xref: /petsc/src/snes/tutorials/ex19.c (revision 6a98f8dc3f2c9149905a87dc2e9d0fedaf64e09a)
1 
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' = '>' */
11 
12 /*
13       See src/ksp/ksp/tutorials/ex45.c
14 */
15 
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*/
22 
23 
24 /*F-----------------------------------------------------------------------
25 
26     We thank David E. Keyes for contributing the driven cavity discretization within this example code.
27 
28     This problem is modeled by the partial differential equation system
29 
30 \begin{eqnarray}
31         - \triangle U - \nabla_y \Omega & = & 0  \\
32         - \triangle V + \nabla_x\Omega & = & 0  \\
33         - \triangle \Omega + \nabla \cdot ([U*\Omega,V*\Omega]) - GR* \nabla_x T & = & 0  \\
34         - \triangle T + PR* \nabla \cdot ([U*T,V*T]) & = & 0
35 \end{eqnarray}
36 
37     in the unit square, which is uniformly discretized in each of x and y in this simple encoding.
38 
39     No-slip, rigid-wall Dirichlet conditions are used for $ [U,V]$.
40     Dirichlet conditions are used for Omega, based on the definition of
41     vorticity: $ \Omega = - \nabla_y U + \nabla_x V$, where along each
42     constant coordinate boundary, the tangential derivative is zero.
43     Dirichlet conditions are used for T on the left and right walls,
44     and insulation homogeneous Neumann conditions are used for T on
45     the top and bottom walls.
46 
47     A finite difference approximation with the usual 5-point stencil
48     is used to discretize the boundary value problem to obtain a
49     nonlinear system of equations.  Upwinding is used for the divergence
50     (convective) terms and central for the gradient (source) terms.
51 
52     The Jacobian can be either
53       * formed via finite differencing using coloring (the default), or
54       * applied matrix-free via the option -snes_mf
55         (for larger grid problems this variant may not converge
56         without a preconditioner due to ill-conditioning).
57 
58   ------------------------------------------------------------------------F*/
59 
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
78 
79 /*
80    User-defined routines and data structures
81 */
82 typedef struct {
83   PetscScalar u,v,omega,temp;
84 } Field;
85 
86 PetscErrorCode FormFunctionLocal(DMDALocalInfo*,Field**,Field**,void*);
87 
88 typedef struct {
89   PetscReal   lidvelocity,prandtl,grashof;  /* physical parameters */
90   PetscBool   draw_contours;                /* flag - 1 indicates drawing contours */
91 } AppCtx;
92 
93 extern PetscErrorCode FormInitialGuess(AppCtx*,DM,Vec);
94 extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*);
95 
96 int main(int argc,char **argv)
97 {
98   AppCtx         user;                /* user-defined work context */
99   PetscInt       mx,my,its;
100   PetscErrorCode ierr;
101   MPI_Comm       comm;
102   SNES           snes;
103   DM             da;
104   Vec            x;
105 
106   ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
107 
108   PetscFunctionBeginUser;
109   comm = PETSC_COMM_WORLD;
110   ierr = SNESCreate(comm,&snes);CHKERRQ(ierr);
111 
112   /*
113       Create distributed array object to manage parallel grid and vectors
114       for principal unknowns (x) and governing residuals (f)
115   */
116   ierr = DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,4,1,0,0,&da);CHKERRQ(ierr);
117   ierr = DMSetFromOptions(da);CHKERRQ(ierr);
118   ierr = DMSetUp(da);CHKERRQ(ierr);
119   ierr = SNESSetDM(snes,(DM)da);CHKERRQ(ierr);
120   ierr = SNESSetNGS(snes, NonlinearGS, (void*)&user);CHKERRQ(ierr);
121 
122   ierr = 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);CHKERRQ(ierr);
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;
129 
130   ierr = PetscOptionsGetReal(NULL,NULL,"-lidvelocity",&user.lidvelocity,NULL);CHKERRQ(ierr);
131   ierr = PetscOptionsGetReal(NULL,NULL,"-prandtl",&user.prandtl,NULL);CHKERRQ(ierr);
132   ierr = PetscOptionsGetReal(NULL,NULL,"-grashof",&user.grashof,NULL);CHKERRQ(ierr);
133   ierr = PetscOptionsHasName(NULL,NULL,"-contours",&user.draw_contours);CHKERRQ(ierr);
134 
135   ierr = DMDASetFieldName(da,0,"x_velocity");CHKERRQ(ierr);
136   ierr = DMDASetFieldName(da,1,"y_velocity");CHKERRQ(ierr);
137   ierr = DMDASetFieldName(da,2,"Omega");CHKERRQ(ierr);
138   ierr = DMDASetFieldName(da,3,"temperature");CHKERRQ(ierr);
139 
140   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141      Create user context, set problem data, create vector data structures.
