Actual source code: ex5.c

petsc-master 2019-12-13
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  2: static char help[] = "Bratu nonlinear PDE in 2d.\n\
  3: We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
  4: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
  5: The command line options include:\n\
  6:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
  7:      problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n\
  8:   -m_par/n_par <parameter>, where <parameter> indicates an integer\n \
  9:       that MMS3 will be evaluated with 2^m_par, 2^n_par";

 11: /*T
 12:    Concepts: SNES^parallel Bratu example
 13:    Concepts: DMDA^using distributed arrays;
 14:    Concepts: IS coloirng types;
 15:    Processors: n
 16: T*/



 20: /* ------------------------------------------------------------------------

 22:     Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 23:     the partial differential equation

 25:             -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,

 27:     with boundary conditions

 29:              u = 0  for  x = 0, x = 1, y = 0, y = 1.

 31:     A finite difference approximation with the usual 5-point stencil
 32:     is used to discretize the boundary value problem to obtain a nonlinear
 33:     system of equations.


 36:       This example shows how geometric multigrid can be run transparently with a nonlinear solver so long
 37:       as SNESSetDM() is provided. Example usage

 39:       ./ex5 -pc_type mg -ksp_monitor  -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17
 40:              -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full

 42:       or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
 43:          multigrid levels, it will be determined automatically based on the number of refinements done)

 45:       ./ex5 -pc_type mg -ksp_monitor  -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
 46:              -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full

 48:   ------------------------------------------------------------------------- */

 50: /*
 51:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
 52:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
 53: */
 54:  #include <petscdm.h>
 55:  #include <petscdmda.h>
 56:  #include <petscsnes.h>
 57:  #include <petscmatlab.h>
 58: #include <petsc/private/snesimpl.h> /* For SNES_Solve event */

 60: /*
 61:    User-defined application context - contains data needed by the
 62:    application-provided call-back routines, FormJacobianLocal() and
 63:    FormFunctionLocal().
 64: */
 65: typedef struct AppCtx AppCtx;
 66: struct AppCtx {
 67:   PetscReal param;          /* test problem parameter */
 68:   PetscInt  m,n;            /* MMS3 parameters */
 69:   PetscErrorCode (*mms_solution)(AppCtx*,const DMDACoor2d*,PetscScalar*);
 70:   PetscErrorCode (*mms_forcing)(AppCtx*,const DMDACoor2d*,PetscScalar*);
 71: };

 73: /*
 74:    User-defined routines
 75: */
 76: extern PetscErrorCode FormInitialGuess(DM,AppCtx*,Vec);
 77: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
 78: extern PetscErrorCode FormExactSolution(DM,AppCtx*,Vec);
 79: extern PetscErrorCode ZeroBCSolution(AppCtx*,const DMDACoor2d*,PetscScalar*);
 80: extern PetscErrorCode MMSSolution1(AppCtx*,const DMDACoor2d*,PetscScalar*);
 81: extern PetscErrorCode MMSForcing1(AppCtx*,const DMDACoor2d*,PetscScalar*);
 82: extern PetscErrorCode MMSSolution2(AppCtx*,const DMDACoor2d*,PetscScalar*);
 83: extern PetscErrorCode MMSForcing2(AppCtx*,const DMDACoor2d*,PetscScalar*);
 84: extern PetscErrorCode MMSSolution3(AppCtx*,const DMDACoor2d*,PetscScalar*);
 85: extern PetscErrorCode MMSForcing3(AppCtx*,const DMDACoor2d*,PetscScalar*);
 86: extern PetscErrorCode MMSSolution4(AppCtx*,const DMDACoor2d*,PetscScalar*);
 87: extern PetscErrorCode MMSForcing4(AppCtx*,const DMDACoor2d*,PetscScalar*);
 88: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,Mat,AppCtx*);
 89: extern PetscErrorCode FormObjectiveLocal(DMDALocalInfo*,PetscScalar**,PetscReal*,AppCtx*);
 90: #if defined(PETSC_HAVE_MATLAB_ENGINE)
 91: extern PetscErrorCode FormFunctionMatlab(SNES,Vec,Vec,void*);
 92: #endif
 93: extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);

