xref: /petsc/src/snes/tutorials/ex19.c (revision 9371c9d470a9602b6d10a8bf50c9b2280a79e45a)
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 /*F-----------------------------------------------------------------------
17 
18     We thank David E. Keyes for contributing the driven cavity discretization within this example code.
19 
20     This problem is modeled by the partial differential equation system
21 
22 \begin{eqnarray}
23         - \triangle U - \nabla_y \Omega & = & 0  \\
24         - \triangle V + \nabla_x\Omega & = & 0  \\
25         - \triangle \Omega + \nabla \cdot ([U*\Omega,V*\Omega]) - GR* \nabla_x T & = & 0  \\
26         - \triangle T + PR* \nabla \cdot ([U*T,V*T]) & = & 0
27 \end{eqnarray}
28 
29     in the unit square, which is uniformly discretized in each of x and y in this simple encoding.
30 
31     No-slip, rigid-wall Dirichlet conditions are used for $ [U,V]$.
32     Dirichlet conditions are used for Omega, based on the definition of
33     vorticity: $ \Omega = - \nabla_y U + \nabla_x V$, where along each
34     constant coordinate boundary, the tangential derivative is zero.
35     Dirichlet conditions are used for T on the left and right walls,
36     and insulation homogeneous Neumann conditions are used for T on
37     the top and bottom walls.
38 
39     A finite difference approximation with the usual 5-point stencil
40     is used to discretize the boundary value problem to obtain a
41     nonlinear system of equations.  Upwinding is used for the divergence
42     (convective) terms and central for the gradient (source) terms.
43 
44     The Jacobian can be either
45       * formed via finite differencing using coloring (the default), or
46       * applied matrix-free via the option -snes_mf
47         (for larger grid problems this variant may not converge
48         without a preconditioner due to ill-conditioning).
49 
50   ------------------------------------------------------------------------F*/
51 
52 /*
53    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
54    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
55    file automatically includes:
56      petscsys.h       - base PETSc routines   petscvec.h - vectors
57      petscmat.h - matrices
58      petscis.h     - index sets            petscksp.h - Krylov subspace methods
59      petscviewer.h - viewers               petscpc.h  - preconditioners
60      petscksp.h   - linear solvers
61 */
62 #if defined(PETSC_APPLE_FRAMEWORK)
63 #import <PETSc/petscsnes.h>
64 #import <PETSc/petscdmda.h>
65 #else
66 #include <petscsnes.h>
67 #include <petscdm.h>
68 #include <petscdmda.h>
69 #endif
70 
71 /*
72    User-defined routines and data structures
73 */
74 typedef struct {
75   PetscScalar u, v, omega, temp;
76 } Field;
77 
78 PetscErrorCode FormFunctionLocal(DMDALocalInfo *, Field **, Field **, void *);
79 
80 typedef struct {
81   PetscReal lidvelocity, prandtl, grashof; /* physical parameters */
82   PetscBool draw_contours;                 /* flag - 1 indicates drawing contours */
83 } AppCtx;
84 
85 extern PetscErrorCode FormInitialGuess(AppCtx *, DM, Vec);
86 extern PetscErrorCode NonlinearGS(SNES, Vec, Vec, void *);
87 
88 int main(int argc, char **argv) {
89   AppCtx   user; /* user-defined work context */
90   PetscInt mx, my, its;
91   MPI_Comm comm;
92   SNES     snes;
93   DM       da;
94   Vec      x;
95 
96   PetscFunctionBeginUser;
97   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
98   comm = PETSC_COMM_WORLD;
99   PetscCall(SNESCreate(comm, &snes));
100 
101   /*
102       Create distributed array object to manage parallel grid and vectors
103       for principal unknowns (x) and governing residuals (f)
104   */
105   PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 4, 1, 0, 0, &da));
106   PetscCall(DMSetFromOptions(da));
107   PetscCall(DMSetUp(da));
108   PetscCall(SNESSetDM(snes, (DM)da));
