Actual source code: ex19.c

petsc-master 2018-11-13
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  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/examples/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).

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

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

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

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

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

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

106:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return(1);

109:   comm = PETSC_COMM_WORLD;
110:   SNESCreate(comm,&snes);

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

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

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

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

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:      Create user context, set problem data, create vector data structures.
142:      Also, compute the initial guess.
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:      Create nonlinear solver context

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


155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      Solve the nonlinear system
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158:   DMCreateGlobalVector(da,&x);
159:   FormInitialGuess(&user,da,x);

161:   SNESSolve(snes,NULL,x);

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

166:   /*
167:      Visualize solution
168:   */
169:   if (user.draw_contours) {
170:     VecView(x,PETSC_VIEWER_DRAW_WORLD);
171:   }

173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174:      Free work space.  All PETSc objects should be destroyed when they
175:      are no longer needed.
176:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177:   VecDestroy(&x);
178:   DMDestroy(&da);
179:   SNESDestroy(&snes);
180:   PetscFinalize();
181:   return ierr;
182: }

184: /* ------------------------------------------------------------------- */

186: /*
187:    FormInitialGuess - Forms initial approximation.

189:    Input Parameters:
190:    user - user-defined application context
191:    X - vector

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

204:   grashof = user->grashof;

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

209:   /*
210:      Get local grid boundaries (for 2-dimensional DMDA):
211:        xs, ys   - starting grid indices (no ghost points)
212:        xm, ym   - widths of local grid (no ghost points)
213:   */
214:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

216:   /*
217:      Get a pointer to vector data.
218:        - For default PETSc vectors, VecGetArray() returns a pointer to
219:          the data array.  Otherwise, the routine is implementation dependent.
220:        - You MUST call VecRestoreArray() when you no longer need access to
221:          the array.
222:   */
223:   DMDAVecGetArray(da,X,&x);

225:   /*
226:      Compute initial guess over the locally owned part of the grid
227:      Initial condition is motionless fluid and equilibrium temperature
228:   */
229:   for (j=ys; j<ys+ym; j++) {
230:     for (i=xs; i<xs+xm; i++) {
231:       x[j][i].u     = 0.0;
232:       x[j][i].v     = 0.0;
233:       x[j][i].omega = 0.0;
234:       x[j][i].temp  = (grashof>0)*i*dx;
235:     }
236:   }

238:   /*
239:      Restore vector
240:   */
241:   DMDAVecRestoreArray(da,X,&x);
242:   return(0);
243: }

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

255:   grashof = user->grashof;
256:   prandtl = user->prandtl;
257:   lid     = user->lidvelocity;

259:   /*
260:      Define mesh intervals ratios for uniform grid.

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


266:   */
267:   dhx   = (PetscReal)(info->mx-1);  dhy = (PetscReal)(info->my-1);
268:   hx    = 1.0/dhx;                   hy = 1.0/dhy;
269:   hxdhy = hx*dhy;                 hydhx = hy*dhx;

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

273:   /* Test whether we are on the bottom edge of the global array */
274:   if (yints == 0) {
275:     j     = 0;
276:     yints = yints + 1;
277:     /* bottom edge */
278:     for (i=info->xs; i<info->xs+info->xm; i++) {
279:       f[j][i].u     = x[j][i].u;
280:       f[j][i].v     = x[j][i].v;
281:       f[j][i].omega = x[j][i].omega + (x[j+1][i].u - x[j][i].u)*dhy;
282:       f[j][i].temp  = x[j][i].temp-x[j+1][i].temp;
283:     }
284:   }

286:   /* Test whether we are on the top edge of the global array */
287:   if (yinte == info->my) {
288:     j     = info->my - 1;
289:     yinte = yinte - 1;
290:     /* top edge */
291:     for (i=info->xs; i<info->xs+info->xm; i++) {
292:       f[j][i].u     = x[j][i].u - lid;
293:       f[j][i].v     = x[j][i].v;
294:       f[j][i].omega = x[j][i].omega + (x[j][i].u - x[j-1][i].u)*dhy;
295:       f[j][i].temp  = x[j][i].temp-x[j-1][i].temp;
296:     }
297:   }