 95: int main(int argc,char **argv)
 96: {
 97:   SNES           snes;                         /* nonlinear solver */
 98:   Vec            x;                            /* solution vector */
 99:   AppCtx         user;                         /* user-defined work context */
100:   PetscInt       its;                          /* iterations for convergence */
102:   PetscReal      bratu_lambda_max = 6.81;
103:   PetscReal      bratu_lambda_min = 0.;
104:   PetscInt       MMS              = 0;
105:   PetscBool      flg              = PETSC_FALSE;
106:   DM             da;
107: #if defined(PETSC_HAVE_MATLAB_ENGINE)
108:   Vec            r               = NULL;
109:   PetscBool      matlab_function = PETSC_FALSE;
110: #endif
111:   KSP            ksp;
112:   PetscInt       lits,slits;

114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115:      Initialize program
116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:      Initialize problem parameters
122:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123:   user.param = 6.0;
124:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
125:   if (user.param > bratu_lambda_max || user.param < bratu_lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda, %g, is out of range, [%g, %g]", user.param, bratu_lambda_min, bratu_lambda_max);
126:   PetscOptionsGetInt(NULL,NULL,"-mms",&MMS,NULL);
127:   if (MMS == 3) {
128:     PetscInt mPar = 2, nPar = 1;
129:     PetscOptionsGetInt(NULL,NULL,"-m_par",&mPar,NULL);
130:     PetscOptionsGetInt(NULL,NULL,"-n_par",&nPar,NULL);
131:     user.m = PetscPowInt(2,mPar);
132:     user.n = PetscPowInt(2,nPar);
133:   }

135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136:      Create nonlinear solver context
137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138:   SNESCreate(PETSC_COMM_WORLD,&snes);
139:   SNESSetCountersReset(snes,PETSC_FALSE);
140:   SNESSetNGS(snes, NonlinearGS, NULL);

142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143:      Create distributed array (DMDA) to manage parallel grid and vectors
144:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
146:   DMSetFromOptions(da);
147:   DMSetUp(da);
148:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
149:   DMSetApplicationContext(da,&user);
150:   SNESSetDM(snes,da);
151:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:      Extract global vectors from DMDA; then duplicate for remaining
153:      vectors that are the same types
154:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155:   DMCreateGlobalVector(da,&x);

157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158:      Set local function evaluation routine
159:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160:   user.mms_solution = ZeroBCSolution;
161:   switch (MMS) {
162:   case 0: user.mms_solution = NULL; user.mms_forcing = NULL;
163:   case 1: user.mms_solution = MMSSolution1; user.mms_forcing = MMSForcing1; break;
164:   case 2: user.mms_solution = MMSSolution2; user.mms_forcing = MMSForcing2; break;
165:   case 3: user.mms_solution = MMSSolution3; user.mms_forcing = MMSForcing3; break;
166:   case 4: user.mms_solution = MMSSolution4; user.mms_forcing = MMSForcing4; break;
167:   default: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_USER,"Unknown MMS type %d",MMS);
168:   }
169:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(DMDASNESFunction)FormFunctionLocal,&user);
170:   PetscOptionsGetBool(NULL,NULL,"-fd",&flg,NULL);
171:   if (!flg) {
172:     DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);
173:   }

175:   PetscOptionsGetBool(NULL,NULL,"-obj",&flg,NULL);
176:   if (flg) {
177:     DMDASNESSetObjectiveLocal(da,(DMDASNESObjective)FormObjectiveLocal,&user);
178:   }

180: #if defined(PETSC_HAVE_MATLAB_ENGINE)
181:   PetscOptionsGetBool(NULL,NULL,"-matlab_function",&matlab_function,0);
182:   if (matlab_function) {
183:     VecDuplicate(x,&r);
184:     SNESSetFunction(snes,r,FormFunctionMatlab,&user);
185:   }
186: #endif

188:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189:      Customize nonlinear solver; set runtime options
190:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191:   SNESSetFromOptions(snes);

193:   FormInitialGuess(da,&user,x);

195:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196:      Solve nonlinear system
197:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198:   SNESSolve(snes,NULL,x);
199:   SNESGetIterationNumber(snes,&its);

201:   SNESGetLinearSolveIterations(snes,&slits);
202:   SNESGetKSP(snes,&ksp);
203:   KSPGetTotalIterations(ksp,&lits);
204:   if (lits != slits) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Number of total linear iterations reported by SNES %D does not match reported by KSP %D",slits,lits);
205:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
206:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209:      If using MMS, check the l_2 error
210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211:   if (MMS) {
212:     Vec       e;
213:     PetscReal errorl2, errorinf;
214:     PetscInt  N;

