Actual source code: ex19.c

  1: /* Portions of this code are under:
  2:    Copyright (C) 2022 Advanced Micro Devices, Inc. All rights reserved.
  3: */
  4: static char help[] = "Nonlinear driven cavity with multigrid in 2d.\n \
  5:   \n\
  6: The 2D driven cavity problem is solved in a velocity-vorticity formulation.\n\
  7: The flow can be driven with the lid or with bouyancy or both:\n\
  8:   -lidvelocity &ltlid&gt, where &ltlid&gt = dimensionless velocity of lid\n\
  9:   -grashof &ltgr&gt, where &ltgr&gt = dimensionless temperature gradent\n\
 10:   -prandtl &ltpr&gt, where &ltpr&gt = dimensionless thermal/momentum diffusity ratio\n\
 11:  -contours : draw contour plots of solution\n\n";
 12: /* in HTML, '&lt' = '<' and '&gt' = '>' */

 14: /*
 15:       See src/ksp/ksp/tutorials/ex45.c
 16: */

 18: /*F-----------------------------------------------------------------------

 20:     We thank David E. Keyes for contributing the driven cavity discretization within this example code.

 22:     This problem is modeled by the partial differential equation system

 24: \begin{eqnarray}
 25:         - \triangle U - \nabla_y \Omega & = & 0  \\
 26:         - \triangle V + \nabla_x\Omega & = & 0  \\
 27:         - \triangle \Omega + \nabla \cdot ([U*\Omega,V*\Omega]) - GR* \nabla_x T & = & 0  \\
 28:         - \triangle T + PR* \nabla \cdot ([U*T,V*T]) & = & 0
 29: \end{eqnarray}

 31:     in the unit square, which is uniformly discretized in each of x and y in this simple encoding.

 33:     No-slip, rigid-wall Dirichlet conditions are used for $ [U,V]$.
 34:     Dirichlet conditions are used for Omega, based on the definition of
 35:     vorticity: $ \Omega = - \nabla_y U + \nabla_x V$, where along each
 36:     constant coordinate boundary, the tangential derivative is zero.
 37:     Dirichlet conditions are used for T on the left and right walls,
 38:     and insulation homogeneous Neumann conditions are used for T on
 39:     the top and bottom walls.

 41:     A finite difference approximation with the usual 5-point stencil
 42:     is used to discretize the boundary value problem to obtain a
 43:     nonlinear system of equations.  Upwinding is used for the divergence
 44:     (convective) terms and central for the gradient (source) terms.

 46:     The Jacobian can be either
 47:       * formed via finite differencing using coloring (the default), or
 48:       * applied matrix-free via the option -snes_mf
 49:         (for larger grid problems this variant may not converge
 50:         without a preconditioner due to ill-conditioning).

 52:   ------------------------------------------------------------------------F*/

 54: /*
 55:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
 56:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
 57:    file automatically includes:
 58:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 59:      petscmat.h - matrices
 60:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 61:      petscviewer.h - viewers               petscpc.h  - preconditioners
 62:      petscksp.h   - linear solvers
 63: */
 64: #if defined(PETSC_APPLE_FRAMEWORK)
 65:   #import <PETSc/petscsnes.h>
 66:   #import <PETSc/petscdmda.h>
 67: #else
 68: #include <petscsnes.h>
 69: #include <petscdm.h>
 70: #include <petscdmda.h>
 71: #endif

 73: /*
 74:    User-defined routines and data structures
 75: */
 76: typedef struct {
 77:   PetscScalar u, v, omega, temp;
 78: } Field;

 80: PetscErrorCode FormFunctionLocal(DMDALocalInfo *, Field **, Field **, void *);

 82: typedef struct {
 83:   PetscReal lidvelocity, prandtl, grashof; /* physical parameters */
 84:   PetscBool draw_contours;                 /* flag - 1 indicates drawing contours */
 85: } AppCtx;

 87: extern PetscErrorCode FormInitialGuess(AppCtx *, DM, Vec);
 88: extern PetscErrorCode NonlinearGS(SNES, Vec, Vec, void *);

 90: int main(int argc, char **argv)
 91: {
 92:   AppCtx   user; /* user-defined work context */
 93:   PetscInt mx, my, its;
 94:   MPI_Comm comm;
 95:   SNES     snes;
 96:   DM       da;
 97:   Vec      x;

100:   PetscInitialize(&argc, &argv, (char *)0, help);
101:   comm = PETSC_COMM_WORLD;
102:   SNESCreate(comm, &snes);

104:   /*
105:       Create distributed array object to manage parallel grid and vectors
106:       for principal unknowns (x) and governing residuals (f)
107:   */
108:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 4, 1, 0, 0, &da);
109:   DMSetFromOptions(da);
110:   DMSetUp(da);
111:   SNESSetDM(snes, (DM)da);
112:   SNESSetNGS(snes, NonlinearGS, (void *)&user);

114:   DMDAGetInfo(da, 0, &mx, &my, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE);
115:   /*
116:      Problem parameters (velocity of lid, prandtl, and grashof numbers)
117:   */
118:   user.lidvelocity = 1.0 / (mx * my);
119:   user.prandtl     = 1.0;
120:   user.grashof     = 1.0;

122:   PetscOptionsGetReal(NULL, NULL, "-lidvelocity", &user.lidvelocity, NULL);
123:   PetscOptionsGetReal(NULL, NULL, "-prandtl", &user.prandtl, NULL);
124:   PetscOptionsGetReal(NULL, NULL, "-grashof", &user.grashof, NULL);
125:   PetscOptionsHasName(NULL, NULL, "-contours", &user.draw_contours);

127:   DMDASetFieldName(da, 0, "x_velocity");
128:   DMDASetFieldName(da, 1, "y_velocity");
129:   DMDASetFieldName(da, 2, "Omega");
130:   DMDASetFieldName(da, 3, "temperature");

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:      Create user context, set problem data, create vector data structures.
134:      Also, compute the initial guess.
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138:      Create nonlinear solver context

140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141:   DMSetApplicationContext(da, &user);
142:   DMDASNESSetFunctionLocal(da, INSERT_VALUES, (PetscErrorCode(*)(DMDALocalInfo *, void *, void *, void *))FormFunctionLocal, &user);
143:   SNESSetFromOptions(snes);
144:   PetscPrintf(comm, "lid velocity = %g, prandtl # = %g, grashof # = %g\n", (double)user.lidvelocity, (double)user.prandtl, (double)user.grashof);

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Solve the nonlinear system
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   DMCreateGlobalVector(da, &x);
150:   FormInitialGuess(&user, da, x);

152:   SNESSolve(snes, NULL, x);

154:   SNESGetIterationNumber(snes, &its);
155:   PetscPrintf(comm, "Number of SNES iterations = %" PetscInt_FMT "\n", its);

157:   /*
158:      Visualize solution
159:   */
160:   if (user.draw_contours) VecView(x, PETSC_VIEWER_DRAW_WORLD);

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:      Free work space.  All PETSc objects should be destroyed when they
164:      are no longer needed.
165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166:   VecDestroy(&x);
167:   DMDestroy(&da);
168:   SNESDestroy(&snes);
169:   PetscFinalize();
170:   return 0;
171: }

173: /* ------------------------------------------------------------------- */

175: /*
176:    FormInitialGuess - Forms initial approximation.

