Actual source code: ex19.c


  2: static char help[] = "Nonlinear driven cavity with multigrid in 2d.\n \
  3:   \n\
  4: The 2D driven cavity problem is solved in a velocity-vorticity formulation.\n\
  5: The flow can be driven with the lid or with bouyancy or both:\n\
  6:   -lidvelocity &ltlid&gt, where &ltlid&gt = dimensionless velocity of lid\n\
  7:   -grashof &ltgr&gt, where &ltgr&gt = dimensionless temperature gradent\n\
  8:   -prandtl &ltpr&gt, where &ltpr&gt = dimensionless thermal/momentum diffusity ratio\n\
  9:  -contours : draw contour plots of solution\n\n";
 10: /* in HTML, '&lt' = '<' and '&gt' = '>' */

 12: /*
 13:       See src/ksp/ksp/tutorials/ex45.c
 14: */

 16: /*T
 17:    Concepts: SNES^solving a system of nonlinear equations (parallel multicomponent example);
 18:    Concepts: DMDA^using distributed arrays;
 19:    Concepts: multicomponent
 20:    Processors: n
 21: T*/


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

This problem is modeled by the partial differential equation system

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

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

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

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

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

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

 78: /*
 79:    User-defined routines and data structures
 80: */
 81: typedef struct {
 82:   PetscScalar u,v,omega,temp;
 83: } Field;

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

 87: typedef struct {
 88:   PetscReal   lidvelocity,prandtl,grashof;  /* physical parameters */
 89:   PetscBool   draw_contours;                /* flag - 1 indicates drawing contours */
 90: } AppCtx;

 92: extern PetscErrorCode FormInitialGuess(AppCtx*,DM,Vec);
 93: extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);

 95: int main(int argc,char **argv)
 96: {
 97:   AppCtx         user;                /* user-defined work context */
 98:   PetscInt       mx,my,its;
 99:   MPI_Comm       comm;
100:   SNES           snes;
101:   DM             da;
102:   Vec            x;

104:   PetscInitialize(&argc,&argv,(char*)0,help);

107:   comm = PETSC_COMM_WORLD;
108:   SNESCreate(comm,&snes);

110:   /*
111:       Create distributed array object to manage parallel grid and vectors
112:       for principal unknowns (x) and governing residuals (f)
113:   */
114:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,4,1,0,0,&da);
115:   DMSetFromOptions(da);
116:   DMSetUp(da);
117:   SNESSetDM(snes,(DM)da);
118:   SNESSetNGS(snes, NonlinearGS, (void*)&user);

120:   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);
121:   /*
122:      Problem parameters (velocity of lid, prandtl, and grashof numbers)
123:   */
124:   user.lidvelocity = 1.0/(mx*my);
125:   user.prandtl     = 1.0;
126:   user.grashof     = 1.0;

128:   PetscOptionsGetReal(NULL,NULL,"-lidvelocity",&user.lidvelocity,NULL);
129:   PetscOptionsGetReal(NULL,NULL,"-prandtl",&user.prandtl,NULL);
130:   PetscOptionsGetReal(NULL,NULL,"-grashof",&user.grashof,NULL);
131:   PetscOptionsHasName(NULL,NULL,"-contours",&user.draw_contours);

133:   DMDASetFieldName(da,0,"x_velocity");
134:   DMDASetFieldName(da,1,"y_velocity");
135:   DMDASetFieldName(da,2,"Omega");
136:   DMDASetFieldName(da,3,"temperature");

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139:      Create user context, set problem data, create vector data structures.
140:      Also, compute the initial guess.
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:      Create nonlinear solver context

146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147:   DMSetApplicationContext(da,&user);
148:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);
149:   SNESSetFromOptions(snes);
150:   PetscPrintf(comm,"lid velocity = %g, prandtl # = %g, grashof # = %g\n",(double)user.lidvelocity,(double)user.prandtl,(double)user.grashof);