299:   /* Test whether we are on the left edge of the global array */
300:   if (xints == 0) {
301:     i     = 0;
302:     xints = xints + 1;
303:     /* left edge */
304:     for (j=info->ys; j<info->ys+info->ym; j++) {
305:       f[j][i].u     = x[j][i].u;
306:       f[j][i].v     = x[j][i].v;
307:       f[j][i].omega = x[j][i].omega - (x[j][i+1].v - x[j][i].v)*dhx;
308:       f[j][i].temp  = x[j][i].temp;
309:     }
310:   }

312:   /* Test whether we are on the right edge of the global array */
313:   if (xinte == info->mx) {
314:     i     = info->mx - 1;
315:     xinte = xinte - 1;
316:     /* right edge */
317:     for (j=info->ys; j<info->ys+info->ym; j++) {
318:       f[j][i].u     = x[j][i].u;
319:       f[j][i].v     = x[j][i].v;
320:       f[j][i].omega = x[j][i].omega - (x[j][i].v - x[j][i-1].v)*dhx;
321:       f[j][i].temp  = x[j][i].temp - (PetscReal)(grashof>0);
322:     }
323:   }

325:   /* Compute over the interior points */
326:   for (j=yints; j<yinte; j++) {
327:     for (i=xints; i<xinte; i++) {

329:       /*
330:        convective coefficients for upwinding
331:       */
332:       vx  = x[j][i].u; avx = PetscAbsScalar(vx);
333:       vxp = .5*(vx+avx); vxm = .5*(vx-avx);
334:       vy  = x[j][i].v; avy = PetscAbsScalar(vy);
335:       vyp = .5*(vy+avy); vym = .5*(vy-avy);

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

343:       /* V velocity */
344:       u         = x[j][i].v;
345:       uxx       = (2.0*u - x[j][i-1].v - x[j][i+1].v)*hydhx;
346:       uyy       = (2.0*u - x[j-1][i].v - x[j+1][i].v)*hxdhy;
347:       f[j][i].v = uxx + uyy + .5*(x[j][i+1].omega-x[j][i-1].omega)*hy;

349:       /* Omega */
350:       u             = x[j][i].omega;
351:       uxx           = (2.0*u - x[j][i-1].omega - x[j][i+1].omega)*hydhx;
352:       uyy           = (2.0*u - x[j-1][i].omega - x[j+1][i].omega)*hxdhy;
353:       f[j][i].omega = uxx + uyy + (vxp*(u - x[j][i-1].omega) + vxm*(x[j][i+1].omega - u))*hy +
354:                       (vyp*(u - x[j-1][i].omega) + vym*(x[j+1][i].omega - u))*hx -
355:                       .5*grashof*(x[j][i+1].temp - x[j][i-1].temp)*hy;

357:       /* Temperature */
358:       u            = x[j][i].temp;
359:       uxx          = (2.0*u - x[j][i-1].temp - x[j][i+1].temp)*hydhx;
360:       uyy          = (2.0*u - x[j-1][i].temp - x[j+1][i].temp)*hxdhy;
361:       f[j][i].temp =  uxx + uyy  + prandtl*((vxp*(u - x[j][i-1].temp) + vxm*(x[j][i+1].temp - u))*hy +
362:                                             (vyp*(u - x[j-1][i].temp) + vym*(x[j+1][i].temp - u))*hx);
363:     }
364:   }

366:   /*
367:      Flop count (multiply-adds are counted as 2 operations)
368:   */
369:   PetscLogFlops(84.0*info->ym*info->xm);
370:   return(0);
371: }

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

402:   grashof = user->grashof;
403:   prandtl = user->prandtl;
404:   lid     = user->lidvelocity;
405:   tot_its = 0;
406:   SNESNGSGetTolerances(snes,&rtol,&atol,&stol,&max_its);
407:   SNESNGSGetSweeps(snes,&sweeps);
408:   SNESGetDM(snes,(DM*)&da);
409:   DMGetLocalVector(da,&localX);
410:   if (B) {
411:     DMGetLocalVector(da,&localB);
412:   }
413:   /*
414:      Scatter ghost points to local vector, using the 2-step process
415:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
416:   */
417:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
418:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
419:   if (B) {
420:     DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);
421:     DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);
422:   }
423:   DMDAGetLocalInfo(da,&info);
424:   DMDAVecGetArray(da,localX,&x);
425:   if (B) {
426:     DMDAVecGetArrayRead(da,localB,&b);
427:   }
428:   /* looks like a combination of the formfunction / formjacobian routines */
429:   dhx   = (PetscReal)(info.mx-1);dhy   = (PetscReal)(info.my-1);
430:   hx    = 1.0/dhx;               hy    = 1.0/dhy;
431:   hxdhy = hx*dhy;                hydhx = hy*dhx;