142      Also, compute the initial guess.
143      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144 
145   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146      Create nonlinear solver context
147 
148      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149   ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
150   ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
151   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
152   ierr = PetscPrintf(comm,"lid velocity = %g, prandtl # = %g, grashof # = %g\n",(double)user.lidvelocity,(double)user.prandtl,(double)user.grashof);CHKERRQ(ierr);
153 
154 
155   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156      Solve the nonlinear system
157      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158   ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
159   ierr = FormInitialGuess(&user,da,x);CHKERRQ(ierr);
160 
161   ierr = SNESSolve(snes,NULL,x);CHKERRQ(ierr);
162 
163   ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
164   ierr = PetscPrintf(comm,"Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
165 
166   /*
167      Visualize solution
168   */
169   if (user.draw_contours) {
170     ierr = VecView(x,PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
171   }
172 
173   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174      Free work space.  All PETSc objects should be destroyed when they
175      are no longer needed.
176      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177   ierr = VecDestroy(&x);CHKERRQ(ierr);
178   ierr = DMDestroy(&da);CHKERRQ(ierr);
179   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
180   ierr = PetscFinalize();
181   return ierr;
182 }
183 
184 /* ------------------------------------------------------------------- */
185 
186 /*
187    FormInitialGuess - Forms initial approximation.
188 
189    Input Parameters:
190    user - user-defined application context
191    X - vector
192 
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;
199   PetscErrorCode ierr;
200   PetscReal      grashof,dx;
201   Field          **x;
202 
203   PetscFunctionBeginUser;
204   grashof = user->grashof;
205 
206   ierr = DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
207   dx   = 1.0/(mx-1);
208 
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   ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
215 
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   ierr = DMDAVecGetArrayWrite(da,X,&x);CHKERRQ(ierr);
224 
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   }
237 
238   /*
239      Restore vector
240   */
241   ierr = DMDAVecRestoreArrayWrite(da,X,&x);CHKERRQ(ierr);
242   PetscFunctionReturn(0);
243 }
244 
245 PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
246 {
247   AppCtx         *user = (AppCtx*)ptr;
248   PetscErrorCode ierr;
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;
253 
254   PetscFunctionBeginUser;
255   grashof = user->grashof;
256   prandtl = user->prandtl;
257   lid     = user->lidvelocity;
258 
259   /*
260      Define mesh intervals ratios for uniform grid.
261 
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.
264 
265 
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;
270 
271   xints = info->xs; xinte = info->xs+info->xm; yints = info->ys; yinte = info->ys+info->ym;
272 
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   }
285 
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   }
298 
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   }
311 
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   }
324 
325   /* Compute over the interior points */
326   for (j=yints; j<yinte; j++) {
327     for (i=xints; i<xinte; i++) {
328 
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);
336 
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;
342 
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;
348 
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;
356 
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   }
365 
366   /*
367      Flop count (multiply-adds are counted as 2 operations)
368   */
369   ierr = PetscLogFlops(84.0*info->ym*info->xm);CHKERRQ(ierr);
370   PetscFunctionReturn(0);
371 }
372 
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;
380   PetscErrorCode ierr;
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;
400 
401   PetscFunctionBeginUser;
402   grashof = user->grashof;
403   prandtl = user->prandtl;
404   lid     = user->lidvelocity;
405   tot_its = 0;
406   ierr    = SNESNGSGetTolerances(snes,&rtol,&atol,&stol,&max_its);CHKERRQ(ierr);
407   ierr    = SNESNGSGetSweeps(snes,&sweeps);CHKERRQ(ierr);
408   ierr    = SNESGetDM(snes,(DM*)&da);CHKERRQ(ierr);
409   ierr    = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
410   if (B) {
411     ierr = DMGetLocalVector(da,&localB);CHKERRQ(ierr);
412   }
413   /*
414      Scatter ghost points to local vector, using the 2-step process
415         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
416   */
417   ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
418   ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
419   if (B) {
420     ierr = DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);CHKERRQ(ierr);
421     ierr = DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);CHKERRQ(ierr);
422   }
423   ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
424   ierr = DMDAVecGetArrayWrite(da,localX,&x);CHKERRQ(ierr);
425   if (B) {
426     ierr = DMDAVecGetArrayRead(da,localB,&b);CHKERRQ(ierr);
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;
432 
433   xints = info.xs; xinte = info.xs+info.xm; yints = info.ys; yinte = info.ys+info.ym;
434 
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++) {
441 
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   }
453 