216:     VecDuplicate(x, &e);
217:     PetscObjectViewFromOptions((PetscObject) x, NULL, "-sol_view");
218:     FormExactSolution(da, &user, e);
219:     PetscObjectViewFromOptions((PetscObject) e, NULL, "-exact_view");
220:     VecAXPY(e, -1.0, x);
221:     PetscObjectViewFromOptions((PetscObject) e, NULL, "-error_view");
222:     VecNorm(e, NORM_2, &errorl2);
223:     VecNorm(e, NORM_INFINITY, &errorinf);
224:     VecGetSize(e, &N);
225:     PetscPrintf(PETSC_COMM_WORLD, "N: %D error L2 %g inf %g\n", N, (double) errorl2/PetscSqrtReal(N), (double) errorinf);
226:     VecDestroy(&e);
227:     PetscLogEventSetDof(SNES_Solve, 0, N);
228:     PetscLogEventSetError(SNES_Solve, 0, errorl2/PetscSqrtReal(N));
229:   }

231:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232:      Free work space.  All PETSc objects should be destroyed when they
233:      are no longer needed.
234:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235: #if defined(PETSC_HAVE_MATLAB_ENGINE)
236:   VecDestroy(&r);
237: #endif
238:   VecDestroy(&x);
239:   SNESDestroy(&snes);
240:   DMDestroy(&da);
241:   PetscFinalize();
242:   return ierr;
243: }
244: /* ------------------------------------------------------------------- */
245: /*
246:    FormInitialGuess - Forms initial approximation.

248:    Input Parameters:
249:    da - The DM
250:    user - user-defined application context

252:    Output Parameter:
253:    X - vector
254:  */
255: PetscErrorCode FormInitialGuess(DM da,AppCtx *user,Vec X)
256: {
257:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
259:   PetscReal      lambda,temp1,temp,hx,hy;
260:   PetscScalar    **x;

263:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

265:   lambda = user->param;
266:   hx     = 1.0/(PetscReal)(Mx-1);
267:   hy     = 1.0/(PetscReal)(My-1);
268:   temp1  = lambda/(lambda + 1.0);

270:   /*
271:      Get a pointer to vector data.
272:        - For default PETSc vectors, VecGetArray() returns a pointer to
273:          the data array.  Otherwise, the routine is implementation dependent.
274:        - You MUST call VecRestoreArray() when you no longer need access to
275:          the array.
276:   */
277:   DMDAVecGetArray(da,X,&x);

279:   /*
280:      Get local grid boundaries (for 2-dimensional DMDA):
281:        xs, ys   - starting grid indices (no ghost points)
282:        xm, ym   - widths of local grid (no ghost points)

284:   */
285:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

287:   /*
288:      Compute initial guess over the locally owned part of the grid
289:   */
290:   for (j=ys; j<ys+ym; j++) {
291:     temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
292:     for (i=xs; i<xs+xm; i++) {
293:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
294:         /* boundary conditions are all zero Dirichlet */
295:         x[j][i] = 0.0;
296:       } else {
297:         x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
298:       }
299:     }
300:   }

302:   /*
303:      Restore vector
304:   */
305:   DMDAVecRestoreArray(da,X,&x);
306:   return(0);
307: }

309: /*
310:   FormExactSolution - Forms MMS solution

312:   Input Parameters:
313:   da - The DM
314:   user - user-defined application context

316:   Output Parameter:
317:   X - vector
318:  */
319: PetscErrorCode FormExactSolution(DM da, AppCtx *user, Vec U)
320: {
321:   DM             coordDA;
322:   Vec            coordinates;
323:   DMDACoor2d   **coords;
324:   PetscScalar  **u;
325:   PetscInt       xs, ys, xm, ym, i, j;

329:   DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
330:   DMGetCoordinateDM(da, &coordDA);
331:   DMGetCoordinates(da, &coordinates);
332:   DMDAVecGetArray(coordDA, coordinates, &coords);
333:   DMDAVecGetArray(da, U, &u);
334:   for (j = ys; j < ys+ym; ++j) {
335:     for (i = xs; i < xs+xm; ++i) {
336:       user->mms_solution(user,&coords[j][i],&u[j][i]);
337:     }
338:   }
339:   DMDAVecRestoreArray(da, U, &u);
340:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
341:   return(0);
342: }