433:   xints = info.xs; xinte = info.xs+info.xm; yints = info.ys; yinte = info.ys+info.ym;

435:   /* Set the boundary conditions on the momentum equations */
436:   /* Test whether we are on the bottom edge of the global array */
437:   if (yints == 0) {
438:     j     = 0;
439:     /* bottom edge */
440:     for (i=info.xs; i<info.xs+info.xm; i++) {

442:       if (B) {
443:         bjiu = b[j][i].u;
444:         bjiv = b[j][i].v;
445:       } else {
446:         bjiu = 0.0;
447:         bjiv = 0.0;
448:       }
449:       x[j][i].u = 0.0 + bjiu;
450:       x[j][i].v = 0.0 + bjiv;
451:     }
452:   }

454:   /* Test whether we are on the top edge of the global array */
455:   if (yinte == info.my) {
456:     j     = info.my - 1;
457:     /* top edge */
458:     for (i=info.xs; i<info.xs+info.xm; i++) {
459:       if (B) {
460:         bjiu = b[j][i].u;
461:         bjiv = b[j][i].v;
462:       } else {
463:         bjiu = 0.0;
464:         bjiv = 0.0;
465:       }
466:       x[j][i].u = lid + bjiu;
467:       x[j][i].v = bjiv;
468:     }
469:   }

471:   /* Test whether we are on the left edge of the global array */
472:   if (xints == 0) {
473:     i     = 0;
474:     /* left edge */
475:     for (j=info.ys; j<info.ys+info.ym; j++) {
476:       if (B) {
477:         bjiu = b[j][i].u;
478:         bjiv = b[j][i].v;
479:       } else {
480:         bjiu = 0.0;
481:         bjiv = 0.0;
482:       }
483:       x[j][i].u = 0.0 + bjiu;
484:       x[j][i].v = 0.0 + bjiv;
485:     }
486:   }

488:   /* Test whether we are on the right edge of the global array */
489:   if (xinte == info.mx) {
490:     i     = info.mx - 1;
491:     /* right edge */
492:     for (j=info.ys; j<info.ys+info.ym; j++) {
493:       if (B) {
494:         bjiu = b[j][i].u;
495:         bjiv = b[j][i].v;
496:       } else {
497:         bjiu = 0.0;
498:         bjiv = 0.0;
499:       }
500:       x[j][i].u = 0.0 + bjiu;
501:       x[j][i].v = 0.0 + bjiv;
502:     }
503:   }

505:   for (k=0; k < sweeps; k++) {
506:     for (j=info.ys; j<info.ys + info.ym; j++) {
507:       for (i=info.xs; i<info.xs + info.xm; i++) {
508:         ptconverged = PETSC_FALSE;
509:         pfnorm0     = 0.0;
510:         fu          = 0.0;
511:         fv          = 0.0;
512:         fomega      = 0.0;
513:         ftemp       = 0.0;
514:         /*  Run Newton's method on a single grid point */
515:         for (l = 0; l < max_its && !ptconverged; l++) {
516:           if (B) {
517:             bjiu     = b[j][i].u;
518:             bjiv     = b[j][i].v;
519:             bjiomega = b[j][i].omega;
520:             bjitemp  = b[j][i].temp;
521:           } else {
522:             bjiu     = 0.0;
523:             bjiv     = 0.0;
524:             bjiomega = 0.0;
525:             bjitemp  = 0.0;
526:           }