178:    Input Parameters:
179:    user - user-defined application context
180:    X - vector

182:    Output Parameter:
183:    X - vector
184: */
185: PetscErrorCode FormInitialGuess(AppCtx *user, DM da, Vec X)
186: {
187:   PetscInt  i, j, mx, xs, ys, xm, ym;
188:   PetscReal grashof, dx;
189:   Field   **x;

192:   grashof = user->grashof;

194:   DMDAGetInfo(da, 0, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
195:   dx = 1.0 / (mx - 1);

197:   /*
198:      Get local grid boundaries (for 2-dimensional DMDA):
199:        xs, ys   - starting grid indices (no ghost points)
200:        xm, ym   - widths of local grid (no ghost points)
201:   */
202:   DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);

204:   /*
205:      Get a pointer to vector data.
206:        - For default PETSc vectors, VecGetArray() returns a pointer to
207:          the data array.  Otherwise, the routine is implementation dependent.
208:        - You MUST call VecRestoreArray() when you no longer need access to
209:          the array.
210:   */
211:   DMDAVecGetArrayWrite(da, X, &x);

213:   /*
214:      Compute initial guess over the locally owned part of the grid
215:      Initial condition is motionless fluid and equilibrium temperature
216:   */
217:   for (j = ys; j < ys + ym; j++) {
218:     for (i = xs; i < xs + xm; i++) {
219:       x[j][i].u     = 0.0;
220:       x[j][i].v     = 0.0;
221:       x[j][i].omega = 0.0;
222:       x[j][i].temp  = (grashof > 0) * i * dx;
223:     }
224:   }

226:   /*
227:      Restore vector
228:   */
229:   DMDAVecRestoreArrayWrite(da, X, &x);
230:   return 0;
231: }

233: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, Field **x, Field **f, void *ptr)
234: {
235:   AppCtx     *user = (AppCtx *)ptr;
236:   PetscInt    xints, xinte, yints, yinte, i, j;
237:   PetscReal   hx, hy, dhx, dhy, hxdhy, hydhx;
238:   PetscReal   grashof, prandtl, lid;
239:   PetscScalar u, uxx, uyy, vx, vy, avx, avy, vxp, vxm, vyp, vym;

242:   grashof = user->grashof;
243:   prandtl = user->prandtl;
244:   lid     = user->lidvelocity;

246:   /*
247:      Define mesh intervals ratios for uniform grid.

249:      Note: FD formulae below are normalized by multiplying through by
250:      local volume element (i.e. hx*hy) to obtain coefficients O(1) in two dimensions.

252:   */
253:   dhx   = (PetscReal)(info->mx - 1);
254:   dhy   = (PetscReal)(info->my - 1);
255:   hx    = 1.0 / dhx;
256:   hy    = 1.0 / dhy;
257:   hxdhy = hx * dhy;
258:   hydhx = hy * dhx;

260:   xints = info->xs;
261:   xinte = info->xs + info->xm;
262:   yints = info->ys;
263:   yinte = info->ys + info->ym;

265:   /* Test whether we are on the bottom edge of the global array */
266:   if (yints == 0) {
267:     j     = 0;
268:     yints = yints + 1;
269:     /* bottom edge */
270:     for (i = info->xs; i < info->xs + info->xm; i++) {
271:       f[j][i].u     = x[j][i].u;
272:       f[j][i].v     = x[j][i].v;
273:       f[j][i].omega = x[j][i].omega + (x[j + 1][i].u - x[j][i].u) * dhy;
274:       f[j][i].temp  = x[j][i].temp - x[j + 1][i].temp;
275:     }
276:   }

278:   /* Test whether we are on the top edge of the global array */
279:   if (yinte == info->my) {
280:     j     = info->my - 1;
281:     yinte = yinte - 1;
282:     /* top edge */
283:     for (i = info->xs; i < info->xs + info->xm; i++) {
284:       f[j][i].u     = x[j][i].u - lid;
285:       f[j][i].v     = x[j][i].v;
286:       f[j][i].omega = x[j][i].omega + (x[j][i].u - x[j - 1][i].u) * dhy;
287:       f[j][i].temp  = x[j][i].temp - x[j - 1][i].temp;
288:     }
289:   }

291:   /* Test whether we are on the left edge of the global array */
292:   if (xints == 0) {
293:     i     = 0;
294:     xints = xints + 1;
295:     /* left edge */
296:     for (j = info->ys; j < info->ys + info->ym; j++) {
297:       f[j][i].u     = x[j][i].u;
298:       f[j][i].v     = x[j][i].v;
299:       f[j][i].omega = x[j][i].omega - (x[j][i + 1].v - x[j][i].v) * dhx;
300:       f[j][i].temp  = x[j][i].temp;
301:     }
302:   }

304:   /* Test whether we are on the right edge of the global array */
305:   if (xinte == info->mx) {
306:     i     = info->mx - 1;
307:     xinte = xinte - 1;
308:     /* right edge */
309:     for (j = info->ys; j < info->ys + info->ym; j++) {
310:       f[j][i].u     = x[j][i].u;
311:       f[j][i].v     = x[j][i].v;
312:       f[j][i].omega = x[j][i].omega - (x[j][i].v - x[j][i - 1].v) * dhx;
313:       f[j][i].temp  = x[j][i].temp - (PetscReal)(grashof > 0);
314:     }
315:   }

317:   /* Compute over the interior points */
318:   for (j = yints; j < yinte; j++) {
319:     for (i = xints; i < xinte; i++) {
320:       /*
321:        convective coefficients for upwinding
322:       */
323:       vx  = x[j][i].u;
324:       avx = PetscAbsScalar(vx);
325:       vxp = .5 * (vx + avx);
326:       vxm = .5 * (vx - avx);
327:       vy  = x[j][i].v;
328:       avy = PetscAbsScalar(vy);
329:       vyp = .5 * (vy + avy);
330:       vym = .5 * (vy - avy);

332:       /* U velocity */
333:       u         = x[j][i].u;
334:       uxx       = (2.0 * u - x[j][i - 1].u - x[j][i + 1].u) * hydhx;
335:       uyy       = (2.0 * u - x[j - 1][i].u - x[j + 1][i].u) * hxdhy;
336:       f[j][i].u = uxx + uyy - .5 * (x[j + 1][i].omega - x[j - 1][i].omega) * hx;