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   }
470 
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   }
487 
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   }
504 
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           }
527 
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;
559 
560             if (PetscRealPart(vy) > 0.0) dfodv = (u - x[j-1][i].omega)*hx;
561             else dfodv = (x[j+1][i].omega - u)*hx;
562 
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;
571 
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;
574 
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;
586 
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   ierr = DMDAVecRestoreArrayWrite(da,localX,&x);CHKERRQ(ierr);
638   if (B) {
639     ierr = DMDAVecRestoreArrayRead(da,localB,&b);CHKERRQ(ierr);
640   }
641   ierr = DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
642   ierr = DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
643   ierr = PetscLogFlops(tot_its*(84.0 + 41.0 + 26.0));CHKERRQ(ierr);
644   ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
645   if (B) {
646     ierr = DMRestoreLocalVector(da,&localB);CHKERRQ(ierr);
647   }
648   PetscFunctionReturn(0);
649 }
650 
651 
652 /*TEST
653 
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
658 
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
664 
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
670 
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
676 
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
682 
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
688 
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
695 
696    test:
697       suffix: 17
698       args: -snes_monitor_short -ksp_pc_side right
699       requires: !single
700 
701    test:
702       suffix: 18
703       args: -ksp_monitor_snes_lg -ksp_pc_side right
704       requires: x !single
705 
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
711 
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
716       output_file: output/ex19_2.out
717       requires: !single
718 
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
724 
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
731 
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
736 
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
741 
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
747 
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
753 
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
759 
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
765 
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
772 
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
778 
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
784 
785    test:
786       suffix: cgs
787       args: -da_refine 1 -ksp_monitor_short -ksp_type cgs
788       requires: !single
789 
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
794 
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
799 
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
805 
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
811 
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
816 
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
821 
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
827 
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
832 
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
837 
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
843 
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
849 
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
855 
856    test:
857       suffix: fdcoloring_wp
858       args: -da_refine 3 -snes_monitor_short -pc_type mg
859       requires: !single
860 
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
866 
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
872 
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
877 
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
882 
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
887 
888    # HYPRE PtAP broken with complex numbers
889    test:
890       suffix: fieldsplit_hypre
891       nsize: 2
892       requires: hypre mumps !complex
893       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 
895    test:
896       suffix: fieldsplit_mumps
897       nsize: 2
898       requires: mumps
899       args: -pc_type fieldsplit -pc_fieldsplit_block_size 4 -pc_fieldsplit_type SCHUR -pc_fieldsplit_0_fields 0,1,2 -pc_fieldsplit_1_fields 3 -fieldsplit_0_pc_type lu -fieldsplit_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
900       output_file: output/ex19_fieldsplit_5.out
901 
902    test:
903       suffix: greedy_coloring
904       nsize: 2
905       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
906       requires: !single
907 
908    # HYPRE PtAP broken with complex numbers
909    test:
910       suffix: hypre
911       nsize: 2
912       requires: hypre !complex
913       args: -da_refine 3 -snes_monitor_short -pc_type hypre
914 
915    test:
916       suffix: ibcgs
917       nsize: 2
918       args: -ksp_type ibcgs -ksp_monitor_short -da_refine 2 -snes_view
919       requires: !complex !single
920 
921    test:
922       suffix: kaczmarz
923       nsize: 2
924       args: -pc_type kaczmarz -ksp_monitor_short -snes_monitor_short -snes_view
925       requires: !single
926 
927    test:
928       suffix: klu
929       requires: suitesparse
930       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu
931       output_file: output/ex19_superlu.out
932 
933    test:
934       suffix: klu_2
935       requires: suitesparse
936       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_ordering PETSC
937       output_file: output/ex19_superlu.out
938 
939    test:
940       suffix: klu_3
941       requires: suitesparse
