Actual source code: ex58.c
2: #include <petscsnes.h>
3: #include <petscdm.h>
4: #include <petscdmda.h>
6: static const char help[] = "Parallel version of the minimum surface area problem in 2D using DMDA.\n\
7: It solves a system of nonlinear equations in mixed\n\
8: complementarity form.This example is based on a\n\
9: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and\n\
10: boundary values along the edges of the domain, the objective is to find the\n\
11: surface with the minimal area that satisfies the boundary conditions.\n\
12: This application solves this problem using complimentarity -- We are actually\n\
13: solving the system (grad f)_i >= 0, if x_i == l_i \n\
14: (grad f)_i = 0, if l_i < x_i < u_i \n\
15: (grad f)_i <= 0, if x_i == u_i \n\
16: where f is the function to be minimized. \n\
17: \n\
18: The command line options are:\n\
19: -da_grid_x <nx>, where <nx> = number of grid points in the 1st coordinate direction\n\
20: -da_grid_y <ny>, where <ny> = number of grid points in the 2nd coordinate direction\n\
21: -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise\n\
22: -lb <value>, lower bound on the variables\n\
23: -ub <value>, upper bound on the variables\n\n";
25: /*
26: User-defined application context - contains data needed by the
27: application-provided call-back routines, FormJacobian() and
28: FormFunction().
29: */
31: /*
32: This is a new version of the ../tests/ex8.c code
34: 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
36: Or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
37: multigrid levels, it will be determined automatically based on the number of refinements done)
39: ./ex58 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
40: -mg_levels_ksp_monitor -snes_vi_monitor -mg_levels_pc_type sor -pc_mg_type full
42: */
44: typedef struct {
45: PetscScalar *bottom, *top, *left, *right;
46: PetscScalar lb, ub;
47: } AppCtx;
49: /* -------- User-defined Routines --------- */
51: extern PetscErrorCode FormBoundaryConditions(SNES, AppCtx **);
52: extern PetscErrorCode DestroyBoundaryConditions(AppCtx **);
53: extern PetscErrorCode ComputeInitialGuess(SNES, Vec, void *);
54: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void *);
55: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
56: extern PetscErrorCode FormBounds(SNES, Vec, Vec);
58: int main(int argc, char **argv)
59: {
60: Vec x, r; /* solution and residual vectors */
61: SNES snes; /* nonlinear solver context */
62: Mat J; /* Jacobian matrix */
63: DM da;
66: PetscInitialize(&argc, &argv, (char *)0, help);
68: /* Create distributed array to manage the 2d grid */
69: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da);
70: DMSetFromOptions(da);
71: DMSetUp(da);
73: /* Extract global vectors from DMDA; */
74: DMCreateGlobalVector(da, &x);
75: VecDuplicate(x, &r);
77: DMSetMatType(da, MATAIJ);
78: DMCreateMatrix(da, &J);
80: /* Create nonlinear solver context */
81: SNESCreate(PETSC_COMM_WORLD, &snes);
82: SNESSetDM(snes, da);
84: /* Set function evaluation and Jacobian evaluation routines */
85: SNESSetFunction(snes, r, FormGradient, NULL);
86: SNESSetJacobian(snes, J, J, FormJacobian, NULL);
88: SNESSetComputeApplicationContext(snes, (PetscErrorCode(*)(SNES, void **))FormBoundaryConditions, (PetscErrorCode(*)(void **))DestroyBoundaryConditions);
90: SNESSetComputeInitialGuess(snes, ComputeInitialGuess, NULL);
92: SNESVISetComputeVariableBounds(snes, FormBounds);
94: SNESSetFromOptions(snes);
96: /* Solve the application */
97: SNESSolve(snes, NULL, x);
99: /* Free memory */
100: VecDestroy(&x);
101: VecDestroy(&r);
102: MatDestroy(&J);
103: SNESDestroy(&snes);
105: /* Free user-created data structures */
106: DMDestroy(&da);
108: PetscFinalize();
109: return 0;
110: }
112: /* -------------------------------------------------------------------- */
114: /* FormBounds - sets the upper and lower bounds
116: Input Parameters:
117: . snes - the SNES context
119: Output Parameters:
120: . xl - lower bounds
121: . xu - upper bounds
122: */
123: PetscErrorCode FormBounds(SNES snes, Vec xl, Vec xu)
124: {
125: AppCtx *ctx;
128: SNESGetApplicationContext(snes, &ctx);
129: VecSet(xl, ctx->lb);
130: VecSet(xu, ctx->ub);
131: return 0;
132: }
134: /* -------------------------------------------------------------------- */
136: /* FormGradient - Evaluates gradient of f.