338:       /* V velocity */
339:       u         = x[j][i].v;
340:       uxx       = (2.0 * u - x[j][i - 1].v - x[j][i + 1].v) * hydhx;
341:       uyy       = (2.0 * u - x[j - 1][i].v - x[j + 1][i].v) * hxdhy;
342:       f[j][i].v = uxx + uyy + .5 * (x[j][i + 1].omega - x[j][i - 1].omega) * hy;

344:       /* Omega */
345:       u             = x[j][i].omega;
346:       uxx           = (2.0 * u - x[j][i - 1].omega - x[j][i + 1].omega) * hydhx;
347:       uyy           = (2.0 * u - x[j - 1][i].omega - x[j + 1][i].omega) * hxdhy;
348:       f[j][i].omega = uxx + uyy + (vxp * (u - x[j][i - 1].omega) + vxm * (x[j][i + 1].omega - u)) * hy + (vyp * (u - x[j - 1][i].omega) + vym * (x[j + 1][i].omega - u)) * hx - .5 * grashof * (x[j][i + 1].temp - x[j][i - 1].temp) * hy;

350:       /* Temperature */
351:       u            = x[j][i].temp;
352:       uxx          = (2.0 * u - x[j][i - 1].temp - x[j][i + 1].temp) * hydhx;
353:       uyy          = (2.0 * u - x[j - 1][i].temp - x[j + 1][i].temp) * hxdhy;
354:       f[j][i].temp = uxx + uyy + prandtl * ((vxp * (u - x[j][i - 1].temp) + vxm * (x[j][i + 1].temp - u)) * hy + (vyp * (u - x[j - 1][i].temp) + vym * (x[j + 1][i].temp - u)) * hx);
355:     }
356:   }

358:   /*
359:      Flop count (multiply-adds are counted as 2 operations)
360:   */
361:   PetscLogFlops(84.0 * info->ym * info->xm);
362:   return 0;
363: }

365: /*
366:     Performs sweeps of point block nonlinear Gauss-Seidel on all the local grid points
367: */
368: PetscErrorCode NonlinearGS(SNES snes, Vec X, Vec B, void *ctx)
369: {
370:   DMDALocalInfo info;
371:   Field       **x, **b;
372:   Vec           localX, localB;
373:   DM            da;
374:   PetscInt      xints, xinte, yints, yinte, i, j, k, l;
375:   PetscInt      max_its, tot_its;
376:   PetscInt      sweeps;
377:   PetscReal     rtol, atol, stol;
378:   PetscReal     hx, hy, dhx, dhy, hxdhy, hydhx;
379:   PetscReal     grashof, prandtl, lid;
380:   PetscScalar   u, uxx, uyy, vx, vy, avx, avy, vxp, vxm, vyp, vym;
381:   PetscScalar   fu, fv, fomega, ftemp;
382:   PetscScalar   dfudu;
383:   PetscScalar   dfvdv;
384:   PetscScalar   dfodu, dfodv, dfodo;
385:   PetscScalar   dftdu, dftdv, dftdt;
386:   PetscScalar   yu = 0, yv = 0, yo = 0, yt = 0;
387:   PetscScalar   bjiu, bjiv, bjiomega, bjitemp;
388:   PetscBool     ptconverged;
389:   PetscReal     pfnorm, pfnorm0, pynorm, pxnorm;
390:   AppCtx       *user = (AppCtx *)ctx;

393:   grashof = user->grashof;
394:   prandtl = user->prandtl;
395:   lid     = user->lidvelocity;
396:   tot_its = 0;
397:   SNESNGSGetTolerances(snes, &rtol, &atol, &stol, &max_its);
398:   SNESNGSGetSweeps(snes, &sweeps);
399:   SNESGetDM(snes, (DM *)&da);
400:   DMGetLocalVector(da, &localX);
401:   if (B) DMGetLocalVector(da, &localB);
402:   /*
403:      Scatter ghost points to local vector, using the 2-step process
404:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
405:   */
406:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
407:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
408:   if (B) {
409:     DMGlobalToLocalBegin(da, B, INSERT_VALUES, localB);
410:     DMGlobalToLocalEnd(da, B, INSERT_VALUES, localB);
411:   }
412:   DMDAGetLocalInfo(da, &info);
413:   DMDAVecGetArrayWrite(da, localX, &x);
414:   if (B) DMDAVecGetArrayRead(da, localB, &b);
415:   /* looks like a combination of the formfunction / formjacobian routines */
416:   dhx   = (PetscReal)(info.mx - 1);
417:   dhy   = (PetscReal)(info.my - 1);
418:   hx    = 1.0 / dhx;
419:   hy    = 1.0 / dhy;
420:   hxdhy = hx * dhy;
421:   hydhx = hy * dhx;

423:   xints = info.xs;
424:   xinte = info.xs + info.xm;
425:   yints = info.ys;
426:   yinte = info.ys + info.ym;

428:   /* Set the boundary conditions on the momentum equations */
429:   /* Test whether we are on the bottom edge of the global array */
430:   if (yints == 0) {
431:     j = 0;
432:     /* bottom edge */
433:     for (i = info.xs; i < info.xs + info.xm; i++) {
434:       if (B) {
435:         bjiu = b[j][i].u;
436:         bjiv = b[j][i].v;
437:       } else {
438:         bjiu = 0.0;
439:         bjiv = 0.0;
440:       }
441:       x[j][i].u = 0.0 + bjiu;
442:       x[j][i].v = 0.0 + bjiv;
443:     }
444:   }

446:   /* Test whether we are on the top edge of the global array */
447:   if (yinte == info.my) {
448:     j = info.my - 1;
449:     /* top edge */
450:     for (i = info.xs; i < info.xs + info.xm; i++) {
451:       if (B) {
452:         bjiu = b[j][i].u;
453:         bjiv = b[j][i].v;
454:       } else {
455:         bjiu = 0.0;
456:         bjiv = 0.0;
457:       }
458:       x[j][i].u = lid + bjiu;
459:       x[j][i].v = bjiv;
460:     }
461:   }

463:   /* Test whether we are on the left edge of the global array */
464:   if (xints == 0) {
465:     i = 0;
466:     /* left edge */
467:     for (j = info.ys; j < info.ys + info.ym; j++) {
468:       if (B) {
469:         bjiu = b[j][i].u;
470:         bjiv = b[j][i].v;
471:       } else {
472:         bjiu = 0.0;
473:         bjiv = 0.0;
474:       }
475:       x[j][i].u = 0.0 + bjiu;
476:       x[j][i].v = 0.0 + bjiv;
477:     }
478:   }

