d4 * d4) + d1 * d4) / (f2 * f2 * f2);
363: hr = (-hydhx * (1.0 + d5 * d5) + d2 * d5) / (f5 * f5 * f5) + (-hydhx * (1.0 + d3 * d3) + d2 * d3) / (f4 * f4 * f4);
364: ht = (-hxdhy * (1.0 + d8 * d8) + d3 * d8) / (f3 * f3 * f3) + (-hxdhy * (1.0 + d2 * d2) + d2 * d3) / (f4 * f4 * f4);
365: hb = (-hxdhy * (1.0 + d6 * d6) + d4 * d6) / (f6 * f6 * f6) + (-hxdhy * (1.0 + d1 * d1) + d1 * d4) / (f2 * f2 * f2);
367: hbr = -d2 * d5 / (f5 * f5 * f5) - d4 * d6 / (f6 * f6 * f6);
368: htl = -d1 * d7 / (f1 * f1 * f1) - d3 * d8 / (f3 * f3 * f3);
370: hc = hydhx * (1.0 + d7 * d7) / (f1 * f1 * f1) + hxdhy * (1.0 + d8 * d8) / (f3 * f3 * f3) + hydhx * (1.0 + d5 * d5) / (f5 * f5 * f5) + hxdhy * (1.0 + d6 * d6) / (f6 * f6 * f6) + (hxdhy * (1.0 + d1 * d1) + hydhx * (1.0 + d4 * d4) - 2.0 * d1 * d4) / (f2 * f2 * f2) + (hxdhy * (1.0 + d2 * d2) + hydhx * (1.0 + d3 * d3) - 2.0 * d2 * d3) / (f4 * f4 * f4);
372: hl /= 2.0;
373: hr /= 2.0;
374: ht /= 2.0;
375: hb /= 2.0;
376: hbr /= 2.0;
377: htl /= 2.0;
378: hc /= 2.0;
380: k = 0;
381: row.i = i;
382: row.j = j;
383: /* Bottom */
384: if (j > 0) {
385: v[k] = hb;
386: col[k].i = i;
387: col[k].j = j - 1;
388: k++;
389: }
391: /* Bottom right */
392: if (j > 0 && i < mx - 1) {
393: v[k] = hbr;
394: col[k].i = i + 1;
395: col[k].j = j - 1;
396: k++;
397: }
399: /* left */
400: if (i > 0) {
401: v[k] = hl;
402: col[k].i = i - 1;
403: col[k].j = j;
404: k++;
405: }
407: /* Centre */
408: v[k] = hc;
409: col[k].i = row.i;
410: col[k].j = row.j;
411: k++;
413: /* Right */
414: if (i < mx - 1) {
415: v[k] = hr;
416: col[k].i = i + 1;
417: col[k].j = j;
418: k++;
419: }
421: /* Top left */
422: if (i > 0 && j < my - 1) {
423: v[k] = htl;
424: col[k].i = i - 1;
425: col[k].j = j + 1;
426: k++;
427: }
429: /* Top */
430: if (j < my - 1) {
431: v[k] = ht;
432: col[k].i = i;
433: col[k].j = j + 1;
434: k++;
435: }
437: PetscCall(MatSetValuesStencil(H, 1, &row, k, col, v, INSERT_VALUES));
438: }
439: }
441: /* Assemble the matrix */
442: PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
443: PetscCall(DMDAVecRestoreArray(da, localX, &x));
444: PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
445: PetscCall(DMRestoreLocalVector(da, &localX));
447: PetscCall(PetscLogFlops(199.0 * mx * my));
448: PetscFunctionReturn(PETSC_SUCCESS);
449: }
451: /* ------------------------------------------------------------------- */
452: /*
453: FormBoundaryConditions - Calculates the boundary conditions for
454: the region.