138: Input Parameters:
139: . snes - the SNES context
140: . X - input vector
141: . ptr - optional user-defined context, as set by SNESSetFunction()
143: Output Parameters:
144: . G - vector containing the newly evaluated gradient
145: */
146: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
147: {
148: AppCtx *user;
149: PetscInt i, j;
150: PetscInt mx, my;
151: PetscScalar hx, hy, hydhx, hxdhy;
152: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
153: PetscScalar df1dxc, df2dxc, df3dxc, df4dxc, df5dxc, df6dxc;
154: PetscScalar **g, **x;
155: PetscInt xs, xm, ys, ym;
156: Vec localX;
157: DM da;
160: SNESGetDM(snes, &da);
161: SNESGetApplicationContext(snes, &user);
162: 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);
163: hx = 1.0 / (mx + 1);
164: hy = 1.0 / (my + 1);
165: hydhx = hy / hx;
166: hxdhy = hx / hy;
168: VecSet(G, 0.0);
170: /* Get local vector */
171: DMGetLocalVector(da, &localX);
172: /* Get ghost points */
173: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
174: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
175: /* Get pointer to local vector data */
176: DMDAVecGetArray(da, localX, &x);
177: DMDAVecGetArray(da, G, &g);
179: DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
180: /* Compute function over the locally owned part of the mesh */
181: for (j = ys; j < ys + ym; j++) {
182: for (i = xs; i < xs + xm; i++) {
183: xc = x[j][i];
184: xlt = xrb = xl = xr = xb = xt = xc;
186: if (i == 0) { /* left side */
187: xl = user->left[j + 1];
188: xlt = user->left[j + 2];
189: } else xl = x[j][i - 1];
191: if (j == 0) { /* bottom side */
192: xb = user->bottom[i + 1];
193: xrb = user->bottom[i + 2];
194: } else xb = x[j - 1][i];
196: if (i + 1 == mx) { /* right side */
197: xr = user->right[j + 1];
198: xrb = user->right[j];
199: } else xr = x[j][i + 1];
201: if (j + 1 == 0 + my) { /* top side */
202: xt = user->top[i + 1];
203: xlt = user->top[i];
204: } else xt = x[j + 1][i];
206: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1]; /* left top side */
207: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1]; /* right bottom */
209: d1 = (xc - xl);
210: d2 = (xc - xr);
211: d3 = (xc - xt);
212: d4 = (xc - xb);
213: d5 = (xr - xrb);
214: d6 = (xrb - xb);
215: d7 = (xlt - xl);
216: d8 = (xt - xlt);
218: df1dxc = d1 * hydhx;
219: df2dxc = (d1 * hydhx + d4 * hxdhy);
220: df3dxc = d3 * hxdhy;
221: df4dxc = (d2 * hydhx + d3 * hxdhy);
222: df5dxc = d2 * hydhx;
223: df6dxc = d4 * hxdhy;
225: d1 /= hx;
226: d2 /= hx;
227: d3 /= hy;
228: d4 /= hy;
229: d5 /= hy;
230: d6 /= hx;
231: d7 /= hy;
232: d8 /= hx;
234: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
235: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
236: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
237: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
238: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
239: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
241: df1dxc /= f1;
242: df2dxc /= f2;
243: df3dxc /= f3;
244: df4dxc /= f4;
245: df5dxc /= f5;
246: df6dxc /= f6;
248: g[j][i] = (df1dxc + df2dxc + df3dxc + df4dxc + df5dxc + df6dxc) / 2.0;
249: }
250: }
252: /* Restore vectors */
253: DMDAVecRestoreArray(da, localX, &x);
254: DMDAVecRestoreArray(da, G, &g);
255: DMRestoreLocalVector(da, &localX);
256: PetscLogFlops(67.0 * mx * my);
257: return 0;
258: }
260: /* ------------------------------------------------------------------- */
261: /*
262: FormJacobian - Evaluates Jacobian matrix.