480:   /* Test whether we are on the right edge of the global array */
481:   if (xinte == info.mx) {
482:     i = info.mx - 1;
483:     /* right edge */
484:     for (j = info.ys; j < info.ys + info.ym; j++) {
485:       if (B) {
486:         bjiu = b[j][i].u;
487:         bjiv = b[j][i].v;
488:       } else {
489:         bjiu = 0.0;
490:         bjiv = 0.0;
491:       }
492:       x[j][i].u = 0.0 + bjiu;
493:       x[j][i].v = 0.0 + bjiv;
494:     }
495:   }

497:   for (k = 0; k < sweeps; k++) {
498:     for (j = info.ys; j < info.ys + info.ym; j++) {
499:       for (i = info.xs; i < info.xs + info.xm; i++) {
500:         ptconverged = PETSC_FALSE;
501:         pfnorm0     = 0.0;
502:         fu          = 0.0;
503:         fv          = 0.0;
504:         fomega      = 0.0;
505:         ftemp       = 0.0;
506:         /*  Run Newton's method on a single grid point */
507:         for (l = 0; l < max_its && !ptconverged; l++) {
508:           if (B) {
509:             bjiu     = b[j][i].u;
510:             bjiv     = b[j][i].v;
511:             bjiomega = b[j][i].omega;
512:             bjitemp  = b[j][i].temp;
513:           } else {
514:             bjiu     = 0.0;
515:             bjiv     = 0.0;
516:             bjiomega = 0.0;
517:             bjitemp  = 0.0;
518:           }

520:           if (i != 0 && i != info.mx - 1 && j != 0 && j != info.my - 1) {
521:             /* U velocity */
522:             u     = x[j][i].u;
523:             uxx   = (2.0 * u - x[j][i - 1].u - x[j][i + 1].u) * hydhx;
524:             uyy   = (2.0 * u - x[j - 1][i].u - x[j + 1][i].u) * hxdhy;
525:             fu    = uxx + uyy - .5 * (x[j + 1][i].omega - x[j - 1][i].omega) * hx - bjiu;
526:             dfudu = 2.0 * (hydhx + hxdhy);
527:             /* V velocity */
528:             u     = x[j][i].v;
529:             uxx   = (2.0 * u - x[j][i - 1].v - x[j][i + 1].v) * hydhx;
530:             uyy   = (2.0 * u - x[j - 1][i].v - x[j + 1][i].v) * hxdhy;
531:             fv    = uxx + uyy + .5 * (x[j][i + 1].omega - x[j][i - 1].omega) * hy - bjiv;
532:             dfvdv = 2.0 * (hydhx + hxdhy);
533:             /*
534:              convective coefficients for upwinding
535:              */
536:             vx  = x[j][i].u;
537:             avx = PetscAbsScalar(vx);
538:             vxp = .5 * (vx + avx);
539:             vxm = .5 * (vx - avx);
540:             vy  = x[j][i].v;
541:             avy = PetscAbsScalar(vy);
542:             vyp = .5 * (vy + avy);
543:             vym = .5 * (vy - avy);
544:             /* Omega */
545:             u      = x[j][i].omega;
546:             uxx    = (2.0 * u - x[j][i - 1].omega - x[j][i + 1].omega) * hydhx;
547:             uyy    = (2.0 * u - x[j - 1][i].omega - x[j + 1][i].omega) * hxdhy;
548:             fomega = uxx + uyy + (vxp * (u - x[j][i - 1].omega) + vxm * (x[j][i + 1].omega - u)) * hy + (vyp * (u - x[j - 1][i].omega) + vym * (x[j + 1][i].omega - u)) * hx - .5 * grashof * (x[j][i + 1].temp - x[j][i - 1].temp) * hy - bjiomega;
549:             /* convective coefficient derivatives */
550:             dfodo = 2.0 * (hydhx + hxdhy) + ((vxp - vxm) * hy + (vyp - vym) * hx);
551:             if (PetscRealPart(vx) > 0.0) dfodu = (u - x[j][i - 1].omega) * hy;
552:             else dfodu = (x[j][i + 1].omega - u) * hy;

554:             if (PetscRealPart(vy) > 0.0) dfodv = (u - x[j - 1][i].omega) * hx;
555:             else dfodv = (x[j + 1][i].omega - u) * hx;

557:             /* Temperature */
558:             u     = x[j][i].temp;
559:             uxx   = (2.0 * u - x[j][i - 1].temp - x[j][i + 1].temp) * hydhx;
560:             uyy   = (2.0 * u - x[j - 1][i].temp - x[j + 1][i].temp) * hxdhy;
561:             ftemp = uxx + uyy + prandtl * ((vxp * (u - x[j][i - 1].temp) + vxm * (x[j][i + 1].temp - u)) * hy + (vyp * (u - x[j - 1][i].temp) + vym * (x[j + 1][i].temp - u)) * hx) - bjitemp;
562:             dftdt = 2.0 * (hydhx + hxdhy) + prandtl * ((vxp - vxm) * hy + (vyp - vym) * hx);
563:             if (PetscRealPart(vx) > 0.0) dftdu = prandtl * (u - x[j][i - 1].temp) * hy;
564:             else dftdu = prandtl * (x[j][i + 1].temp - u) * hy;

566:             if (PetscRealPart(vy) > 0.0) dftdv = prandtl * (u - x[j - 1][i].temp) * hx;
567:             else dftdv = prandtl * (x[j + 1][i].temp - u) * hx;

569:             /* invert the system:
570:              [ dfu / du     0        0        0    ][yu] = [fu]
571:              [     0    dfv / dv     0        0    ][yv]   [fv]
572:              [ dfo / du dfo / dv dfo / do     0    ][yo]   [fo]
573:              [ dft / du dft / dv     0    dft / dt ][yt]   [ft]
574:              by simple back-substitution
575:            */
576:             yu = fu / dfudu;
577:             yv = fv / dfvdv;
578:             yo = (fomega - (dfodu * yu + dfodv * yv)) / dfodo;
579:             yt = (ftemp - (dftdu * yu + dftdv * yv)) / dftdt;