344: PetscErrorCode ZeroBCSolution(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
345: {
346:   u[0] = 0.;
347:   return 0;
348: }

350: /* The functions below evaluate the MMS solution u(x,y) and associated forcing

352:      f(x,y) = -u_xx - u_yy - lambda exp(u)

354:   such that u(x,y) is an exact solution with f(x,y) as the right hand side forcing term.
355:  */
356: PetscErrorCode MMSSolution1(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
357: {
358:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
359:   u[0] = x*(1 - x)*y*(1 - y);
360:   PetscLogFlops(5);
361:   return 0;
362: }
363: PetscErrorCode MMSForcing1(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
364: {
365:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
366:   f[0] = 2*x*(1 - x) + 2*y*(1 - y) - user->param*PetscExpReal(x*(1 - x)*y*(1 - y));
367:   return 0;
368: }

370: PetscErrorCode MMSSolution2(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
371: {
372:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
373:   u[0] = PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y);
374:   PetscLogFlops(5);
375:   return 0;
376: }
377: PetscErrorCode MMSForcing2(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
378: {
379:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
380:   f[0] = 2*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y) - user->param*PetscExpReal(PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y));
381:   return 0;
382: }

384: PetscErrorCode MMSSolution3(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
385: {
386:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
387:   u[0] = PetscSinReal(user->m*PETSC_PI*x*(1-y))*PetscSinReal(user->n*PETSC_PI*y*(1-x));
388:   PetscLogFlops(5);
389:   return 0;
390: }
391: PetscErrorCode MMSForcing3(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
392: {
393:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
394:   PetscReal m = user->m, n = user->n, lambda = user->param;
395:   f[0] = (-(PetscExpReal(PetscSinReal(m*PETSC_PI*x*(1 - y))*PetscSinReal(n*PETSC_PI*(1 - x)*y))*lambda)
396:           + PetscSqr(PETSC_PI)*(-2*m*n*((-1 + x)*x + (-1 + y)*y)*PetscCosReal(m*PETSC_PI*x*(-1 + y))*PetscCosReal(n*PETSC_PI*(-1 + x)*y)
397:                                 + (PetscSqr(m)*(PetscSqr(x) + PetscSqr(-1 + y)) + PetscSqr(n)*(PetscSqr(-1 + x) + PetscSqr(y)))
398:                                 *PetscSinReal(m*PETSC_PI*x*(-1 + y))*PetscSinReal(n*PETSC_PI*(-1 + x)*y)));
399:   return 0;
400: }

402: PetscErrorCode MMSSolution4(AppCtx *user,const DMDACoor2d *c,PetscScalar *u)
403: {
404:   const PetscReal Lx = 1.,Ly = 1.;
405:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
406:   u[0] = (PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y));
407:   PetscLogFlops(9);
408:   return 0;
409: }
410: PetscErrorCode MMSForcing4(AppCtx *user,const DMDACoor2d *c,PetscScalar *f)
411: {
412:   const PetscReal Lx = 1.,Ly = 1.;
413:   PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y);
414:   f[0] = (2*PetscSqr(x)*(PetscSqr(x)-PetscSqr(Lx))*(PetscSqr(Ly)-6*PetscSqr(y))
415:           + 2*PetscSqr(y)*(PetscSqr(Lx)-6*PetscSqr(x))*(PetscSqr(y)-PetscSqr(Ly))
416:           - user->param*PetscExpReal((PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y))));
417:   return 0;
418: }

420: /* ------------------------------------------------------------------- */
421: /*
422:    FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch


425:  */
426: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
427: {
429:   PetscInt       i,j;
430:   PetscReal      lambda,hx,hy,hxdhy,hydhx;
431:   PetscScalar    u,ue,uw,un,us,uxx,uyy,mms_solution,mms_forcing;
432:   DMDACoor2d     c;