528:           if (i != 0 && i != info.mx - 1 && j != 0 && j != info.my-1) {
529:             /* U velocity */
530:             u     = x[j][i].u;
531:             uxx   = (2.0*u - x[j][i-1].u - x[j][i+1].u)*hydhx;
532:             uyy   = (2.0*u - x[j-1][i].u - x[j+1][i].u)*hxdhy;
533:             fu    = uxx + uyy - .5*(x[j+1][i].omega-x[j-1][i].omega)*hx - bjiu;
534:             dfudu = 2.0*(hydhx + hxdhy);
535:             /* V velocity */
536:             u     = x[j][i].v;
537:             uxx   = (2.0*u - x[j][i-1].v - x[j][i+1].v)*hydhx;
538:             uyy   = (2.0*u - x[j-1][i].v - x[j+1][i].v)*hxdhy;
539:             fv    = uxx + uyy + .5*(x[j][i+1].omega-x[j][i-1].omega)*hy - bjiv;
540:             dfvdv = 2.0*(hydhx + hxdhy);
541:             /*
542:              convective coefficients for upwinding
543:              */
544:             vx  = x[j][i].u; avx = PetscAbsScalar(vx);
545:             vxp = .5*(vx+avx); vxm = .5*(vx-avx);
546:             vy  = x[j][i].v; avy = PetscAbsScalar(vy);
547:             vyp = .5*(vy+avy); vym = .5*(vy-avy);
548:             /* Omega */
549:             u      = x[j][i].omega;
550:             uxx    = (2.0*u - x[j][i-1].omega - x[j][i+1].omega)*hydhx;
551:             uyy    = (2.0*u - x[j-1][i].omega - x[j+1][i].omega)*hxdhy;
552:             fomega = uxx + uyy +  (vxp*(u - x[j][i-1].omega) + vxm*(x[j][i+1].omega - u))*hy +
553:                      (vyp*(u - x[j-1][i].omega) + vym*(x[j+1][i].omega - u))*hx -
554:                      .5*grashof*(x[j][i+1].temp - x[j][i-1].temp)*hy - bjiomega;
555:             /* convective coefficient derivatives */
556:             dfodo = 2.0*(hydhx + hxdhy) + ((vxp - vxm)*hy + (vyp - vym)*hx);
557:             if (PetscRealPart(vx) > 0.0) dfodu = (u - x[j][i-1].omega)*hy;
558:             else dfodu = (x[j][i+1].omega - u)*hy;

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

563:             /* Temperature */
564:             u     = x[j][i].temp;
565:             uxx   = (2.0*u - x[j][i-1].temp - x[j][i+1].temp)*hydhx;
566:             uyy   = (2.0*u - x[j-1][i].temp - x[j+1][i].temp)*hxdhy;
567:             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;
568:             dftdt = 2.0*(hydhx + hxdhy) + prandtl*((vxp - vxm)*hy + (vyp - vym)*hx);
569:             if (PetscRealPart(vx) > 0.0) dftdu = prandtl*(u - x[j][i-1].temp)*hy;
570:             else dftdu = prandtl*(x[j][i+1].temp - u)*hy;

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

575:             /* invert the system:
576:              [ dfu / du     0        0        0    ][yu] = [fu]
577:              [     0    dfv / dv     0        0    ][yv]   [fv]
578:              [ dfo / du dfo / dv dfo / do     0    ][yo]   [fo]
579:              [ dft / du dft / dv     0    dft / dt ][yt]   [ft]
580:              by simple back-substitution
581:            */
582:             yu = fu / dfudu;
583:             yv = fv / dfvdv;
584:             yo = (fomega - (dfodu*yu + dfodv*yv)) / dfodo;
585:             yt = (ftemp - (dftdu*yu + dftdv*yv)) / dftdt;