581:             x[j][i].u     = x[j][i].u - yu;
582:             x[j][i].v     = x[j][i].v - yv;
583:             x[j][i].temp  = x[j][i].temp - yt;
584:             x[j][i].omega = x[j][i].omega - yo;
585:           }
586:           if (i == 0) {
587:             fomega        = x[j][i].omega - (x[j][i + 1].v - x[j][i].v) * dhx - bjiomega;
588:             ftemp         = x[j][i].temp - bjitemp;
589:             yo            = fomega;
590:             yt            = ftemp;
591:             x[j][i].omega = x[j][i].omega - fomega;
592:             x[j][i].temp  = x[j][i].temp - ftemp;
593:           }
594:           if (i == info.mx - 1) {
595:             fomega        = x[j][i].omega - (x[j][i].v - x[j][i - 1].v) * dhx - bjiomega;
596:             ftemp         = x[j][i].temp - (PetscReal)(grashof > 0) - bjitemp;
597:             yo            = fomega;
598:             yt            = ftemp;
599:             x[j][i].omega = x[j][i].omega - fomega;
600:             x[j][i].temp  = x[j][i].temp - ftemp;
601:           }
602:           if (j == 0) {
603:             fomega        = x[j][i].omega + (x[j + 1][i].u - x[j][i].u) * dhy - bjiomega;
604:             ftemp         = x[j][i].temp - x[j + 1][i].temp - bjitemp;
605:             yo            = fomega;
606:             yt            = ftemp;
607:             x[j][i].omega = x[j][i].omega - fomega;
608:             x[j][i].temp  = x[j][i].temp - ftemp;
609:           }
610:           if (j == info.my - 1) {
611:             fomega        = x[j][i].omega + (x[j][i].u - x[j - 1][i].u) * dhy - bjiomega;
612:             ftemp         = x[j][i].temp - x[j - 1][i].temp - bjitemp;
613:             yo            = fomega;
614:             yt            = ftemp;
615:             x[j][i].omega = x[j][i].omega - fomega;
616:             x[j][i].temp  = x[j][i].temp - ftemp;
617:           }
618:           tot_its++;
619:           pfnorm = PetscRealPart(fu * fu + fv * fv + fomega * fomega + ftemp * ftemp);
620:           pfnorm = PetscSqrtReal(pfnorm);
621:           pynorm = PetscRealPart(yu * yu + yv * yv + yo * yo + yt * yt);
622:           pynorm = PetscSqrtReal(pynorm);
623:           pxnorm = PetscRealPart(x[j][i].u * x[j][i].u + x[j][i].v * x[j][i].v + x[j][i].omega * x[j][i].omega + x[j][i].temp * x[j][i].temp);
624:           pxnorm = PetscSqrtReal(pxnorm);
625:           if (l == 0) pfnorm0 = pfnorm;
626:           if (rtol * pfnorm0 > pfnorm || atol > pfnorm || pxnorm * stol > pynorm) ptconverged = PETSC_TRUE;
627:         }
628:       }
629:     }
630:   }
631:   DMDAVecRestoreArrayWrite(da, localX, &x);
632:   if (B) DMDAVecRestoreArrayRead(da, localB, &b);
633:   DMLocalToGlobalBegin(da, localX, INSERT_VALUES, X);
634:   DMLocalToGlobalEnd(da, localX, INSERT_VALUES, X);
635:   PetscLogFlops(tot_its * (84.0 + 41.0 + 26.0));
636:   DMRestoreLocalVector(da, &localX);
637:   if (B) DMRestoreLocalVector(da, &localB);
638:   return 0;
639: }

641: /*TEST

643:    test:
644:       nsize: 2
645:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full
646:       requires: !single

648:    test:
649:       suffix: 10
650:       nsize: 3
651:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type symmetric_multiplicative -snes_view -da_refine 1 -ksp_type fgmres
652:       requires: !single

654:    test:
655:       suffix: 11
656:       nsize: 4
657:       requires: pastix
658:       args: -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_pc_factor_mat_solver_type pastix -pc_redundant_number 2 -da_refine 4 -ksp_type fgmres

660:    test:
661:       suffix: 12
662:       nsize: 12
663:       requires: pastix
664:       args: -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_pc_factor_mat_solver_type pastix -pc_redundant_number 5 -da_refine 4 -ksp_type fgmres

666:    test:
667:       suffix: 13
668:       nsize: 3
669:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type multiplicative -snes_view -da_refine 1 -ksp_type fgmres -snes_mf_operator
670:       requires: !single

672:    test:
673:       suffix: 14
674:       nsize: 4
675:       args: -snes_monitor_short -pc_type mg -dm_mat_type baij -mg_coarse_pc_type bjacobi -da_refine 3 -ksp_type fgmres
676:       requires: !single

678:    test:
679:       suffix: 14_ds
680:       nsize: 4
681:       args: -snes_converged_reason -pc_type mg -dm_mat_type baij -mg_coarse_pc_type bjacobi -da_refine 3 -ksp_type fgmres -mat_fd_type ds
682:       output_file: output/ex19_2.out
683:       requires: !single

685:    test:
686:       suffix: 17
687:       args: -snes_monitor_short -ksp_pc_side right
688:       requires: !single

690:    test:
691:       suffix: 18
692:       args: -snes_monitor_ksp draw::draw_lg -ksp_pc_side right
693:       requires: x !single

695:    test:
696:       suffix: 19
697:       nsize: 2
698:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -snes_type newtontrdc
699:       requires: !single

701:    test:
702:       suffix: 20
703:       nsize: 2
704:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -snes_type newtontrdc -snes_trdc_use_cauchy false
705:       requires: !single

707:    test:
708:       suffix: 2
709:       nsize: 4
710:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
711:       requires: !single

713:    test:
714:       suffix: 2_bcols1
715:       nsize: 4
716:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols
717:       output_file: output/ex19_2.out
718:       requires: !single

720:    test:
721:       suffix: 3
722:       nsize: 4
723:       requires: mumps
724:       args: -da_refine 3 -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_ksp_type preonly -redundant_pc_factor_mat_solver_type mumps -pc_redundant_number 2

726:    test:
727:       suffix: 4
728:       nsize: 12
729:       requires: mumps
730:       args: -da_refine 3 -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_ksp_type preonly -redundant_pc_factor_mat_solver_type mumps -pc_redundant_number 5
731:       output_file: output/ex19_3.out

733:    test:
734:       suffix: 6
735:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -ksp_type fgmres -da_refine 1
736:       requires: !single

738:    test:
739:       suffix: 7
740:       nsize: 3
741:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -da_refine 1 -ksp_type fgmres

743:       requires: !single
744:    test:
745:       suffix: 8
746:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_block_size 2 -pc_fieldsplit_0_fields 0,1 -pc_fieldsplit_1_fields 0,1 -pc_fieldsplit_type multiplicative -snes_view -fieldsplit_pc_type lu -da_refine 1 -ksp_type fgmres
747:       requires: !single

749:    test:
750:       suffix: 9
751:       nsize: 3
752:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type multiplicative -snes_view -da_refine 1 -ksp_type fgmres
753:       requires: !single

755:    test:
756:       suffix: aspin
757:       nsize: 4
758:       args: -da_refine 3 -da_overlap 2 -snes_monitor_short -snes_type aspin -grashof 4e4 -lidvelocity 100 -ksp_monitor_short
759:       requires: !single