435:   lambda = user->param;
436:   hx     = 1.0/(PetscReal)(info->mx-1);
437:   hy     = 1.0/(PetscReal)(info->my-1);
438:   hxdhy  = hx/hy;
439:   hydhx  = hy/hx;
440:   /*
441:      Compute function over the locally owned part of the grid
442:   */
443:   for (j=info->ys; j<info->ys+info->ym; j++) {
444:     for (i=info->xs; i<info->xs+info->xm; i++) {
445:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
446:         c.x = i*hx; c.y = j*hy;
447:         user->mms_solution(user,&c,&mms_solution);
448:         f[j][i] = 2.0*(hydhx+hxdhy)*(x[j][i] - mms_solution);
449:       } else {
450:         u  = x[j][i];
451:         uw = x[j][i-1];
452:         ue = x[j][i+1];
453:         un = x[j-1][i];
454:         us = x[j+1][i];

456:         /* Enforce boundary conditions at neighboring points -- setting these values causes the Jacobian to be symmetric. */
457:         if (i-1 == 0) {c.x = (i-1)*hx; c.y = j*hy; user->mms_solution(user,&c,&uw);}
458:         if (i+1 == info->mx-1) {c.x = (i+1)*hx; c.y = j*hy; user->mms_solution(user,&c,&ue);}
459:         if (j-1 == 0) {c.x = i*hx; c.y = (j-1)*hy; user->mms_solution(user,&c,&un);}
460:         if (j+1 == info->my-1) {c.x = i*hx; c.y = (j+1)*hy; user->mms_solution(user,&c,&us);}

462:         uxx     = (2.0*u - uw - ue)*hydhx;
463:         uyy     = (2.0*u - un - us)*hxdhy;
464:         mms_forcing = 0;
465:         c.x = i*hx; c.y = j*hy;
466:         if (user->mms_forcing) {user->mms_forcing(user,&c,&mms_forcing);}
467:         f[j][i] = uxx + uyy - hx*hy*(lambda*PetscExpScalar(u) + mms_forcing);
468:       }
469:     }
470:   }
471:   PetscLogFlops(11.0*info->ym*info->xm);
472:   return(0);
473: }

475: /* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */
476: PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user)
477: {
479:   PetscInt       i,j;
480:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc,lobj=0;
481:   PetscScalar    u,ue,uw,un,us,uxux,uyuy;
482:   MPI_Comm       comm;

485:   *obj   = 0;
486:   PetscObjectGetComm((PetscObject)info->da,&comm);
487:   lambda = user->param;
488:   hx     = 1.0/(PetscReal)(info->mx-1);
489:   hy     = 1.0/(PetscReal)(info->my-1);
490:   sc     = hx*hy*lambda;
491:   hxdhy  = hx/hy;
492:   hydhx  = hy/hx;
493:   /*
494:      Compute function over the locally owned part of the grid
495:   */
496:   for (j=info->ys; j<info->ys+info->ym; j++) {
497:     for (i=info->xs; i<info->xs+info->xm; i++) {
498:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
499:         lobj += PetscRealPart((hydhx + hxdhy)*x[j][i]*x[j][i]);
500:       } else {
501:         u  = x[j][i];
502:         uw = x[j][i-1];
503:         ue = x[j][i+1];
504:         un = x[j-1][i];
505:         us = x[j+1][i];

507:         if (i-1 == 0) uw = 0.;
508:         if (i+1 == info->mx-1) ue = 0.;
509:         if (j-1 == 0) un = 0.;
510:         if (j+1 == info->my-1) us = 0.;

512:         /* F[u] = 1/2\int_{\omega}\nabla^2u(x)*u(x)*dx */

514:         uxux = u*(2.*u - ue - uw)*hydhx;
515:         uyuy = u*(2.*u - un - us)*hxdhy;

517:         lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u));
518:       }
519:     }
520:   }
521:   PetscLogFlops(12.0*info->ym*info->xm);
522:   MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);
523:   return(0);
524: }

526: /*
527:    FormJacobianLocal - Evaluates Jacobian matrix on local process patch
528: */
529: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,Mat jacpre,AppCtx *user)
530: {
532:   PetscInt       i,j,k;
533:   MatStencil     col[5],row;
534:   PetscScalar    lambda,v[5],hx,hy,hxdhy,hydhx,sc;
535:   DM             coordDA;
536:   Vec            coordinates;
537:   DMDACoor2d   **coords;