152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153:      Solve the nonlinear system
154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155:   DMCreateGlobalVector(da,&x);
156:   FormInitialGuess(&user,da,x);

158:   SNESSolve(snes,NULL,x);

160:   SNESGetIterationNumber(snes,&its);
161:   PetscPrintf(comm,"Number of SNES iterations = %D\n", its);

163:   /*
164:      Visualize solution
165:   */
166:   if (user.draw_contours) {
167:     VecView(x,PETSC_VIEWER_DRAW_WORLD);
168:   }

170:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171:      Free work space.  All PETSc objects should be destroyed when they
172:      are no longer needed.
173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174:   VecDestroy(&x);
175:   DMDestroy(&da);
176:   SNESDestroy(&snes);
177:   PetscFinalize();
178:   return 0;
179: }

181: /* ------------------------------------------------------------------- */

183: /*
184:    FormInitialGuess - Forms initial approximation.

186:    Input Parameters:
187:    user - user-defined application context
188:    X - vector

190:    Output Parameter:
191:    X - vector
192: */
193: PetscErrorCode FormInitialGuess(AppCtx *user,DM da,Vec X)
194: {
195:   PetscInt       i,j,mx,xs,ys,xm,ym;
196:   PetscReal      grashof,dx;
197:   Field          **x;

200:   grashof = user->grashof;

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

205:   /*
206:      Get local grid boundaries (for 2-dimensional DMDA):
207:        xs, ys   - starting grid indices (no ghost points)
208:        xm, ym   - widths of local grid (no ghost points)
209:   */
210:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

212:   /*
213:      Get a pointer to vector data.
214:        - For default PETSc vectors, VecGetArray() returns a pointer to
215:          the data array.  Otherwise, the routine is implementation dependent.
216:        - You MUST call VecRestoreArray() when you no longer need access to
217:          the array.
218:   */
219:   DMDAVecGetArrayWrite(da,X,&x);

221:   /*
222:      Compute initial guess over the locally owned part of the grid
223:      Initial condition is motionless fluid and equilibrium temperature
224:   */
225:   for (j=ys; j<ys+ym; j++) {
226:     for (i=xs; i<xs+xm; i++) {
227:       x[j][i].u     = 0.0;
228:       x[j][i].v     = 0.0;
229:       x[j][i].omega = 0.0;
230:       x[j][i].temp  = (grashof>0)*i*dx;
231:     }
232:   }

234:   /*
235:      Restore vector
236:   */
237:   DMDAVecRestoreArrayWrite(da,X,&x);
238:   return 0;
239: }

241: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
242: {
243:   AppCtx         *user = (AppCtx*)ptr;
244:   PetscInt       xints,xinte,yints,yinte,i,j;
245:   PetscReal      hx,hy,dhx,dhy,hxdhy,hydhx;
246:   PetscReal      grashof,prandtl,lid;
247:   PetscScalar    u,uxx,uyy,vx,vy,avx,avy,vxp,vxm,vyp,vym;

250:   grashof = user->grashof;
251:   prandtl = user->prandtl;
252:   lid     = user->lidvelocity;

254:   /*
255:      Define mesh intervals ratios for uniform grid.

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

260:   */
261:   dhx   = (PetscReal)(info->mx-1);  dhy = (PetscReal)(info->my-1);
262:   hx    = 1.0/dhx;                   hy = 1.0/dhy;
263:   hxdhy = hx*dhy;                 hydhx = hy*dhx;

265:   xints = info->xs; xinte = info->xs+info->xm; yints = info->ys; yinte = info->ys+info->ym;

267:   /* Test whether we are on the bottom edge of the global array */
268:   if (yints == 0) {
269:     j     = 0;
270:     yints = yints + 1;
271:     /* bottom edge */
272:     for (i=info->xs; i<info->xs+info->xm; i++) {
273:       f[j][i].u     = x[j][i].u;
274:       f[j][i].v     = x[j][i].v;
275:       f[j][i].omega = x[j][i].omega + (x[j+1][i].u - x[j][i].u)*dhy;
276:       f[j][i].temp  = x[j][i].temp-x[j+1][i].temp;
277:     }
278:   }