587:             x[j][i].u     = x[j][i].u - yu;
588:             x[j][i].v     = x[j][i].v - yv;
589:             x[j][i].temp  = x[j][i].temp - yt;
590:             x[j][i].omega = x[j][i].omega - yo;
591:           }
592:           if (i == 0) {
593:             fomega        = x[j][i].omega - (x[j][i+1].v - x[j][i].v)*dhx - bjiomega;
594:             ftemp         = x[j][i].temp - bjitemp;
595:             yo            = fomega;
596:             yt            = ftemp;
597:             x[j][i].omega = x[j][i].omega - fomega;
598:             x[j][i].temp  = x[j][i].temp - ftemp;
599:           }
600:           if (i == info.mx - 1) {
601:             fomega        = x[j][i].omega - (x[j][i].v - x[j][i-1].v)*dhx - bjiomega;
602:             ftemp         = x[j][i].temp - (PetscReal)(grashof>0) - bjitemp;
603:             yo            = fomega;
604:             yt            = ftemp;
605:             x[j][i].omega = x[j][i].omega - fomega;
606:             x[j][i].temp  = x[j][i].temp - ftemp;
607:           }
608:           if (j == 0) {
609:             fomega        = x[j][i].omega + (x[j+1][i].u - x[j][i].u)*dhy - bjiomega;
610:             ftemp         = x[j][i].temp-x[j+1][i].temp - bjitemp;
611:             yo            = fomega;
612:             yt            = ftemp;
613:             x[j][i].omega = x[j][i].omega - fomega;
614:             x[j][i].temp  = x[j][i].temp - ftemp;
615:           }
616:           if (j == info.my - 1) {
617:             fomega        = x[j][i].omega + (x[j][i].u - x[j-1][i].u)*dhy - bjiomega;
618:             ftemp         = x[j][i].temp-x[j-1][i].temp - bjitemp;
619:             yo            = fomega;
620:             yt            = ftemp;
621:             x[j][i].omega = x[j][i].omega - fomega;
622:             x[j][i].temp  = x[j][i].temp - ftemp;
623:           }
624:           tot_its++;
625:           pfnorm = PetscRealPart(fu*fu + fv*fv + fomega*fomega + ftemp*ftemp);
626:           pfnorm = PetscSqrtReal(pfnorm);
627:           pynorm = PetscRealPart(yu*yu + yv*yv + yo*yo + yt*yt);
628:           pynorm = PetscSqrtReal(pynorm);
629:           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);
630:           pxnorm = PetscSqrtReal(pxnorm);
631:           if (l == 0) pfnorm0 = pfnorm;
632:           if (rtol*pfnorm0 >pfnorm || atol > pfnorm || pxnorm*stol > pynorm) ptconverged = PETSC_TRUE;
633:         }
634:       }
635:     }
636:   }
637:   DMDAVecRestoreArray(da,localX,&x);
638:   if (B) {
639:     DMDAVecRestoreArrayRead(da,localB,&b);
640:   }
641:   DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
642:   DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
643:   PetscLogFlops(tot_its*(84.0 + 41.0 + 26.0));
644:   DMRestoreLocalVector(da,&localX);
645:   if (B) {
646:     DMRestoreLocalVector(da,&localB);
647:   }
648:   return(0);
649: }


652: /*TEST

654:    test:
655:       nsize: 2
656:       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full
657:       requires: !single

659:    test:
660:       suffix: 10
661:       nsize: 3
662:       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type symmetric_multiplicative -snes_view -da_refine 1 -ksp_type fgmres
663:       requires: !single

665:    test:
666:       suffix: 11
667:       nsize: 4
668:       requires: pastix
669:       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

671:    test:
672:       suffix: 12
673:       nsize: 12
674:       requires: pastix
675:       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

677:    test:
678:       suffix: 13
679:       nsize: 3
680:       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
681:       requires: !single

683:    test:
684:       suffix: 14
685:       nsize: 4
686:       args: -snes_monitor_short -pc_type mg -dm_mat_type baij -mg_coarse_pc_type bjacobi -da_refine 3 -ksp_type fgmres
687:       requires: !single

689:    test:
690:       suffix: 14_ds
691:       nsize: 4
692:       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
693:       output_file: output/ex19_2.out
694:       requires: !single

696:    test:
697:       suffix: 17
698:       args: -snes_monitor_short -ksp_pc_side right
699:       requires: !single

701:    test:
702:       suffix: 18
703:       args: -ksp_monitor_snes_lg -ksp_pc_side right
704:       requires: x !single

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

712:    test:
713:       suffix: 2_bcols1
714:       nsize: 4
715:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols 1> ex19_1.tmp 2>&1
716:       output_file: output/ex19_2.out
717:       requires: !single

719:    test:
720:       suffix: 3
721:       nsize: 4
722:       requires: mumps
723:       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