540:   lambda = user->param;
541:   /* Extract coordinates */
542:   DMGetCoordinateDM(info->da, &coordDA);
543:   DMGetCoordinates(info->da, &coordinates);
544:   DMDAVecGetArray(coordDA, coordinates, &coords);
545:   hx     = info->xm > 1 ? PetscRealPart(coords[info->ys][info->xs+1].x) - PetscRealPart(coords[info->ys][info->xs].x) : 1.0;
546:   hy     = info->ym > 1 ? PetscRealPart(coords[info->ys+1][info->xs].y) - PetscRealPart(coords[info->ys][info->xs].y) : 1.0;
547:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
548:   hxdhy  = hx/hy;
549:   hydhx  = hy/hx;
550:   sc     = hx*hy*lambda;


553:   /*
554:      Compute entries for the locally owned part of the Jacobian.
555:       - Currently, all PETSc parallel matrix formats are partitioned by
556:         contiguous chunks of rows across the processors.
557:       - Each processor needs to insert only elements that it owns
558:         locally (but any non-local elements will be sent to the
559:         appropriate processor during matrix assembly).
560:       - Here, we set all entries for a particular row at once.
561:       - We can set matrix entries either using either
562:         MatSetValuesLocal() or MatSetValues(), as discussed above.
563:   */
564:   for (j=info->ys; j<info->ys+info->ym; j++) {
565:     for (i=info->xs; i<info->xs+info->xm; i++) {
566:       row.j = j; row.i = i;
567:       /* boundary points */
568:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
569:         v[0] =  2.0*(hydhx + hxdhy);
570:         MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES);
571:       } else {
572:         k = 0;
573:         /* interior grid points */
574:         if (j-1 != 0) {
575:           v[k]     = -hxdhy;
576:           col[k].j = j - 1; col[k].i = i;
577:           k++;
578:         }
579:         if (i-1 != 0) {
580:           v[k]     = -hydhx;
581:           col[k].j = j;     col[k].i = i-1;
582:           k++;
583:         }

585:         v[k] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[k].j = row.j; col[k].i = row.i; k++;

587:         if (i+1 != info->mx-1) {
588:           v[k]     = -hydhx;
589:           col[k].j = j;     col[k].i = i+1;
590:           k++;
591:         }
592:         if (j+1 != info->mx-1) {
593:           v[k]     = -hxdhy;
594:           col[k].j = j + 1; col[k].i = i;
595:           k++;
596:         }
597:         MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES);
598:       }
599:     }
600:   }

602:   /*
603:      Assemble matrix, using the 2-step process:
604:        MatAssemblyBegin(), MatAssemblyEnd().
605:   */
606:   MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY);
607:   MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY);
608:   /*
609:      Tell the matrix we will never add a new nonzero location to the
610:      matrix. If we do, it will generate an error.
611:   */
612:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
613:   return(0);
614: }

616: #if defined(PETSC_HAVE_MATLAB_ENGINE)
617: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
618: {
619:   AppCtx         *user = (AppCtx*)ptr;
621:   PetscInt       Mx,My;
622:   PetscReal      lambda,hx,hy;
623:   Vec            localX,localF;
624:   MPI_Comm       comm;
625:   DM             da;

628:   SNESGetDM(snes,&da);
629:   DMGetLocalVector(da,&localX);
630:   DMGetLocalVector(da,&localF);
631:   PetscObjectSetName((PetscObject)localX,"localX");
632:   PetscObjectSetName((PetscObject)localF,"localF");
633:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

635:   lambda = user->param;
636:   hx     = 1.0/(PetscReal)(Mx-1);
637:   hy     = 1.0/(PetscReal)(My-1);

639:   PetscObjectGetComm((PetscObject)snes,&comm);
640:   /*
641:      Scatter ghost points to local vector,using the 2-step process
642:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
643:      By placing code between these two statements, computations can be
644:      done while messages are in transition.
645:   */
646:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
647:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
648:   PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
649:   PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
650:   PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);

652:   /*
653:      Insert values into global vector
654:   */
655:   DMLocalToGlobalBegin(da,localF,INSERT_VALUES,F);
656:   DMLocalToGlobalEnd(da,localF,INSERT_VALUES,F);
657:   DMRestoreLocalVector(da,&localX);
658:   DMRestoreLocalVector(da,&localF);
659:   return(0);
660: }
661: #endif