280:   /* Test whether we are on the top edge of the global array */
281:   if (yinte == info->my) {
282:     j     = info->my - 1;
283:     yinte = yinte - 1;
284:     /* top edge */
285:     for (i=info->xs; i<info->xs+info->xm; i++) {
286:       f[j][i].u     = x[j][i].u - lid;
287:       f[j][i].v     = x[j][i].v;
288:       f[j][i].omega = x[j][i].omega + (x[j][i].u - x[j-1][i].u)*dhy;
289:       f[j][i].temp  = x[j][i].temp-x[j-1][i].temp;
290:     }
291:   }

293:   /* Test whether we are on the left edge of the global array */
294:   if (xints == 0) {
295:     i     = 0;
296:     xints = xints + 1;
297:     /* left edge */
298:     for (j=info->ys; j<info->ys+info->ym; j++) {
299:       f[j][i].u     = x[j][i].u;
300:       f[j][i].v     = x[j][i].v;
301:       f[j][i].omega = x[j][i].omega - (x[j][i+1].v - x[j][i].v)*dhx;
302:       f[j][i].temp  = x[j][i].temp;
303:     }
304:   }

306:   /* Test whether we are on the right edge of the global array */
307:   if (xinte == info->mx) {
308:     i     = info->mx - 1;
309:     xinte = xinte - 1;
310:     /* right edge */
311:     for (j=info->ys; j<info->ys+info->ym; j++) {
312:       f[j][i].u     = x[j][i].u;
313:       f[j][i].v     = x[j][i].v;
314:       f[j][i].omega = x[j][i].omega - (x[j][i].v - x[j][i-1].v)*dhx;
315:       f[j][i].temp  = x[j][i].temp - (PetscReal)(grashof>0);
316:     }
317:   }

319:   /* Compute over the interior points */
320:   for (j=yints; j<yinte; j++) {
321:     for (i=xints; i<xinte; i++) {

323:       /*
324:        convective coefficients for upwinding
325:       */
326:       vx  = x[j][i].u; avx = PetscAbsScalar(vx);
327:       vxp = .5*(vx+avx); vxm = .5*(vx-avx);
328:       vy  = x[j][i].v; avy = PetscAbsScalar(vy);
329:       vyp = .5*(vy+avy); vym = .5*(vy-avy);

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

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

343:       /* Omega */
344:       u             = x[j][i].omega;
345:       uxx           = (2.0*u - x[j][i-1].omega - x[j][i+1].omega)*hydhx;
346:       uyy           = (2.0*u - x[j-1][i].omega - x[j+1][i].omega)*hxdhy;
347:       f[j][i].omega = uxx + uyy + (vxp*(u - x[j][i-1].omega) + vxm*(x[j][i+1].omega - u))*hy +
348:                       (vyp*(u - x[j-1][i].omega) + vym*(x[j+1][i].omega - u))*hx -
349:                       .5*grashof*(x[j][i+1].temp - x[j][i-1].temp)*hy;

351:       /* Temperature */
352:       u            = x[j][i].temp;
353:       uxx          = (2.0*u - x[j][i-1].temp - x[j][i+1].temp)*hydhx;
354:       uyy          = (2.0*u - x[j-1][i].temp - x[j+1][i].temp)*hxdhy;
355:       f[j][i].temp =  uxx + uyy  + prandtl*((vxp*(u - x[j][i-1].temp) + vxm*(x[j][i+1].temp - u))*hy +
356:                                             (vyp*(u - x[j-1][i].temp) + vym*(x[j+1][i].temp - u))*hx);
357:     }
358:   }

360:   /*
361:      Flop count (multiply-adds are counted as 2 operations)
362:   */
363:   PetscLogFlops(84.0*info->ym*info->xm);
364:   return 0;
365: }

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

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

426:   xints = info.xs; xinte = info.xs+info.xm; yints = info.ys; 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++) {

