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: 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
33: Or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
34: multigrid levels, it will be determined automatically based on the number of refinements done)
36: ./ex58 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
37: -mg_levels_ksp_monitor -snes_vi_monitor -mg_levels_pc_type sor -pc_mg_type full
39: */
41: typedef struct {
42: PetscScalar *bottom, *top, *left, *right;
43: PetscScalar lb, ub;
44: } AppCtx;
46: /* -------- User-defined Routines --------- */
48: extern PetscErrorCode FormBoundaryConditions(SNES, void **);
49: extern PetscErrorCode DestroyBoundaryConditions(void **);
50: extern PetscErrorCode ComputeInitialGuess(SNES, Vec, void *);
51: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void *);
52: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
53: extern PetscErrorCode FormBounds(SNES, Vec, Vec);
55: int main(int argc, char **argv)
56: {
57: Vec x, r; /* solution and residual vectors */
58: SNES snes; /* nonlinear solver context */
59: Mat J; /* Jacobian matrix */
60: DM da;
62: PetscFunctionBeginUser;
63: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
65: /* Create distributed array to manage the 2d grid */
66: 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));
67: PetscCall(DMSetFromOptions(da));
68: PetscCall(DMSetUp(da));
70: /* Extract global vectors from DMDA; */
71: PetscCall(DMCreateGlobalVector(da, &x));
72: PetscCall(VecDuplicate(x, &r));
74: PetscCall(DMSetMatType(da, MATAIJ));
75: PetscCall(DMCreateMatrix(da, &J));
77: /* Create nonlinear solver context */
78: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
79: PetscCall(SNESSetDM(snes, da));
81: /* Set function evaluation and Jacobian evaluation routines */
82: PetscCall(SNESSetFunction(snes, r, FormGradient, NULL));
83: PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL));
85: PetscCall(SNESSetComputeApplicationContext(snes, (PetscErrorCode (*)(SNES, void **))FormBoundaryConditions, (PetscCtxDestroyFn *)DestroyBoundaryConditions));
87: PetscCall(SNESSetComputeInitialGuess(snes, ComputeInitialGuess, NULL));
89: PetscCall(SNESVISetComputeVariableBounds(snes, FormBounds));
91: PetscCall(SNESSetFromOptions(snes));
93: /* Solve the application */
94: PetscCall(SNESSolve(snes, NULL, x));
96: /* Free memory */
97: PetscCall(VecDestroy(&x));
98: PetscCall(VecDestroy(&r));
99: PetscCall(MatDestroy(&J));
100: PetscCall(SNESDestroy(&snes));
102: /* Free user-created data structures */
103: PetscCall(DMDestroy(&da));
105: PetscCall(PetscFinalize());
106: return 0;
107: }
109: /* -------------------------------------------------------------------- */
111: /* FormBounds - sets the upper and lower bounds
113: Input Parameters:
114: . snes - the SNES context
116: Output Parameters:
117: . xl - lower bounds
118: . xu - upper bounds
119: */
120: PetscErrorCode FormBounds(SNES snes, Vec xl, Vec xu)
121: {
122: AppCtx *ctx;
124: PetscFunctionBeginUser;
125: PetscCall(SNESGetApplicationContext(snes, &ctx));
126: PetscCall(VecSet(xl, ctx->lb));
127: PetscCall(VecSet(xu, ctx->ub));
128: PetscFunctionReturn(PETSC_SUCCESS);
129: }
131: /* -------------------------------------------------------------------- */
133: /* FormGradient - Evaluates gradient of f.