663: /* ------------------------------------------------------------------- */
664: /*
665:       Applies some sweeps on nonlinear Gauss-Seidel on each process

667:  */
668: PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx)
669: {
670:   PetscInt       i,j,k,Mx,My,xs,ys,xm,ym,its,tot_its,sweeps,l;
672:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc;
673:   PetscScalar    **x,**b,bij,F,F0=0,J,u,un,us,ue,eu,uw,uxx,uyy,y;
674:   PetscReal      atol,rtol,stol;
675:   DM             da;
676:   AppCtx         *user;
677:   Vec            localX,localB;

680:   tot_its = 0;
681:   SNESNGSGetSweeps(snes,&sweeps);
682:   SNESNGSGetTolerances(snes,&atol,&rtol,&stol,&its);
683:   SNESGetDM(snes,&da);
684:   DMGetApplicationContext(da,(void**)&user);

686:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

688:   lambda = user->param;
689:   hx     = 1.0/(PetscReal)(Mx-1);
690:   hy     = 1.0/(PetscReal)(My-1);
691:   sc     = hx*hy*lambda;
692:   hxdhy  = hx/hy;
693:   hydhx  = hy/hx;


696:   DMGetLocalVector(da,&localX);
697:   if (B) {
698:     DMGetLocalVector(da,&localB);
699:   }
700:   for (l=0; l<sweeps; l++) {

702:     DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
703:     DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
704:     if (B) {
705:       DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);
706:       DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);
707:     }
708:     /*
709:      Get a pointer to vector data.
710:      - For default PETSc vectors, VecGetArray() returns a pointer to
711:      the data array.  Otherwise, the routine is implementation dependent.
712:      - You MUST call VecRestoreArray() when you no longer need access to
713:      the array.
714:      */
715:     DMDAVecGetArray(da,localX,&x);
716:     if (B) DMDAVecGetArray(da,localB,&b);
717:     /*
718:      Get local grid boundaries (for 2-dimensional DMDA):
719:      xs, ys   - starting grid indices (no ghost points)
720:      xm, ym   - widths of local grid (no ghost points)
721:      */
722:     DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

724:     for (j=ys; j<ys+ym; j++) {
725:       for (i=xs; i<xs+xm; i++) {
726:         if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
727:           /* boundary conditions are all zero Dirichlet */
728:           x[j][i] = 0.0;
729:         } else {
730:           if (B) bij = b[j][i];
731:           else   bij = 0.;

733:           u  = x[j][i];
734:           un = x[j-1][i];
735:           us = x[j+1][i];
736:           ue = x[j][i-1];
737:           uw = x[j][i+1];

739:           for (k=0; k<its; k++) {
740:             eu  = PetscExpScalar(u);
741:             uxx = (2.0*u - ue - uw)*hydhx;
742:             uyy = (2.0*u - un - us)*hxdhy;
743:             F   = uxx + uyy - sc*eu - bij;
744:             if (k == 0) F0 = F;
745:             J  = 2.0*(hydhx + hxdhy) - sc*eu;
746:             y  = F/J;
747:             u -= y;
748:             tot_its++;

750:             if (atol > PetscAbsReal(PetscRealPart(F)) ||
751:                 rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) ||
752:                 stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) {
753:               break;
754:             }
755:           }
756:           x[j][i] = u;
757:         }
758:       }
759:     }
760:     /*
761:      Restore vector
762:      */
763:     DMDAVecRestoreArray(da,localX,&x);
764:     DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
765:     DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
766:   }
767:   PetscLogFlops(tot_its*(21.0));
768:   DMRestoreLocalVector(da,&localX);
769:   if (B) {
770:     DMDAVecRestoreArray(da,localB,&b);
771:     DMRestoreLocalVector(da,&localB);
772:   }
773:   return(0);
774: }

776: /*TEST

778:    test:
779:      suffix: asm_0
780:      requires: !single
781:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu

783:    test:
784:      suffix: msm_0
785:      requires: !single
786:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu

788:    test:
789:      suffix: asm_1
790:      requires: !single
791:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

793:    test:
794:      suffix: msm_1
795:      requires: !single
796:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

798:    test:
799:      suffix: asm_2
800:      requires: !single
801:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

803:    test:
804:      suffix: msm_2
805:      requires: !single
806:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

808:    test:
809:      suffix: asm_3
810:      requires: !single
811:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