264: Input Parameters:
265: . snes - SNES context
266: . X - input vector
267: . ptr - optional user-defined context, as set by SNESSetJacobian()
269: Output Parameters:
270: . tH - Jacobian matrix
272: */
273: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
274: {
275: AppCtx *user;
276: PetscInt i, j, k;
277: PetscInt mx, my;
278: MatStencil row, col[7];
279: PetscScalar hx, hy, hydhx, hxdhy;
280: PetscScalar f1, f2, f3, f4, f5, f6, d1, d2, d3, d4, d5, d6, d7, d8, xc, xl, xr, xt, xb, xlt, xrb;
281: PetscScalar hl, hr, ht, hb, hc, htl, hbr;
282: PetscScalar **x, v[7];
283: PetscBool assembled;
284: PetscInt xs, xm, ys, ym;
285: Vec localX;
286: DM da;
289: SNESGetDM(snes, &da);
290: SNESGetApplicationContext(snes, &user);
291: 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);
292: hx = 1.0 / (mx + 1);
293: hy = 1.0 / (my + 1);
294: hydhx = hy / hx;
295: hxdhy = hx / hy;
297: /* Set various matrix options */
298: MatAssembled(H, &assembled);
299: if (assembled) MatZeroEntries(H);
301: /* Get local vector */
302: DMGetLocalVector(da, &localX);
303: /* Get ghost points */
304: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
305: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
307: /* Get pointers to vector data */
308: DMDAVecGetArray(da, localX, &x);
310: DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
311: /* Compute Jacobian over the locally owned part of the mesh */
312: for (j = ys; j < ys + ym; j++) {
313: for (i = xs; i < xs + xm; i++) {
314: xc = x[j][i];
315: xlt = xrb = xl = xr = xb = xt = xc;
317: /* Left */
318: if (i == 0) {
319: xl = user->left[j + 1];
320: xlt = user->left[j + 2];
321: } else xl = x[j][i - 1];
323: /* Bottom */
324: if (j == 0) {
325: xb = user->bottom[i + 1];
326: xrb = user->bottom[i + 2];
327: } else xb = x[j - 1][i];
329: /* Right */
330: if (i + 1 == mx) {
331: xr = user->right[j + 1];
332: xrb = user->right[j];
333: } else xr = x[j][i + 1];
335: /* Top */
336: if (j + 1 == my) {
337: xt = user->top[i + 1];
338: xlt = user->top[i];
339: } else xt = x[j + 1][i];
341: /* Top left */
342: if (i > 0 && j + 1 < my) xlt = x[j + 1][i - 1];
344: /* Bottom right */
345: if (j > 0 && i + 1 < mx) xrb = x[j - 1][i + 1];
347: d1 = (xc - xl) / hx;
348: d2 = (xc - xr) / hx;
349: d3 = (xc - xt) / hy;
350: d4 = (xc - xb) / hy;
351: d5 = (xrb - xr) / hy;
352: d6 = (xrb - xb) / hx;
353: d7 = (xlt - xl) / hy;
354: d8 = (xlt - xt) / hx;
356: f1 = PetscSqrtScalar(1.0 + d1 * d1 + d7 * d7);