435:       if (B) {
436:         bjiu = b[j][i].u;
437:         bjiv = b[j][i].v;
438:       } else {
439:         bjiu = 0.0;
440:         bjiv = 0.0;
441:       }
442:       x[j][i].u = 0.0 + bjiu;
443:       x[j][i].v = 0.0 + bjiv;
444:     }
445:   }

447:   /* Test whether we are on the top edge of the global array */
448:   if (yinte == info.my) {
449:     j     = info.my - 1;
450:     /* top edge */
451:     for (i=info.xs; i<info.xs+info.xm; i++) {
452:       if (B) {
453:         bjiu = b[j][i].u;
454:         bjiv = b[j][i].v;
455:       } else {
456:         bjiu = 0.0;
457:         bjiv = 0.0;
458:       }
459:       x[j][i].u = lid + bjiu;
460:       x[j][i].v = bjiv;
461:     }
462:   }

464:   /* Test whether we are on the left edge of the global array */
465:   if (xints == 0) {
466:     i     = 0;
467:     /* left edge */
468:     for (j=info.ys; j<info.ys+info.ym; j++) {
469:       if (B) {
470:         bjiu = b[j][i].u;
471:         bjiv = b[j][i].v;
472:       } else {
473:         bjiu = 0.0;
474:         bjiv = 0.0;
475:       }
476:       x[j][i].u = 0.0 + bjiu;
477:       x[j][i].v = 0.0 + bjiv;
478:     }
479:   }

481:   /* Test whether we are on the right edge of the global array */
482:   if (xinte == info.mx) {
483:     i     = info.mx - 1;
484:     /* right edge */
485:     for (j=info.ys; j<info.ys+info.ym; j++) {
486:       if (B) {
487:         bjiu = b[j][i].u;
488:         bjiv = b[j][i].v;
489:       } else {
490:         bjiu = 0.0;
491:         bjiv = 0.0;
492:       }
493:       x[j][i].u = 0.0 + bjiu;
494:       x[j][i].v = 0.0 + bjiv;
495:     }
496:   }

498:   for (k=0; k < sweeps; k++) {
499:     for (j=info.ys; j<info.ys + info.ym; j++) {
500:       for (i=info.xs; i<info.xs + info.xm; i++) {
501:         ptconverged = PETSC_FALSE;
502:         pfnorm0     = 0.0;
503:         fu          = 0.0;
504:         fv          = 0.0;
505:         fomega      = 0.0;
506:         ftemp       = 0.0;
507:         /*  Run Newton's method on a single grid point */
508:         for (l = 0; l < max_its && !ptconverged; l++) {
509:           if (B) {
510:             bjiu     = b[j][i].u;
511:             bjiv     = b[j][i].v;
512:             bjiomega = b[j][i].omega;
513:             bjitemp  = b[j][i].temp;
514:           } else {
515:             bjiu     = 0.0;
516:             bjiv     = 0.0;
517:             bjiomega = 0.0;
518:             bjitemp  = 0.0;
519:           }