135: Input Parameters:
136: . snes - the SNES context
137: . X - input vector
138: . ptr - optional user-defined context, as set by SNESSetFunction()
140: Output Parameters:
141: . G - vector containing the newly evaluated gradient
142: */
143: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
144: {
145: AppCtx *user;
146: PetscInt i, j;
147: PetscInt mx, my;
148: PetscScalar hx, hy, hydhx, hxdhy;
149: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
150: PetscScalar df1dxc, df2dxc, df3dxc, df4dxc, df5dxc, df6dxc;
151: PetscScalar **g, **x;
152: PetscInt xs, xm, ys, ym;
153: Vec localX;
154: DM da;
156: PetscFunctionBeginUser;
157: PetscCall(SNESGetDM(snes, &da));
158: PetscCall(SNESGetApplicationContext(snes, &user));
159: 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));
160: hx = 1.0 / (mx + 1);
161: hy = 1.0 / (my + 1);
162: hydhx = hy / hx;
163: hxdhy = hx / hy;
165: PetscCall(VecSet(G, 0.0));
167: /* Get local vector */
168: PetscCall(DMGetLocalVector(da, &localX));
169: /* Get ghost points */
170: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
171: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
172: /* Get pointer to local vector data */
173: PetscCall(DMDAVecGetArray(da, localX, &x));
174: PetscCall(DMDAVecGetArray(da, G, &g));
176: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
177: /* Compute function over the locally owned part of the mesh */
178: for (j = ys; j < ys + ym; j++) {
179: for (i = xs; i < xs + xm; i++) {
180: xc = x[j][i];
181: xlt = xrb = xl = xr = xb = xt = xc;
183: if (i == 0) { /* left side */
184: xl = user->left[j + 1];
185: xlt = user->left[j + 2];
186: } else xl = x[j][i - 1];
188: if (j == 0) { /* bottom side */
189: xb = user->bottom[i + 1];
190: xrb = user->bottom[i + 2];
191: } else xb = x[j - 1][i];
193: if (i + 1 == mx) { /* right side */
194: xr = user->right[j + 1];
195: xrb = user->right[j];
196: } else xr = x[j][i + 1];
198: if (j + 1 == 0 + my) { /* top side */
199: xt = user->top[i + 1];
200: xlt = user->top[i];
201: } else xt = x[j + 1][i];
203: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1]; /* left top side */
204: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1]; /* right bottom */
206: d1 = (xc - xl);
207: d2 = (xc - xr);
208: d3 = (xc - xt);
209: d4 = (xc - xb);
210: d5 = (xr - xrb);
211: d6 = (xrb - xb);
212: d7 = (xlt - xl);
213: d8 = (xt - xlt);
215: df1dxc = d1 * hydhx;
216: df2dxc = (d1 * hydhx + d4 * hxdhy);
217: df3dxc = d3 * hxdhy;
218: df4dxc = (d2 * hydhx + d3 * hxdhy);
219: df5dxc = d2 * hydhx;
220: df6dxc = d4 * hxdhy;
222: d1 /= hx;
223: d2 /= hx;
224: d3 /= hy;
225: d4 /= hy;
226: d5 /= hy;
227: d6 /= hx;
228: d7 /= hy;
229: d8 /= hx;
231: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
232: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
233: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
234: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
235: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
236: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
238: df1dxc /= f1;
239: df2dxc /= f2;
240: df3dxc /= f3;
241: df4dxc /= f4;
242: df5dxc /= f5;
243: df6dxc /= f6;
245: g[j][i] = (df1dxc + df2dxc + df3dxc + df4dxc + df5dxc + df6dxc) / 2.0;
246: }
247: }
249: /* Restore vectors */
250: PetscCall(DMDAVecRestoreArray(da, localX, &x));
251: PetscCall(DMDAVecRestoreArray(da, G, &g));
252: PetscCall(DMRestoreLocalVector(da, &localX));
253: PetscCall(PetscLogFlops(67.0 * mx * my));
254: PetscFunctionReturn(PETSC_SUCCESS);
255: }
257: /* ------------------------------------------------------------------- */
258: /*
259: FormJacobian - Evaluates Jacobian matrix.
261: Input Parameters:
262: . snes - SNES context
263: . X - input vector
264: . ptr - optional user-defined context, as set by SNESSetJacobian()
266: Output Parameters:
267: . tH - Jacobian matrix
269: */
270: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
271: {
272: AppCtx *user;
273: PetscInt i, j, k;
274: PetscInt mx, my;
275: MatStencil row, col[7];
276: PetscScalar hx, hy, hydhx, hxdhy;
277: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
278: PetscScalar hl, hr, ht, hb, hc, htl, hbr;
279: PetscScalar **x, v[7];
280: PetscBool assembled;
281: PetscInt xs, xm, ys, ym;
282: Vec localX;
283: DM da;
285: PetscFunctionBeginUser;
286: PetscCall(SNESGetDM(snes, &da));
287: PetscCall(SNESGetApplicationContext(snes, &user));