761:    test:
762:       suffix: bcgsl
763:       nsize: 2
764:       args: -ksp_type bcgsl -ksp_monitor_short -da_refine 2 -ksp_bcgsl_ell 3 -snes_view
765:       requires: !single

767:    test:
768:       suffix: bcols1
769:       nsize: 2
770:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -mat_fd_coloring_bcols 1
771:       output_file: output/ex19_1.out
772:       requires: !single

774:    test:
775:       suffix: bjacobi
776:       nsize: 4
777:       args: -da_refine 4 -ksp_type fgmres -pc_type bjacobi -pc_bjacobi_blocks 2 -sub_ksp_type gmres -sub_ksp_max_it 2 -sub_pc_type bjacobi -sub_sub_ksp_type preonly -sub_sub_pc_type ilu -snes_monitor_short
778:       requires: !single

780:    test:
781:       suffix: cgne
782:       args: -da_refine 2 -pc_type lu -ksp_type cgne -ksp_monitor_short -ksp_converged_reason -ksp_view -ksp_norm_type unpreconditioned
783:       filter: grep -v HERMITIAN
784:       requires: !single

786:    test:
787:       suffix: cgs
788:       args: -da_refine 1 -ksp_monitor_short -ksp_type cgs
789:       requires: !single

791:    test:
792:       suffix: composite_fieldsplit
793:       args: -ksp_type fgmres -pc_type composite -pc_composite_type MULTIPLICATIVE -pc_composite_pcs fieldsplit,none -sub_0_pc_fieldsplit_block_size 4 -sub_0_pc_fieldsplit_type additive -sub_0_pc_fieldsplit_0_fields 0,1,2 -sub_0_pc_fieldsplit_1_fields 3 -snes_monitor_short -ksp_monitor_short
794:       requires: !single

796:    test:
797:       suffix: composite_fieldsplit_bjacobi
798:       args: -ksp_type fgmres -pc_type composite -pc_composite_type MULTIPLICATIVE -pc_composite_pcs fieldsplit,bjacobi -sub_0_pc_fieldsplit_block_size 4 -sub_0_pc_fieldsplit_type additive -sub_0_pc_fieldsplit_0_fields 0,1,2 -sub_0_pc_fieldsplit_1_fields 3 -sub_1_pc_bjacobi_blocks 16 -sub_1_sub_pc_type lu -snes_monitor_short -ksp_monitor_short
799:       requires: !single

801:    test:
802:       suffix: composite_fieldsplit_bjacobi_2
803:       nsize: 4
804:       args: -ksp_type fgmres -pc_type composite -pc_composite_type MULTIPLICATIVE -pc_composite_pcs fieldsplit,bjacobi -sub_0_pc_fieldsplit_block_size 4 -sub_0_pc_fieldsplit_type additive -sub_0_pc_fieldsplit_0_fields 0,1,2 -sub_0_pc_fieldsplit_1_fields 3 -sub_1_pc_bjacobi_blocks 16 -sub_1_sub_pc_type lu -snes_monitor_short -ksp_monitor_short
805:       requires: !single

807:    test:
808:       suffix: composite_gs_newton
809:       nsize: 2
810:       args: -da_refine 3 -grashof 4e4 -lidvelocity 100 -snes_monitor_short -snes_type composite -snes_composite_type additiveoptimal -snes_composite_sneses ngs,newtonls -sub_0_snes_max_it 20 -sub_1_pc_type mg
811:       requires: !single

813:    test:
814:       suffix: cuda
815:       requires: cuda !single
816:       args: -dm_vec_type cuda -dm_mat_type aijcusparse -pc_type none -ksp_type fgmres -snes_monitor_short -snes_rtol 1.e-5

818:    test:
819:       suffix: hip
820:       requires: hip !single
821:       args: -dm_vec_type hip -dm_mat_type aijhipsparse -pc_type none -ksp_type fgmres -snes_monitor_short -snes_rtol 1.e-5

823:    test:
824:       suffix: draw
825:       args: -pc_type fieldsplit -snes_view draw -fieldsplit_x_velocity_pc_type mg -fieldsplit_x_velocity_pc_mg_galerkin pmat -fieldsplit_x_velocity_pc_mg_levels 2 -da_refine 1 -fieldsplit_x_velocity_mg_coarse_pc_type svd
826:       requires: x !single

828:    test:
829:       suffix: drawports
830:       args: -snes_monitor_solution draw::draw_ports -da_refine 1
831:       output_file: output/ex19_draw.out
832:       requires: x !single

834:    test:
835:       suffix: fas
836:       args: -da_refine 4 -snes_monitor_short -snes_type fas -fas_levels_snes_type ngs -fas_levels_snes_ngs_sweeps 3 -fas_levels_snes_ngs_atol 0.0 -fas_levels_snes_ngs_stol 0.0 -grashof 4e4 -snes_fas_smoothup 6 -snes_fas_smoothdown 6 -lidvelocity 100
837:       requires: !single

839:    test:
840:       suffix: fas_full
841:       args: -da_refine 4 -snes_monitor_short -snes_type fas -snes_fas_type full -snes_fas_full_downsweep -fas_levels_snes_type ngs -fas_levels_snes_ngs_sweeps 3 -fas_levels_snes_ngs_atol 0.0 -fas_levels_snes_ngs_stol 0.0 -grashof 4e4 -snes_fas_smoothup 6 -snes_fas_smoothdown 6 -lidvelocity 100
842:       requires: !single

844:    test:
845:       suffix: fdcoloring_ds
846:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
847:       output_file: output/ex19_2.out
848:       requires: !single

850:    test:
851:       suffix: fdcoloring_ds_baij
852:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -dm_mat_type baij
853:       output_file: output/ex19_2.out
854:       requires: !single

856:    test:
857:       suffix: fdcoloring_ds_bcols1
858:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols 1
859:       output_file: output/ex19_2.out
860:       requires: !single

862:    test:
863:       suffix: fdcoloring_wp
864:       args: -da_refine 3 -snes_monitor_short -pc_type mg
865:       requires: !single

867:    test:
868:       suffix: fdcoloring_wp_baij
869:       args: -da_refine 3 -snes_monitor_short -pc_type mg -dm_mat_type baij
870:       output_file: output/ex19_fdcoloring_wp.out
871:       requires: !single

873:    test:
874:       suffix: fdcoloring_wp_bcols1
875:       args: -da_refine 3 -snes_monitor_short -pc_type mg -mat_fd_coloring_bcols 1
876:       output_file: output/ex19_fdcoloring_wp.out
877:       requires: !single