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

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

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

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

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

580:             x[j][i].u     = x[j][i].u - yu;
581:             x[j][i].v     = x[j][i].v - yv;
582:             x[j][i].temp  = x[j][i].temp - yt;
583:             x[j][i].omega = x[j][i].omega - yo;
584:           }
585:           if (i == 0) {
586:             fomega        = x[j][i].omega - (x[j][i+1].v - x[j][i].v)*dhx - bjiomega;
587:             ftemp         = x[j][i].temp - bjitemp;
588:             yo            = fomega;
589:             yt            = ftemp;
590:             x[j][i].omega = x[j][i].omega - fomega;
591:             x[j][i].temp  = x[j][i].temp - ftemp;
592:           }
593:           if (i == info.mx - 1) {
594:             fomega        = x[j][i].omega - (x[j][i].v - x[j][i-1].v)*dhx - bjiomega;
595:             ftemp         = x[j][i].temp - (PetscReal)(grashof>0) - bjitemp;
596:             yo            = fomega;
597:             yt            = ftemp;
598:             x[j][i].omega = x[j][i].omega - fomega;
599:             x[j][i].temp  = x[j][i].temp - ftemp;
600:           }
601:           if (j == 0) {
602:             fomega        = x[j][i].omega + (x[j+1][i].u - x[j][i].u)*dhy - bjiomega;
603:             ftemp         = x[j][i].temp-x[j+1][i].temp - bjitemp;
604:             yo            = fomega;
605:             yt            = ftemp;
606:             x[j][i].omega = x[j][i].omega - fomega;
607:             x[j][i].temp  = x[j][i].temp - ftemp;
608:           }
609:           if (j == info.my - 1) {
610:             fomega        = x[j][i].omega + (x[j][i].u - x[j-1][i].u)*dhy - bjiomega;
611:             ftemp         = x[j][i].temp-x[j-1][i].temp - bjitemp;
612:             yo            = fomega;
613:             yt            = ftemp;
614:             x[j][i].omega = x[j][i].omega - fomega;
615:             x[j][i].temp  = x[j][i].temp - ftemp;
616:           }
617:           tot_its++;
618:           pfnorm = PetscRealPart(fu*fu + fv*fv + fomega*fomega + ftemp*ftemp);
619:           pfnorm = PetscSqrtReal(pfnorm);
620:           pynorm = PetscRealPart(yu*yu + yv*yv + yo*yo + yt*yt);
621:           pynorm = PetscSqrtReal(pynorm);
622:           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);
623:           pxnorm = PetscSqrtReal(pxnorm);
624:           if (l == 0) pfnorm0 = pfnorm;
625:           if (rtol*pfnorm0 >pfnorm || atol > pfnorm || pxnorm*stol > pynorm) ptconverged = PETSC_TRUE;
626:         }
627:       }
628:     }
629:   }
630:   DMDAVecRestoreArrayWrite(da,localX,&x);
631:   if (B) {
632:     DMDAVecRestoreArrayRead(da,localB,&b);
633:   }
634:   DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
635:   DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
636:   PetscLogFlops(tot_its*(84.0 + 41.0 + 26.0));
637:   DMRestoreLocalVector(da,&localX);
638:   if (B) {
639:     DMRestoreLocalVector(da,&localB);
640:   }
641:   return 0;
642: }

644: /*TEST

646:    test:
647:       nsize: 2
648:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full
649:       requires: !single

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

657:    test:
658:       suffix: 11
659:       nsize: 4
660:       requires: pastix
661:       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

663:    test:
664:       suffix: 12
665:       nsize: 12
666:       requires: pastix
667:       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

669:    test:
670:       suffix: 13
671:       nsize: 3
672:       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
673:       requires: !single

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

681:    test:
682:       suffix: 14_ds
683:       nsize: 4
684:       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
685:       output_file: output/ex19_2.out
686:       requires: !single

688:    test:
689:       suffix: 17
690:       args: -snes_monitor_short -ksp_pc_side right
691:       requires: !single

693:    test:
694:       suffix: 18
695:       args: -snes_monitor_ksp draw::draw_lg -ksp_pc_side right
696:       requires: x !single

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

704:    test:
705:       suffix: 20
706:       nsize: 2
707:       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
708:       requires: !single

710:    test:
711:       suffix: 2
712:       nsize: 4
713:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
714:       requires: !single

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

723:    test:
724:       suffix: 3
725:       nsize: 4
726:       requires: mumps
727:       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

729:    test:
730:       suffix: 4
731:       nsize: 12
732:       requires: mumps
733:       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
734:       output_file: output/ex19_3.out

736:    test:
737:       suffix: 6
738:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -ksp_type fgmres -da_refine 1
739:       requires: !single

741:    test:
742:       suffix: 7
743:       nsize: 3
744:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -da_refine 1 -ksp_type fgmres

746:       requires: !single
747:    test:
748:       suffix: 8
749:       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
750:       requires: !single