288: 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));
289: hx = 1.0 / (mx + 1);
290: hy = 1.0 / (my + 1);
291: hydhx = hy / hx;
292: hxdhy = hx / hy;
294: /* Set various matrix options */
295: PetscCall(MatAssembled(H, &assembled));
296: if (assembled) PetscCall(MatZeroEntries(H));
298: /* Get local vector */
299: PetscCall(DMGetLocalVector(da, &localX));
300: /* Get ghost points */
301: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
302: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
304: /* Get pointers to vector data */
305: PetscCall(DMDAVecGetArray(da, localX, &x));
307: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
308: /* Compute Jacobian over the locally owned part of the mesh */
309: for (j = ys; j < ys + ym; j++) {
310: for (i = xs; i < xs + xm; i++) {
311: xc = x[j][i];
312: xlt = xrb = xl = xr = xb = xt = xc;
314: /* Left */
315: if (i == 0) {
316: xl = user->left[j + 1];
317: xlt = user->left[j + 2];
318: } else xl = x[j][i - 1];
320: /* Bottom */
321: if (j == 0) {
322: xb = user->bottom[i + 1];
323: xrb = user->bottom[i + 2];
324: } else xb = x[j - 1][i];
326: /* Right */
327: if (i + 1 == mx) {
328: xr = user->right[j + 1];
329: xrb = user->right[j];
330: } else xr = x[j][i + 1];
332: /* Top */
333: if (j + 1 == my) {
334: xt = user->top[i + 1];
335: xlt = user->top[i];
336: } else xt = x[j + 1][i];
338: /* Top left */
339: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1];
341: /* Bottom right */
342: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1];
344: d1 = (xc - xl) / hx;
345: d2 = (xc - xr) / hx;
346: d3 = (xc - xt) / hy;
347: d4 = (xc - xb) / hy;
348: d5 = (xrb - xr) / hy;
349: d6 = (xrb - xb) / hx;
350: d7 = (xlt - xl) / hy;
351: d8 = (xlt - xt) / hx;
353: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
354: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
355: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
356: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
357: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
358: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
360: hl = (-hydhx * (1.0 + d7 * d7) + d1 * d7) / (f1 * f1 * f1) + (-hydhx * (1.0 + d4 * d4) + d1 * d4) / (f2 * f2 * f2);
361: hr = (-hydhx * (1.0 + d5 * d5) + d2 * d5) / (f5 * f5 * f5) + (-hydhx * (1.0 + d3 * d3) + d2 * d3) / (f4 * f4 * f4);
362: ht = (-hxdhy * (1.0 + d8 * d8) + d3 * d8) / (f3 * f3 * f3) + (-hxdhy * (1.0 + d2 * d2) + d2 * d3) / (f4 * f4 * f4);
363: hb = (-hxdhy * (1.0 + d6 * d6) + d4 * d6) / (f6 * f6 * f6) + (-hxdhy * (1.0 + d1 * d1) + d1 * d4) / (f2 * f2 * f2);
365: hbr = -d2 * d5 / (f5 * f5 * f5) - d4 * d6 / (f6 * f6 * f6);
366: htl = -d1 * d7 / (f1 * f1 * f1) - d3 * d8 / (f3 * f3 * f3);
368: 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);
370: hl /= 2.0;
371: hr /= 2.0;
372: ht /= 2.0;
373: hb /= 2.0;
374: hbr /= 2.0;
375: htl /= 2.0;
376: hc /= 2.0;
378: k = 0;
379: row.i = i;
380: row.j = j;
381: /* Bottom */
382: if (j > 0) {
383: v[k] = hb;
384: col[k].i = i;
385: col[k].j = j - 1;
386: k++;
387: }
389: /* Bottom right */
390: if (j > 0 && i < mx - 1) {
391: v[k] = hbr;
392: col[k].i = i + 1;
393: col[k].j = j - 1;
394: k++;
395: }
397: /* left */
398: if (i > 0) {
399: v[k] = hl;
400: col[k].i = i - 1;
401: col[k].j = j;
402: k++;
403: }
405: /* Centre */
406: v[k] = hc;
407: col[k].i = row.i;
408: col[k].j = row.j;
409: k++;
411: /* Right */
412: if (i < mx - 1) {
413: v[k] = hr;
414: col[k].i = i + 1;
415: col[k].j = j;
416: k++;
417: }
419: /* Top left */
420: if (i > 0 && j < my - 1) {
421: v[k] = htl;
422: col[k].i = i - 1;
423: col[k].j = j + 1;
424: k++;
425: }
427: /* Top */
428: if (j < my - 1) {
429: v[k] = ht;
430: col[k].i = i;
431: col[k].j = j + 1;
432: k++;
433: }
435: PetscCall(MatSetValuesStencil(H, 1, &row, k, col, v, INSERT_VALUES));
436: }
437: }
439: /* Assemble the matrix */
440: PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
441: PetscCall(DMDAVecRestoreArray(da, localX, &x));
442: PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
443: PetscCall(DMRestoreLocalVector(da, &localX));
445: PetscCall(PetscLogFlops(199.0 * mx * my));
446: PetscFunctionReturn(PETSC_SUCCESS);
447: }
449: /* ------------------------------------------------------------------- */
450: /*
451: FormBoundaryConditions - Calculates the boundary conditions for
452: the region.