879:    test:
880:       suffix: fieldsplit_2
881:       args: -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type additive -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -snes_monitor_short -ksp_monitor_short
882:       requires: !single

884:    test:
885:       suffix: fieldsplit_3
886:       args: -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type additive -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -fieldsplit_0_pc_type lu -fieldsplit_1_pc_type lu -snes_monitor_short -ksp_monitor_short
887:       requires: !single

889:    test:
890:       suffix: fieldsplit_4
891:       args: -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type SCHUR -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -fieldsplit_0_pc_type lu -fieldsplit_1_pc_type lu -snes_monitor_short -ksp_monitor_short
892:       requires: !single

894:    # HYPRE PtAP broken with complex numbers
895:    test:
896:       suffix: fieldsplit_hypre
897:       nsize: 2
898:       requires: hypre mumps !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
899:       args: -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type SCHUR -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -fieldsplit_0_pc_type lu -fieldsplit_0_pc_factor_mat_solver_type mumps -fieldsplit_1_pc_type hypre -fieldsplit_1_pc_hypre_type boomeramg -snes_monitor_short -ksp_monitor_short

901:    test:
902:       suffix: fieldsplit_mumps
903:       nsize: 2
904:       requires: mumps
905:       args: -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type SCHUR -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -fieldsplit_0_pc_type lu -fieldsplit_1_pc_type lu -snes_monitor_short -ksp_monitor_short -fieldsplit_0_pc_factor_mat_solver_type mumps -fieldsplit_1_pc_factor_mat_solver_type mumps
906:       output_file: output/ex19_fieldsplit_5.out

908:    test:
909:       suffix: greedy_coloring
910:       nsize: 2
911:       args: -da_refine 3 -snes_monitor_short -snes_fd_color -snes_fd_color_use_mat -mat_coloring_type greedy -mat_coloring_weight_type lf -mat_coloring_view> ex19_greedy_coloring.tmp 2>&1
912:       requires: !single

914:    # HYPRE PtAP broken with complex numbers
915:    test:
916:       suffix: hypre
917:       nsize: 2
918:       requires: hypre !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
919:       args: -da_refine 3 -snes_monitor_short -pc_type hypre -ksp_norm_type unpreconditioned

921:    # ibcgs is broken when using device vectors
922:    test:
923:       suffix: ibcgs
924:       nsize: 2
925:       args: -ksp_type ibcgs -ksp_monitor_short -da_refine 2 -snes_view
926:       requires: !complex !single

928:    test:
929:       suffix: kaczmarz
930:       nsize: 2
931:       args: -pc_type kaczmarz -ksp_monitor_short -snes_monitor_short -snes_view
932:       requires: !single

934:    test:
935:       suffix: klu
936:       requires: suitesparse
937:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu
938:       output_file: output/ex19_superlu.out

940:    test:
941:       suffix: klu_2
942:       requires: suitesparse
943:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -pc_factor_mat_ordering_type nd
944:       output_file: output/ex19_superlu.out

946:    test:
947:       suffix: klu_3
948:       requires: suitesparse
949:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_use_btf 0
950:       output_file: output/ex19_superlu.out

952:    test:
953:       suffix: ml
954:       nsize: 2
955:       requires: ml
956:       args: -da_refine 3 -snes_monitor_short -pc_type ml

958:    test:
959:       suffix: ngmres_fas
960:       args: -da_refine 4 -snes_monitor_short -snes_type ngmres -npc_fas_levels_snes_type ngs -npc_fas_levels_snes_ngs_sweeps 3 -npc_fas_levels_snes_ngs_atol 0.0 -npc_fas_levels_snes_ngs_stol 0.0 -npc_snes_type fas -npc_fas_levels_snes_type ngs -npc_snes_max_it 1 -npc_snes_fas_smoothup 6 -npc_snes_fas_smoothdown 6 -lidvelocity 100 -grashof 4e4
961:       requires: !single

963:    test:
964:       suffix: ngmres_fas_gssecant
965:       args: -da_refine 3 -snes_monitor_short -snes_type ngmres -npc_snes_type fas -npc_fas_levels_snes_type ngs -npc_fas_levels_snes_max_it 6 -npc_fas_levels_snes_ngs_secant -npc_fas_levels_snes_ngs_max_it 1 -npc_fas_coarse_snes_max_it 1 -lidvelocity 100 -grashof 4e4
966:       requires: !single

968:    test:
969:       suffix: ngmres_fas_ms
970:       nsize: 2
971:       args: -snes_grid_sequence 2 -lidvelocity 200 -grashof 1e4 -snes_monitor_short -snes_view -snes_converged_reason -snes_type ngmres -npc_snes_type fas -npc_fas_coarse_snes_type newtonls -npc_fas_coarse_ksp_type preonly -npc_snes_max_it 1
972:       requires: !single

974:    test:
975:       suffix: ngmres_nasm
976:       nsize: 4
977:       args: -da_refine 4 -da_overlap 2 -snes_monitor_short -snes_type ngmres -snes_max_it 10 -npc_snes_type nasm -npc_snes_nasm_type basic -grashof 4e4 -lidvelocity 100
978:       requires: !single

980:    test:
981:       suffix: ngs
982:       args: -snes_type ngs -snes_view -snes_monitor -snes_rtol 1e-4
983:       requires: !single

985:    test:
986:       suffix: ngs_fd
987:       args: -snes_type ngs -snes_ngs_secant -snes_view -snes_monitor -snes_rtol 1e-4
988:       requires: !single

990:    test:
991:       suffix: parms
992:       nsize: 2
993:       requires: parms
994:       args: -pc_type parms -ksp_monitor_short -snes_view

996:    test:
997:       suffix: superlu
998:       requires: superlu
999:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu

1001:    test:
1002:       suffix: superlu_sell
1003:       requires: superlu
1004:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu -dm_mat_type sell -pc_factor_mat_ordering_type natural
1005:       output_file: output/ex19_superlu.out

1007:    test:
1008:       suffix: superlu_dist
1009:       requires: superlu_dist
1010:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1011:       output_file: output/ex19_superlu.out

1013:    test:
1014:       suffix: superlu_dist_2
1015:       nsize: 2
1016:       requires: superlu_dist
1017:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1018:       output_file: output/ex19_superlu.out

1020:    test:
1021:       suffix: superlu_dist_3d
1022:       nsize: 4
1023:       requires: superlu_dist !defined(PETSCTEST_VALGRIND)
1024:       filter: grep -v iam | grep -v openMP
1025:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_3d -mat_superlu_dist_d 2 -snes_view -snes_monitor -ksp_monitor

1027:    test:
1028:       suffix: superlu_equil
1029:       requires: superlu
1030:       args: -da_grid_x 20 -da_grid_y 20 -{snes,ksp}_monitor_short -pc_type lu -pc_factor_mat_solver_type superlu -mat_superlu_equil