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

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

764:    test:
765:       suffix: bcgsl
766:       nsize: 2
767:       args: -ksp_type bcgsl -ksp_monitor_short -da_refine 2 -ksp_bcgsl_ell 3 -snes_view
768:       requires: !single

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

777:    test:
778:       suffix: bjacobi
779:       nsize: 4
780:       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
781:       requires: !single

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

789:    test:
790:       suffix: cgs
791:       args: -da_refine 1 -ksp_monitor_short -ksp_type cgs
792:       requires: !single

794:    test:
795:       suffix: composite_fieldsplit
796:       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
797:       requires: !single

799:    test:
800:       suffix: composite_fieldsplit_bjacobi
801:       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
802:       requires: !single

804:    test:
805:       suffix: composite_fieldsplit_bjacobi_2
806:       nsize: 4
807:       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
808:       requires: !single

810:    test:
811:       suffix: composite_gs_newton
812:       nsize: 2
813:       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
814:       requires: !single

816:    test:
817:       suffix: cuda
818:       requires: cuda !single
819:       args: -dm_vec_type cuda -dm_mat_type aijcusparse -pc_type none -ksp_type fgmres -snes_monitor_short -snes_rtol 1.e-5

821:    test:
822:       suffix: draw
823:       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
824:       requires: x !single

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

832:    test:
833:       suffix: fas
834:       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
835:       requires: !single

837:    test:
838:       suffix: fas_full
839:       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
840:       requires: !single

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

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

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

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

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

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

877:    test:
878:       suffix: fieldsplit_2
879:       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
880:       requires: !single

882:    test:
883:       suffix: fieldsplit_3
884:       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
885:       requires: !single

887:    test:
888:       suffix: fieldsplit_4
889:       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
890:       requires: !single

892:    # HYPRE PtAP broken with complex numbers
893:    test:
894:       suffix: fieldsplit_hypre
895:       nsize: 2
896:       requires: hypre mumps !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
897:       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

899:    test:
900:       suffix: fieldsplit_mumps
901:       nsize: 2
902:       requires: mumps
903:       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
904:       output_file: output/ex19_fieldsplit_5.out

906:    test:
907:       suffix: greedy_coloring
908:       nsize: 2
909:       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
910:       requires: !single

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

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

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

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

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

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

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

956:    test:
957:       suffix: ngmres_fas
958:       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
959:       requires: !single

961:    test:
962:       suffix: ngmres_fas_gssecant
963:       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
964:       requires: !single

966:    test:
967:       suffix: ngmres_fas_ms
968:       nsize: 2
969:       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
970:       requires: !single

972:    test:
973:       suffix: ngmres_nasm
974:       nsize: 4
975:       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
976:       requires: !single

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

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

988:    test:
989:       suffix: parms
990:       nsize: 2
991:       requires: parms
992:       args: -pc_type parms -ksp_monitor_short -snes_view

994:    test:
995:       suffix: superlu
996:       requires: superlu
997:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu

999:    test:
1000:       suffix: superlu_sell
1001:       requires: superlu
1002:       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
1003:       output_file: output/ex19_superlu.out

1005:    test:
1006:       suffix: superlu_dist
1007:       requires: superlu_dist
1008:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1009:       output_file: output/ex19_superlu.out

1011:    test:
1012:       suffix: superlu_dist_2
1013:       nsize: 2
1014:       requires: superlu_dist
1015:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1016:       output_file: output/ex19_superlu.out

1018:    test:
1019:       suffix: superlu_dist_3d
1020:       nsize: 4
1021:       requires: superlu_dist !defined(PETSCTEST_VALGRIND)
1022:       filter: grep -v iam | grep -v openMP
1023:       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

1025:    test:
1026:       suffix: superlu_equil
1027:       requires: superlu
1028:       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

1030:    test:
1031:       suffix: superlu_equil_sell
1032:       requires: superlu
1033:       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
1034:       output_file: output/ex19_superlu_equil.out