942       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_use_btf 0
943       output_file: output/ex19_superlu.out
944 
945    test:
946       suffix: ml
947       nsize: 2
948       requires: ml
949       args: -da_refine 3 -snes_monitor_short -pc_type ml
950 
951    test:
952       suffix: ngmres_fas
953       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
954       requires: !single
955 
956    test:
957       suffix: ngmres_fas_gssecant
958       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
959       requires: !single
960 
961    test:
962       suffix: ngmres_fas_ms
963       nsize: 2
964       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
965       requires: !single
966 
967    test:
968       suffix: ngmres_nasm
969       nsize: 4
970       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
971       requires: !single
972 
973    test:
974       suffix: ngs
975       args: -snes_type ngs -snes_view -snes_monitor -snes_rtol 1e-4
976       requires: !single
977 
978    test:
979       suffix: ngs_fd
980       args: -snes_type ngs -snes_ngs_secant -snes_view -snes_monitor -snes_rtol 1e-4
981       requires: !single
982 
983    test:
984       suffix: parms
985       nsize: 2
986       requires: parms
987       args: -pc_type parms -ksp_monitor_short -snes_view
988 
989    test:
990       suffix: superlu
991       requires: superlu
992       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu
993 
994    test:
995       suffix: superlu_sell
996       requires: superlu
997       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
998       output_file: output/ex19_superlu.out
999 
1000    test:
1001       suffix: superlu_dist
1002       requires: superlu_dist
1003       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1004       output_file: output/ex19_superlu.out
1005 
1006    test:
1007       suffix: superlu_dist_2
1008       nsize: 2
1009       requires: superlu_dist
1010       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1011       output_file: output/ex19_superlu.out
1012 
1013    test:
1014       suffix: superlu_equil
1015       requires: superlu
1016       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
1017 
1018    test:
1019       suffix: superlu_equil_sell
1020       requires: superlu
1021       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
1022       output_file: output/ex19_superlu_equil.out
1023 
1024    test:
1025       suffix: tcqmr
1026       args: -da_refine 1 -ksp_monitor_short -ksp_type tcqmr
1027       requires: !single
1028 
1029    test:
1030       suffix: tfqmr
1031       args: -da_refine 1 -ksp_monitor_short -ksp_type tfqmr
1032       requires: !single
1033 
1034    test:
1035       suffix: umfpack
1036       requires: suitesparse
1037       args: -da_refine 2 -pc_type lu -pc_factor_mat_solver_type umfpack -snes_view -snes_monitor_short -ksp_monitor_short
1038 
1039    test:
1040       suffix: tut_1
1041       nsize: 4
1042       requires: !single
1043       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view
1044 
1045    test:
1046       suffix: tut_2
1047       nsize: 4
1048       requires: !single
1049       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg
1050 
1051    # HYPRE PtAP broken with complex numbers
1052    test:
1053       suffix: tut_3
1054       nsize: 4
1055       requires: hypre !single !complex
1056       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre
1057 
1058    test:
1059       suffix: tut_8
1060       nsize: 4
1061       requires: ml !single
1062       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml
1063 
1064    test:
1065       suffix: tut_4
1066       nsize: 1
1067       requires: !single
1068       args: -da_refine 5 -log_view
1069       filter: head -n 2
1070       filter_output: head -n 2
1071 
1072    test:
1073       suffix: tut_5
1074       nsize: 1
1075       requires: !single
1076       args: -da_refine 5 -log_view -pc_type mg
1077       filter: head -n 2
1078       filter_output: head -n 2
1079 
1080    test:
1081       suffix: tut_6
1082       nsize: 4
1083       requires: !single
1084       args: -da_refine 5 -log_view
1085       filter: head -n 2
1086       filter_output: head -n 2
1087 
1088    test:
1089       suffix: tut_7
1090       nsize: 4
1091       requires: !single
1092       args: -da_refine 5 -log_view -pc_type mg
1093       filter: head -n 2
1094       filter_output: head -n 2
1095 
1096    test:
1097       suffix: cuda_1
1098       nsize: 1
1099       requires: cuda
1100       args: -snes_monitor -dm_mat_type seqaijcusparse -dm_vec_type seqcuda -pc_type gamg -ksp_monitor -mg_levels_ksp_max_it 3
1101 
1102 
1103    test:
1104       suffix: cuda_2
1105       nsize: 3
1106       requires: cuda !single
1107       args: -snes_monitor -dm_mat_type mpiaijcusparse -dm_vec_type mpicuda -pc_type gamg -ksp_monitor  -mg_levels_ksp_max_it 3
1108 
1109    test:
1110       suffix: seqbaijmkl
1111       nsize: 1
1112       requires: define(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1113       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view
1114 
1115    test:
1116       suffix: mpibaijmkl
1117       nsize: 2
1118       requires:  define(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1119       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view
1120 
1121    test:
1122      suffix: cpardiso
1123      nsize: 4
1124      requires: mkl_cpardiso
1125      args: -pc_type lu -pc_factor_mat_solver_type mkl_cpardiso -ksp_monitor
1126 
1127    test:
1128      suffix: logviewmemory
1129      requires: define(PETSC_USE_LOG) !define(PETSC_HAVE_VALGRIND)
1130      args: -log_view -log_view_memory -da_refine 4
1131      filter: grep MatFDColorSetUp | wc -w | xargs  -I % sh -c "expr % \> 21"
1132 
1133 TEST*/
1134