454: Input Parameter:
455: . user - user-defined application context
457: Output Parameter:
458: . user - user-defined application context
459: */
460: PetscErrorCode FormBoundaryConditions(SNES snes, void **inctx)
461: {
462: PetscInt i, j, k, limit = 0, maxits = 5;
463: PetscInt mx, my;
464: PetscInt bsize = 0, lsize = 0, tsize = 0, rsize = 0;
465: PetscScalar one = 1.0, two = 2.0, three = 3.0;
466: PetscScalar det, hx, hy, xt = 0, yt = 0;
467: PetscReal fnorm, tol = 1e-10;
468: PetscScalar u1, u2, nf1, nf2, njac11, njac12, njac21, njac22;
469: PetscScalar b = -0.5, t = 0.5, l = -0.5, r = 0.5;
470: PetscScalar *boundary;
471: AppCtx *user, **ouser = (AppCtx **)inctx;
472: DM da;
474: PetscFunctionBeginUser;
475: PetscCall(SNESGetDM(snes, &da));
476: PetscCall(PetscNew(&user));
477: *ouser = user;
478: user->lb = .05;
479: user->ub = PETSC_INFINITY;
480: 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));
482: /* Check if lower and upper bounds are set */
483: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-lb", &user->lb, 0));
484: PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ub", &user->ub, 0));
485: bsize = mx + 2;
486: lsize = my + 2;
487: rsize = my + 2;
488: tsize = mx + 2;
490: PetscCall(PetscMalloc1(bsize, &user->bottom));
491: PetscCall(PetscMalloc1(tsize, &user->top));
492: PetscCall(PetscMalloc1(lsize, &user->left));
493: PetscCall(PetscMalloc1(rsize, &user->right));
495: hx = (r - l) / (mx + 1.0);
496: hy = (t - b) / (my + 1.0);
498: for (j = 0; j < 4; j++) {
499: if (j == 0) {
500: yt = b;
501: xt = l;
502: limit = bsize;
503: boundary = user->bottom;
504: } else if (j == 1) {
505: yt = t;
506: xt = l;
507: limit = tsize;
508: boundary = user->top;
509: } else if (j == 2) {
510: yt = b;
511: xt = l;
512: limit = lsize;
513: boundary = user->left;
514: } else { /* if (j==3) */
515: yt = b;
516: xt = r;
517: limit = rsize;
518: boundary = user->right;
519: }
521: for (i = 0; i < limit; i++) {
522: u1 = xt;
523: u2 = -yt;
524: for (k = 0; k < maxits; k++) {
525: nf1 = u1 + u1 * u2 * u2 - u1 * u1 * u1 / three - xt;
526: nf2 = -u2 - u1 * u1 * u2 + u2 * u2 * u2 / three - yt;
527: fnorm = PetscRealPart(PetscSqrtScalar(nf1 * nf1 + nf2 * nf2));
528: if (fnorm <= tol) break;
529: njac11 = one + u2 * u2 - u1 * u1;
530: njac12 = two * u1 * u2;
531: njac21 = -two * u1 * u2;
532: njac22 = -one - u1 * u1 + u2 * u2;
533: det = njac11 * njac22 - njac21 * njac12;
534: u1 = u1 - (njac22 * nf1 - njac12 * nf2) / det;
535: u2 = u2 - (njac11 * nf2 - njac21 * nf1) / det;
536: }
538: boundary[i] = u1 * u1 - u2 * u2;
539: if (j == 0 || j == 1) xt = xt + hx;
540: else yt = yt + hy; /* if (j==2 || j==3) */
541: }
542: }
543: PetscFunctionReturn(PETSC_SUCCESS);
544: }
546: PetscErrorCode DestroyBoundaryConditions(void **ouser)
547: {
548: AppCtx *user = (AppCtx *)*ouser;
550: PetscFunctionBeginUser;
551: PetscCall(PetscFree(user->bottom));
552: PetscCall(PetscFree(user->top));
553: PetscCall(PetscFree(user->left));
554: PetscCall(PetscFree(user->right));
555: PetscCall(PetscFree(*ouser));
556: PetscFunctionReturn(PETSC_SUCCESS);
557: }
559: /* ------------------------------------------------------------------- */
560: /*
561: ComputeInitialGuess - Calculates the initial guess
563: Input Parameters:
564: . user - user-defined application context
565: . X - vector for initial guess
567: Output Parameters:
568: . X - newly computed initial guess
569: */
570: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X, void *dummy)
571: {
572: PetscInt i, j, mx, my;
573: DM da;
574: AppCtx *user;
575: PetscScalar **x;
576: PetscInt xs, xm, ys, ym;
578: PetscFunctionBeginUser;
579: PetscCall(SNESGetDM(snes, &da));
580: PetscCall(SNESGetApplicationContext(snes, &user));
582: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
583: 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));
585: /* Get pointers to vector data */
586: PetscCall(DMDAVecGetArray(da, X, &x));
587: /* Perform local computations */
588: for (j = ys; j < ys + ym; j++) {
589: 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;
590: }
591: /* Restore vectors */
592: PetscCall(DMDAVecRestoreArray(da, X, &x));
593: PetscFunctionReturn(PETSC_SUCCESS);
594: }
596: /*TEST
598: test:
599: 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
600: requires: !single
602: test:
603: suffix: 2
604: 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
605: requires: !single
607: TEST*/