725:    test:
726:       suffix: 4
727:       nsize: 12
728:       requires: mumps
729:       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
730:       output_file: output/ex19_3.out

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

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

742:       requires: !single
743:    test:
744:       suffix: 8
745:       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
746:       requires: !single

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

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

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

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

773:    test:
774:       suffix: bjacobi
775:       nsize: 4
776:       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
777:       requires: !single

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

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

790:    test:
791:       suffix: composite_fieldsplit
792:       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
793:       requires: !single

795:    test:
796:       suffix: composite_fieldsplit_bjacobi
797:       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
798:       requires: !single

800:    test:
801:       suffix: composite_fieldsplit_bjacobi_2
802:       nsize: 4
803:       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
804:       requires: !single

806:    test:
807:       suffix: composite_gs_newton
808:       nsize: 2
809:       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
810:       requires: !single

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

817:    test:
818:       suffix: draw
819:       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
820:       requires: x !single

822:    test:
823:       suffix: drawports
824:       args: -snes_monitor_solution draw::draw_ports -da_refine 1
825:       output_file: output/ex19_draw.out
826:       requires: x !single

828:    test:
829:       suffix: fas
830:       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
831:       requires: !single

833:    test:
834:       suffix: fas_full
835:       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
836:       requires: !single

838:    test:
839:       suffix: fdcoloring_ds
840:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
841:       output_file: output/ex19_2.out
842:       requires: !single

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

850:    test:
851:       suffix: fdcoloring_ds_bcols1
852:       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols 1
853:       output_file: output/ex19_2.out
854:       requires: !single

856:    test:
857:       suffix: fdcoloring_wp
858:       args: -da_refine 3 -snes_monitor_short -pc_type mg
859:       requires: !single

861:    test:
862:       suffix: fdcoloring_wp_baij
863:       args: -da_refine 3 -snes_monitor_short -pc_type mg -dm_mat_type baij
864:       output_file: output/ex19_fdcoloring_wp.out
865:       requires: !single

867:    test:
868:       suffix: fdcoloring_wp_bcols1
869:       args: -da_refine 3 -snes_monitor_short -pc_type mg -mat_fd_coloring_bcols 1
870:       output_file: output/ex19_fdcoloring_wp.out
871:       requires: !single

873:    test:
874:       suffix: fieldsplit_2
875:       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
876:       requires: !single

878:    test:
879:       suffix: fieldsplit_3
880:       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
881:       requires: !single

883:    test:
884:       suffix: fieldsplit_4
885:       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
886:       requires: !single

888:    test:
889:       suffix: fieldsplit_hypre
890:       nsize: 2
891:       requires: hypre mumps
892:       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

894:    test:
895:       suffix: fieldsplit_mumps
896:       nsize: 2
897:       requires: mumps
898:       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
899:       output_file: output/ex19_fieldsplit_5.out

901:    test:
902:       suffix: greedy_coloring
903:       nsize: 2
904:       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
905:       requires: !single

907:    test:
908:       suffix: hypre
909:       nsize: 2
910:       requires: hypre
911:       args: -da_refine 3 -snes_monitor_short -pc_type hypre

913:    test:
914:       suffix: ibcgs
915:       nsize: 2
916:       args: -ksp_type ibcgs -ksp_monitor_short -da_refine 2 -snes_view
917:       requires: !complex !single

919:    test:
920:       suffix: kaczmarz
921:       nsize: 2
922:       args: -pc_type kaczmarz -ksp_monitor_short -snes_monitor_short -snes_view
923:       requires: !single

925:    test:
926:       suffix: klu
927:       requires: suitesparse
928:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu
929:       output_file: output/ex19_superlu.out

931:    test:
932:       suffix: klu_2
933:       requires: suitesparse
934:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_ordering PETSC
935:       output_file: output/ex19_superlu.out

937:    test:
938:       suffix: klu_3
939:       requires: suitesparse
940:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_use_btf 0
941:       output_file: output/ex19_superlu.out

943:    test:
944:       suffix: ml
945:       nsize: 2
946:       requires: ml
947:       args: -da_refine 3 -snes_monitor_short -pc_type ml