357: f2 = PetscSqrtScalar(1.0 + d1 * d1 + d4 * d4);
358: f3 = PetscSqrtScalar(1.0 + d3 * d3 + d8 * d8);
359: f4 = PetscSqrtScalar(1.0 + d3 * d3 + d2 * d2);
360: f5 = PetscSqrtScalar(1.0 + d2 * d2 + d5 * d5);
361: f6 = PetscSqrtScalar(1.0 + d4 * d4 + d6 * d6);
363: hl = (-hydhx * (1.0 + d7 * d7) + d1 * d7) / (f1 * f1 * f1) + (-hydhx * (1.0 + d4 * d4) + d1 * d4) / (f2 * f2 * f2);
364: hr = (-hydhx * (1.0 + d5 * d5) + d2 * d5) / (f5 * f5 * f5) + (-hydhx * (1.0 + d3 * d3) + d2 * d3) / (f4 * f4 * f4);
365: ht = (-hxdhy * (1.0 + d8 * d8) + d3 * d8) / (f3 * f3 * f3) + (-hxdhy * (1.0 + d2 * d2) + d2 * d3) / (f4 * f4 * f4);
366: hb = (-hxdhy * (1.0 + d6 * d6) + d4 * d6) / (f6 * f6 * f6) + (-hxdhy * (1.0 + d1 * d1) + d1 * d4) / (f2 * f2 * f2);
368: hbr = -d2 * d5 / (f5 * f5 * f5) - d4 * d6 / (f6 * f6 * f6);
369: htl = -d1 * d7 / (f1 * f1 * f1) - d3 * d8 / (f3 * f3 * f3);
371: 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);
373: hl /= 2.0;
374: hr /= 2.0;
375: ht /= 2.0;
376: hb /= 2.0;
377: hbr /= 2.0;
378: htl /= 2.0;
379: hc /= 2.0;
381: k = 0;
382: row.i = i;
383: row.j = j;
384: /* Bottom */
385: if (j > 0) {
386: v[k] = hb;
387: col[k].i = i;
388: col[k].j = j - 1;
389: k++;
390: }
392: /* Bottom right */
393: if (j > 0 && i < mx - 1) {
394: v[k] = hbr;
395: col[k].i = i + 1;
396: col[k].j = j - 1;
397: k++;
398: }
400: /* left */
401: if (i > 0) {
402: v[k] = hl;
403: col[k].i = i - 1;
404: col[k].j = j;
405: k++;
406: }
408: /* Centre */
409: v[k] = hc;
410: col[k].i = row.i;
411: col[k].j = row.j;
412: k++;
414: /* Right */
415: if (i < mx - 1) {
416: v[k] = hr;
417: col[k].i = i + 1;
418: col[k].j = j;
419: k++;
420: }
422: /* Top left */
423: if (i > 0 && j < my - 1) {
424: v[k] = htl;
425: col[k].i = i - 1;
426: col[k].j = j + 1;
427: k++;
428: }
430: /* Top */
431: if (j < my - 1) {
432: v[k] = ht;
433: col[k].i = i;
434: col[k].j = j + 1;
435: k++;
436: }
438: MatSetValuesStencil(H, 1, &row, k, col, v, INSERT_VALUES);
439: }
440: }
442: /* Assemble the matrix */
443: MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);
444: DMDAVecRestoreArray(da, localX, &x);
445: MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);
446: DMRestoreLocalVector(da, &localX);
448: PetscLogFlops(199.0 * mx * my);
449: return 0;
450: }
452: /* ------------------------------------------------------------------- */
453: /*
454: FormBoundaryConditions - Calculates the boundary conditions for
455: the region.