456: Input Parameter:
457: . user - user-defined application context
459: Output Parameter:
460: . user - user-defined application context
461: */
462: PetscErrorCode FormBoundaryConditions(SNES snes, AppCtx **ouser)
463: {
464: PetscInt i, j, k, limit = 0, maxits = 5;
465: PetscInt mx, my;
466: PetscInt bsize = 0, lsize = 0, tsize = 0, rsize = 0;
467: PetscScalar one = 1.0, two = 2.0, three = 3.0;
468: PetscScalar det, hx, hy, xt = 0, yt = 0;
469: PetscReal fnorm, tol = 1e-10;
470: PetscScalar u1, u2, nf1, nf2, njac11, njac12, njac21, njac22;
471: PetscScalar b = -0.5, t = 0.5, l = -0.5, r = 0.5;
472: PetscScalar *boundary;
473: AppCtx *user;
474: DM da;
476: PetscFunctionBeginUser;
477: PetscCall(SNESGetDM(snes, &da));
478: PetscCall(PetscNew(&user));
479: *ouser = user;
480: user->lb = .05;
481: user->ub = PETSC_INFINITY;
482: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &mx, &my, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
484: /* Check if lower and upper bounds are set */
485: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-lb", &user->lb, 0));
486: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ub", &user->ub, 0));
487: bsize = mx + 2;
488: lsize = my + 2;
489: rsize = my + 2;
490: tsize = mx + 2;
492: PetscCall(PetscMalloc1(bsize, &user->bottom));
493: PetscCall(PetscMalloc1(tsize, &user->top));
494: PetscCall(PetscMalloc1(lsize, &user->left));
495: PetscCall(PetscMalloc1(rsize, &user->right));
497: hx = (r - l) / (mx + 1.0);
498: hy = (t - b) / (my + 1.0);
500: for (j = 0; j < 4; j++) {
501: if (j == 0) {
502: yt = b;
503: xt = l;
504: limit = bsize;
505: boundary = user->bottom;
506: } else if (j == 1) {
507: yt = t;
508: xt = l;
509: limit = tsize;
510: boundary = user->top;
511: } else if (j == 2) {
512: yt = b;
513: xt = l;
514: limit = lsize;
515: boundary = user->left;
516: } else { /* if (j==3) */
517: yt = b;
518: xt = r;
519: limit = rsize;
520: boundary = user->right;
521: }
523: for (i = 0; i < limit; i++) {
524: u1 = xt;
525: u2 = -yt;
526: for (k = 0; k < maxits; k++) {
527: nf1 = u1 + u1 * u2 * u2 - u1 * u1 * u1 / three - xt;
528: nf2 = -u2 - u1 * u1 * u2 + u2 * u2 * u2 / three - yt;
529: fnorm = PetscRealPart(PetscSqrtScalar(nf1 * nf1 + nf2 * nf2));
530: if (fnorm <= tol) break;
531: njac11 = one + u2 * u2 - u1 * u1;
532: njac12 = two * u1 * u2;
533: njac21 = -two * u1 * u2;
534: njac22 = -one - u1 * u1 + u2 * u2;
535: det = njac11 * njac22 - njac21 * njac12;
536: u1 = u1 - (njac22 * nf1 - njac12 * nf2) / det;
537: u2 = u2 - (njac11 * nf2 - njac21 * nf1) / det;
538: }
540: boundary[i] = u1 * u1 - u2 * u2;
541: if (j == 0 || j == 1) xt = xt + hx;
542: else yt = yt + hy; /* if (j==2 || j==3) */
543: }
544: }
545: PetscFunctionReturn(PETSC_SUCCESS);
546: }
548: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
549: {
550: AppCtx *user = *ouser;
552: PetscFunctionBeginUser;
553: PetscCall(PetscFree(user->bottom));
554: PetscCall(PetscFree(user->top));
555: PetscCall(PetscFree(user->left));
556: PetscCall(PetscFree(user->right));
557: PetscCall(PetscFree(*ouser));
558: PetscFunctionReturn(PETSC_SUCCESS);
559: }
561: /* ------------------------------------------------------------------- */
562: /*
563: ComputeInitialGuess - Calculates the initial guess
565: Input Parameters:
566: . user - user-defined application context
567: . X - vector for initial guess
569: Output Parameters:
570: . X - newly computed initial guess
571: */
572: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X, void *dummy)
573: {
574: PetscInt i, j, mx, my;
575: DM da;
576: AppCtx *user;
577: PetscScalar **x;
578: PetscInt xs, xm, ys, ym;
580: PetscFunctionBeginUser;
581: PetscCall(SNESGetDM(snes, &da));
582: PetscCall(SNESGetApplicationContext(snes, &user));
584: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
585: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &mx, &my, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
587: /* Get pointers to vector data */
588: PetscCall(DMDAVecGetArray(da, X, &x));
589: /* Perform local computations */
590: for (j = ys; j < ys + ym; j++) {
591: for (i = xs; i < xs + xm; i++) x[j][i] = (((j + 1.0) * user->bottom[i + 1] + (my - j + 1.0) * user->top[i + 1]) / (my + 2.0) + ((i + 1.0) * user->left[j + 1] + (mx - i + 1.0) * user->right[j + 1]) / (mx + 2.0)) / 2.0;
592: }
593: /* Restore vectors */
594: PetscCall(DMDAVecRestoreArray(da, X, &x));
595: PetscFunctionReturn(PETSC_SUCCESS);
596: }
598: /*TEST
600: test:
601: args: -snes_type vinewtonrsls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
602: requires: !single
604: test:
605: suffix: 2
606: args: -snes_type vinewtonssls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
607: requires: !single
609: TEST*/