949:    test:
950:       suffix: ngmres_fas
951:       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
952:       requires: !single

954:    test:
955:       suffix: ngmres_fas_gssecant
956:       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
957:       requires: !single

959:    test:
960:       suffix: ngmres_fas_ms
961:       nsize: 2
962:       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
963:       requires: !single

965:    test:
966:       suffix: ngmres_nasm
967:       nsize: 4
968:       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
969:       requires: !single

971:    test:
972:       suffix: ngs
973:       args: -ksp_monitor_short -snes_type ngs -snes_view -snes_monitor -snes_rtol 1e-4
974:       requires: !single

976:    test:
977:       suffix: ngs_fd
978:       args: -ksp_monitor_short -snes_type ngs -snes_ngs_secant -snes_view -snes_monitor -snes_rtol 1e-4
979:       requires: !single

981:    test:
982:       suffix: parms
983:       nsize: 2
984:       requires: parms
985:       args: -pc_type parms -ksp_monitor_short -snes_view

987:    test:
988:       suffix: superlu
989:       requires: superlu
990:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu

992:    test:
993:       suffix: superlu_sell
994:       requires: superlu
995:       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
996:       output_file: output/ex19_superlu.out

998:    test:
999:       suffix: superlu_dist
1000:       requires: superlu_dist
1001:       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1002:       output_file: output/ex19_superlu.out

1004:    test:
1005:       suffix: superlu_dist_2
1006:       nsize: 2
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_equil
1013:       requires: superlu
1014:       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

1016:    test:
1017:       suffix: superlu_equil_sell
1018:       requires: superlu
1019:       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
1020:       output_file: output/ex19_superlu_equil.out

1022:    test:
1023:       suffix: tcqmr
1024:       args: -da_refine 1 -ksp_monitor_short -ksp_type tcqmr
1025:       requires: !single

1027:    test:
1028:       suffix: tfqmr
1029:       args: -da_refine 1 -ksp_monitor_short -ksp_type tfqmr
1030:       requires: !single

1032:    test:
1033:       suffix: umfpack
1034:       requires: suitesparse
1035:       args: -da_refine 2 -pc_type lu -pc_factor_mat_solver_type umfpack -snes_view -snes_monitor_short -ksp_monitor_short

1037:    test:
1038:       suffix: tut_1
1039:       nsize: 4
1040:       requires: !single
1041:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view

1043:    test:
1044:       suffix: tut_2
1045:       nsize: 4
1046:       requires: !single
1047:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg

1049:    test:
1050:       suffix: tut_3
1051:       nsize: 4
1052:       requires: hypre !single
1053:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre

1055:    test:
1056:       suffix: tut_8
1057:       nsize: 4
1058:       requires: ml !single
1059:       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml

1061:    test:
1062:       suffix: tut_4
1063:       nsize: 1
1064:       requires: !single
1065:       args: -da_refine 5 -log_view
1066:       filter: head -n 2
1067:       filter_output: head -n 2

1069:    test:
1070:       suffix: tut_5
1071:       nsize: 1
1072:       requires: !single
1073:       args: -da_refine 5 -log_view -pc_type mg
1074:       filter: head -n 2
1075:       filter_output: head -n 2

1077:    test:
1078:       suffix: tut_6
1079:       nsize: 4
1080:       requires: !single
1081:       args: -da_refine 5 -log_view
1082:       filter: head -n 2
1083:       filter_output: head -n 2

1085:    test:
1086:       suffix: tut_7
1087:       nsize: 4
1088:       requires: !single
1089:       args: -da_refine 5 -log_view -pc_type mg
1090:       filter: head -n 2
1091:       filter_output: head -n 2

1093:    test:
1094:       suffix: cuda_1
1095:       nsize: 1
1096:       requires: cuda
1097:       args: -snes_monitor -dm_mat_type seqaijcusparse -dm_vec_type seqcuda -pc_type gamg -ksp_monitor


1100:    test:
1101:       suffix: cuda_2
1102:       nsize: 3
1103:       requires: cuda
1104:       args: -snes_monitor -dm_mat_type mpiaijcusparse -dm_vec_type mpicuda -pc_type gamg -ksp_monitor


1107: TEST*/