813:    test:
814:      suffix: msm_3
815:      requires: !single
816:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

818:    test:
819:      suffix: asm_4
820:      requires: !single
821:      nsize: 2
822:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

824:    test:
825:      suffix: msm_4
826:      requires: !single
827:      nsize: 2
828:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

830:    test:
831:      suffix: asm_5
832:      requires: !single
833:      nsize: 2
834:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8

836:    test:
837:      suffix: msm_5
838:      requires: !single
839:      nsize: 2
840:      args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8

842:    test:
843:      args: -snes_rtol 1.e-5 -pc_type mg -ksp_monitor_short -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17 -mg_levels_ksp_monitor_short -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full
844:      requires: !single

846:    test:
847:      suffix: 2
848:      args: -pc_type mg -ksp_converged_reason -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3 -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full -ksp_atol -1.

850:    test:
851:      suffix: 3
852:      nsize: 2
853:      args: -snes_grid_sequence 2 -snes_mf_operator -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -snes_rtol 1.e-2
854:      filter: grep -v "otal number of function evaluations"

856:    test:
857:      suffix: 4
858:      nsize: 2
859:      args: -snes_grid_sequence 2 -snes_monitor_short -ksp_converged_reason -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -ksp_atol -1

861:    test:
862:      suffix: 5_anderson
863:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type anderson

865:    test:
866:      suffix: 5_aspin
867:      nsize: 4
868:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type aspin -snes_view

870:    test:
871:      suffix: 5_broyden
872:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_qn_type broyden -snes_qn_m 10

874:    test:
875:      suffix: 5_fas
876:      args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6
877:      requires: !single

879:    test:
880:      suffix: 5_fas_additive
881:      args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6 -snes_fas_type additive -snes_max_it 50

883:    test:
884:      suffix: 5_fas_monitor
885:      args: -da_refine 1 -snes_type fas -snes_fas_monitor
886:      requires: !single

888:    test:
889:      suffix: 5_ls
890:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls

892:    test:
893:      suffix: 5_ls_sell_sor
894:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls -dm_mat_type sell -pc_type sor
895:      output_file: output/ex5_5_ls.out

897:    test:
898:      suffix: 5_nasm
899:      nsize: 4
900:      args: -snes_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type nasm -snes_nasm_type restrict -snes_max_it 10

902:    test:
903:      suffix: 5_ncg
904:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ncg -snes_ncg_type fr

906:    test:
907:      suffix: 5_newton_asm_dmda
908:      nsize: 4
909:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type asm -pc_asm_dm_subdomains -malloc_dump
910:      requires: !single

912:    test:
913:      suffix: 5_newton_gasm_dmda
914:      nsize: 4
915:      args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type gasm -malloc_dump
916:      requires: !single

918:    test:
919:      suffix: 5_ngmres
920:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10

922:    test:
923:      suffix: 5_ngmres_fas
924:      args: -snes_rtol 1.e-4 -snes_type ngmres -npc_fas_coarse_snes_max_it 1 -npc_fas_coarse_snes_type newtonls -npc_fas_coarse_pc_type lu -npc_fas_coarse_ksp_type preonly -snes_ngmres_m 10 -snes_monitor_short -npc_snes_max_it 1 -npc_snes_type fas -npc_fas_coarse_ksp_type richardson -da_refine 6

926:    test:
927:      suffix: 5_ngmres_ngs
928:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -npc_snes_type ngs -npc_snes_max_it 1

930:    test:
931:      suffix: 5_ngmres_nrichardson
932:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10 -npc_snes_type nrichardson -npc_snes_max_it 3
933:      output_file: output/ex5_5_ngmres_richardson.out

935:    test:
936:      suffix: 5_nrichardson
937:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type nrichardson

939:    test:
940:      suffix: 5_qn
941:      args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_linesearch_type cp -snes_qn_m 10

943:    test:
944:      suffix: 6
945:      nsize: 4
946:      args: -snes_converged_reason -ksp_converged_reason -da_grid_x 129 -da_grid_y 129 -pc_type mg -pc_mg_levels 8 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.5,0,1.1 -mg_levels_ksp_max_it 2

948:    test:
949:      requires: complex !single
950:      suffix: complex
951:      args: -snes_mf_operator -mat_mffd_complex -snes_monitor

953: TEST*/