1032:    test:
1033:       suffix: superlu_equil_sell
1034:       requires: superlu
1035:       args: -da_grid_x 20 -da_grid_y 20 -{snes,ksp}_monitor_short -pc_type lu -pc_factor_mat_solver_type superlu -mat_superlu_equil -dm_mat_type sell -pc_factor_mat_ordering_type natural
1036:       output_file: output/ex19_superlu_equil.out

1038:    test:
1039:       suffix: tcqmr
1040:       args: -da_refine 1 -ksp_monitor_short -ksp_type tcqmr
1041:       requires: !single

1043:    test:
1044:       suffix: tfqmr
1045:       args: -da_refine 1 -ksp_monitor_short -ksp_type tfqmr
1046:       requires: !single

1048:    test:
1049:       suffix: umfpack
1050:       requires: suitesparse
1051:       args: -da_refine 2 -pc_type lu -pc_factor_mat_solver_type umfpack -snes_view -snes_monitor_short -ksp_monitor_short -pc_factor_mat_ordering_type external

1053:    test:
1054:       suffix: tut_1
1055:       nsize: 4
1056:       requires: !single
1057:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view

1059:    test:
1060:       suffix: tut_2
1061:       nsize: 4
1062:       requires: !single
1063:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg

1065:    # HYPRE PtAP broken with complex numbers
1066:    test:
1067:       suffix: tut_3
1068:       nsize: 4
1069:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
1070:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre

1072:    test:
1073:       suffix: tut_8
1074:       nsize: 4
1075:       requires: ml !single
1076:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml

1078:    test:
1079:       suffix: tut_4
1080:       nsize: 1
1081:       requires: !single
1082:       args: -da_refine 5 -log_view
1083:       filter: head -n 2
1084:       filter_output: head -n 2

1086:    test:
1087:       suffix: tut_5
1088:       nsize: 1
1089:       requires: !single
1090:       args: -da_refine 5 -log_view -pc_type mg
1091:       filter: head -n 2
1092:       filter_output: head -n 2

1094:    test:
1095:       suffix: tut_6
1096:       nsize: 4
1097:       requires: !single
1098:       args: -da_refine 5 -log_view
1099:       filter: head -n 2
1100:       filter_output: head -n 2

1102:    test:
1103:       suffix: tut_7
1104:       nsize: 4
1105:       requires: !single
1106:       args: -da_refine 5 -log_view -pc_type mg
1107:       filter: head -n 2
1108:       filter_output: head -n 2

1110:    test:
1111:       suffix: cuda_1
1112:       nsize: 1
1113:       requires: cuda
1114:       args: -snes_monitor -dm_mat_type seqaijcusparse -dm_vec_type seqcuda -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor -mg_levels_ksp_max_it 3

1116:    test:
1117:       suffix: cuda_2
1118:       nsize: 3
1119:       requires: cuda !single
1120:       args: -snes_monitor -dm_mat_type mpiaijcusparse -dm_vec_type mpicuda -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor  -mg_levels_ksp_max_it 3

1122:    test:
1123:       suffix: cuda_dm_bind_below
1124:       nsize: 2
1125:       requires: cuda
1126:       args: -dm_mat_type aijcusparse -dm_vec_type cuda -da_refine 3 -pc_type mg -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -log_view -pc_mg_log -dm_bind_below 10000
1127:       filter: awk "/Level/ {print \$NF}"

1129:    test:
1130:       suffix: hip_1
1131:       nsize: 1
1132:       requires: hip
1133:       args: -snes_monitor -dm_mat_type mpiaijhipsparse -dm_vec_type hip -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor -mg_levels_ksp_max_it 3

1135:    test:
1136:       suffix: hip_2
1137:       nsize: 3
1138:       requires: hip !single
1139:       args: -snes_monitor -dm_mat_type mpiaijhipsparse -dm_vec_type mpihip -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor  -mg_levels_ksp_max_it 3

1141:    test:
1142:       suffix: hip_dm_bind_below
1143:       nsize: 2
1144:       requires: hip
1145:       args: -dm_mat_type aijhipsparse -dm_vec_type hip -da_refine 3 -pc_type mg -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -log_view -pc_mg_log -dm_bind_below 10000
1146:       filter: awk "/Level/ {print \$NF}"

1148:    test:
1149:       suffix: viennacl_dm_bind_below
1150:       nsize: 2
1151:       requires: viennacl
1152:       args: -dm_mat_type aijviennacl -dm_vec_type viennacl -da_refine 3 -pc_type mg -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -log_view -pc_mg_log -dm_bind_below 10000
1153:       filter: awk "/Level/ {print \$NF}"

1155:    test:
1156:       suffix: seqbaijmkl
1157:       nsize: 1
1158:       requires: defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1159:       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view

1161:    test:
1162:       suffix: mpibaijmkl
1163:       nsize: 2
1164:       requires:  defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1165:       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view

1167:    test:
1168:      suffix: cpardiso
1169:      nsize: 4
1170:      requires: mkl_cpardiso
1171:      args: -pc_type lu -pc_factor_mat_solver_type mkl_cpardiso -ksp_monitor

1173:    test:
1174:      suffix: logviewmemory
1175:      requires: defined(PETSC_USE_LOG) !defined(PETSCTEST_VALGRIND)
1176:      args: -log_view -log_view_memory -da_refine 4
1177:      filter: grep MatFDColorSetUp | wc -w | xargs  -I % sh -c "expr % \> 21"

1179:    test:
1180:      suffix: fs
1181:      args: -pc_type fieldsplit -da_refine 3  -all_ksp_monitor -fieldsplit_y_velocity_pc_type lu  -fieldsplit_temperature_pc_type lu -fieldsplit_x_velocity_pc_type lu  -snes_view

1183:    test:
1184:      suffix: asm_matconvert
1185:      args: -mat_type aij -pc_type asm -pc_asm_sub_mat_type dense -snes_view

1187:    test:
1188:       suffix: euclid
1189:       nsize: 2
1190:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1191:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid

1193:    test:
1194:       suffix: euclid_bj
1195:       nsize: 2
1196:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1197:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_bj

1199:    test:
1200:       suffix: euclid_droptolerance
1201:       nsize: 1
1202:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1203:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_droptolerance .1

1205:    test:
1206:       suffix: failure_size
1207:       nsize: 1
1208:       requires: !defined(PETSC_USE_64BIT_INDICES) !defined(PETSCTEST_VALGRIND)
1209:       args: -da_refine 100 -petsc_ci_portable_error_output -error_output_stdout
1210:       filter: grep -E -v "(options_left|memory block|leaked context|not freed before MPI_Finalize|Could be the program crashed)"

1212: TEST*/