457: Input Parameter:
458: . user - user-defined application context
460: Output Parameter:
461: . user - user-defined application context
462: */
463: PetscErrorCode FormBoundaryConditions(SNES snes, AppCtx **ouser)
464: {
465: PetscInt i, j, k, limit = 0, maxits = 5;
466: PetscInt mx, my;
467: PetscInt bsize = 0, lsize = 0, tsize = 0, rsize = 0;
468: PetscScalar one = 1.0, two = 2.0, three = 3.0;
469: PetscScalar det, hx, hy, xt = 0, yt = 0;
470: PetscReal fnorm, tol = 1e-10;
471: PetscScalar u1, u2, nf1, nf2, njac11, njac12, njac21, njac22;
472: PetscScalar b = -0.5, t = 0.5, l = -0.5, r = 0.5;
473: PetscScalar *boundary;
474: AppCtx *user;
475: DM da;
478: SNESGetDM(snes, &da);
479: PetscNew(&user);
480: *ouser = user;
481: user->lb = .05;
482: user->ub = PETSC_INFINITY;
483: 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);
485: /* Check if lower and upper bounds are set */
486: PetscOptionsGetScalar(NULL, NULL, "-lb", &user->lb, 0);
487: PetscOptionsGetScalar(NULL, NULL, "-ub", &user->ub, 0);
488: bsize = mx + 2;
489: lsize = my + 2;
490: rsize = my + 2;
491: tsize = mx + 2;
493: PetscMalloc1(bsize, &user->bottom);
494: PetscMalloc1(tsize, &user->top);
495: PetscMalloc1(lsize, &user->left);
496: PetscMalloc1(rsize, &user->right);
498: hx = (r - l) / (mx + 1.0);
499: hy = (t - b) / (my + 1.0);
501: for (j = 0; j < 4; j++) {
502: if (j == 0) {
503: yt = b;
504: xt = l;
505: limit = bsize;
506: boundary = user->bottom;
507: } else if (j == 1) {
508: yt = t;
509: xt = l;
510: limit = tsize;
511: boundary = user->top;
512: } else if (j == 2) {
513: yt = b;
514: xt = l;
515: limit = lsize;
516: boundary = user->left;
517: } else { /* if (j==3) */
518: yt = b;
519: xt = r;
520: limit = rsize;
521: boundary = user->right;
522: }
524: for (i = 0; i < limit; i++) {
525: u1 = xt;
526: u2 = -yt;
527: for (k = 0; k < maxits; k++) {
528: nf1 = u1 + u1 * u2 * u2 - u1 * u1 * u1 / three - xt;
529: nf2 = -u2 - u1 * u1 * u2 + u2 * u2 * u2 / three - yt;
530: fnorm = PetscRealPart(PetscSqrtScalar(nf1 * nf1 + nf2 * nf2));
531: if (fnorm <= tol) break;
532: njac11 = one + u2 * u2 - u1 * u1;
533: njac12 = two * u1 * u2;
534: njac21 = -two * u1 * u2;
535: njac22 = -one - u1 * u1 + u2 * u2;
536: det = njac11 * njac22 - njac21 * njac12;
537: u1 = u1 - (njac22 * nf1 - njac12 * nf2) / det;
538: u2 = u2 - (njac11 * nf2 - njac21 * nf1) / det;
539: }
541: boundary[i] = u1 * u1 - u2 * u2;
542: if (j == 0 || j == 1) xt = xt + hx;
543: else yt = yt + hy; /* if (j==2 || j==3) */
544: }
545: }
546: return 0;
547: }
549: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
550: {
551: AppCtx *user = *ouser;
554: PetscFree(user->bottom);
555: PetscFree(user->top);
556: PetscFree(user->left);
557: PetscFree(user->right);
558: PetscFree(*ouser);
559: return 0;
560: }
562: /* ------------------------------------------------------------------- */
563: /*
564: ComputeInitialGuess - Calculates the initial guess
566: Input Parameters:
567: . user - user-defined application context
568: . X - vector for initial guess
570: Output Parameters:
571: . X - newly computed initial guess
572: */
573: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X, void *dummy)
574: {
575: PetscInt i, j, mx, my;
576: DM da;
577: AppCtx *user;
578: PetscScalar **x;
579: PetscInt xs, xm, ys, ym;
582: SNESGetDM(snes, &da);
583: SNESGetApplicationContext(snes, &user);
585: DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
586: 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);
588: /* Get pointers to vector data */
589: DMDAVecGetArray(da, X, &x);
590: /* Perform local computations */
591: for (j = ys; j < ys + ym; j++) {
592: 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;
593: }
594: /* Restore vectors */
595: DMDAVecRestoreArray(da, X, &x);
596: return 0;
597: }
599: /*TEST
601: test:
602: 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
603: requires: !single
605: test:
606: suffix: 2
607: 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
608: requires: !single
610: TEST*/