1036:    test:
1037:       suffix: tcqmr
1038:       args: -da_refine 1 -ksp_monitor_short -ksp_type tcqmr
1039:       requires: !single

1041:    test:
1042:       suffix: tfqmr
1043:       args: -da_refine 1 -ksp_monitor_short -ksp_type tfqmr
1044:       requires: !single

1046:    test:
1047:       suffix: umfpack
1048:       requires: suitesparse
1049:       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

1051:    test:
1052:       suffix: tut_1
1053:       nsize: 4
1054:       requires: !single
1055:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view

1057:    test:
1058:       suffix: tut_2
1059:       nsize: 4
1060:       requires: !single
1061:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg

1063:    # HYPRE PtAP broken with complex numbers
1064:    test:
1065:       suffix: tut_3
1066:       nsize: 4
1067:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
1068:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre

1070:    test:
1071:       suffix: tut_8
1072:       nsize: 4
1073:       requires: ml !single
1074:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml

1076:    test:
1077:       suffix: tut_4
1078:       nsize: 1
1079:       requires: !single
1080:       args: -da_refine 5 -log_view
1081:       filter: head -n 2
1082:       filter_output: head -n 2

1084:    test:
1085:       suffix: tut_5
1086:       nsize: 1
1087:       requires: !single
1088:       args: -da_refine 5 -log_view -pc_type mg
1089:       filter: head -n 2
1090:       filter_output: head -n 2

1092:    test:
1093:       suffix: tut_6
1094:       nsize: 4
1095:       requires: !single
1096:       args: -da_refine 5 -log_view
1097:       filter: head -n 2
1098:       filter_output: head -n 2

1100:    test:
1101:       suffix: tut_7
1102:       nsize: 4
1103:       requires: !single
1104:       args: -da_refine 5 -log_view -pc_type mg
1105:       filter: head -n 2
1106:       filter_output: head -n 2

1108:    test:
1109:       suffix: cuda_1
1110:       nsize: 1
1111:       requires: cuda
1112:       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

1114:    test:
1115:       suffix: cuda_2
1116:       nsize: 3
1117:       requires: cuda !single
1118:       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

1120:    test:
1121:       suffix: cuda_dm_bind_below
1122:       nsize: 2
1123:       requires: cuda
1124:       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
1125:       filter: awk "/Level/ {print \$24}"

1127:    test:
1128:       suffix: viennacl_dm_bind_below
1129:       nsize: 2
1130:       requires: viennacl
1131:       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
1132:       filter: awk "/Level/ {print \$24}"

1134:    test:
1135:       suffix: seqbaijmkl
1136:       nsize: 1
1137:       requires: defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1138:       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view

1140:    test:
1141:       suffix: mpibaijmkl
1142:       nsize: 2
1143:       requires:  defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1144:       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view

1146:    test:
1147:      suffix: cpardiso
1148:      nsize: 4
1149:      requires: mkl_cpardiso
1150:      args: -pc_type lu -pc_factor_mat_solver_type mkl_cpardiso -ksp_monitor

1152:    test:
1153:      suffix: logviewmemory
1154:      requires: defined(PETSC_USE_LOG) !defined(PETSCTEST_VALGRIND)
1155:      args: -log_view -log_view_memory -da_refine 4
1156:      filter: grep MatFDColorSetUp | wc -w | xargs  -I % sh -c "expr % \> 21"

1158:    test:
1159:      suffix: fs
1160:      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

1162:    test:
1163:      suffix: asm_matconvert
1164:      args: -mat_type aij -pc_type asm -pc_asm_sub_mat_type dense -snes_view

1166:    test:
1167:       suffix: euclid
1168:       nsize: 2
1169:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1170:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid

1172:    test:
1173:       suffix: euclid_bj
1174:       nsize: 2
1175:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1176:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_bj

1178:    test:
1179:       suffix: euclid_droptolerance
1180:       nsize: 1
1181:       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1182:       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_droptolerance .1

1184: TEST*/