109   PetscCall(SNESSetNGS(snes, NonlinearGS, (void *)&user));
110 
111   PetscCall(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));
112   /*
113      Problem parameters (velocity of lid, prandtl, and grashof numbers)
114   */
115   user.lidvelocity = 1.0 / (mx * my);
116   user.prandtl     = 1.0;
117   user.grashof     = 1.0;
118 
119   PetscCall(PetscOptionsGetReal(NULL, NULL, "-lidvelocity", &user.lidvelocity, NULL));
120   PetscCall(PetscOptionsGetReal(NULL, NULL, "-prandtl", &user.prandtl, NULL));
121   PetscCall(PetscOptionsGetReal(NULL, NULL, "-grashof", &user.grashof, NULL));
122   PetscCall(PetscOptionsHasName(NULL, NULL, "-contours", &user.draw_contours));
123 
124   PetscCall(DMDASetFieldName(da, 0, "x_velocity"));
125   PetscCall(DMDASetFieldName(da, 1, "y_velocity"));
126   PetscCall(DMDASetFieldName(da, 2, "Omega"));
127   PetscCall(DMDASetFieldName(da, 3, "temperature"));
128 
129   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130      Create user context, set problem data, create vector data structures.
131      Also, compute the initial guess.
132      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133 
134   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135      Create nonlinear solver context
136 
137      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138   PetscCall(DMSetApplicationContext(da, &user));
139   PetscCall(DMDASNESSetFunctionLocal(da, INSERT_VALUES, (PetscErrorCode(*)(DMDALocalInfo *, void *, void *, void *))FormFunctionLocal, &user));
140   PetscCall(SNESSetFromOptions(snes));
141   PetscCall(PetscPrintf(comm, "lid velocity = %g, prandtl # = %g, grashof # = %g\n", (double)user.lidvelocity, (double)user.prandtl, (double)user.grashof));
142 
143   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144      Solve the nonlinear system
145      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146   PetscCall(DMCreateGlobalVector(da, &x));
147   PetscCall(FormInitialGuess(&user, da, x));
148 
149   PetscCall(SNESSolve(snes, NULL, x));
150 
151   PetscCall(SNESGetIterationNumber(snes, &its));
152   PetscCall(PetscPrintf(comm, "Number of SNES iterations = %" PetscInt_FMT "\n", its));
153 
154   /*
155      Visualize solution
156   */
157   if (user.draw_contours) PetscCall(VecView(x, PETSC_VIEWER_DRAW_WORLD));
158 
159   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160      Free work space.  All PETSc objects should be destroyed when they
161      are no longer needed.
162      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163   PetscCall(VecDestroy(&x));
164   PetscCall(DMDestroy(&da));
165   PetscCall(SNESDestroy(&snes));
166   PetscCall(PetscFinalize());
167   return 0;
168 }
169 
170 /* ------------------------------------------------------------------- */
171 
172 /*
173    FormInitialGuess - Forms initial approximation.
174 
175    Input Parameters:
176    user - user-defined application context
177    X - vector
178 
179    Output Parameter:
180    X - vector
181 */
182 PetscErrorCode FormInitialGuess(AppCtx *user, DM da, Vec X) {
183   PetscInt  i, j, mx, xs, ys, xm, ym;
184   PetscReal grashof, dx;
185   Field   **x;
186 
187   PetscFunctionBeginUser;
188   grashof = user->grashof;
189 
190   PetscCall(DMDAGetInfo(da, 0, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
191   dx = 1.0 / (mx - 1);
192 
193   /*
194      Get local grid boundaries (for 2-dimensional DMDA):
195        xs, ys   - starting grid indices (no ghost points)
196        xm, ym   - widths of local grid (no ghost points)
197   */
198   PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
199 
200   /*
201      Get a pointer to vector data.
202        - For default PETSc vectors, VecGetArray() returns a pointer to
203          the data array.  Otherwise, the routine is implementation dependent.
204        - You MUST call VecRestoreArray() when you no longer need access to
205          the array.
206   */
207   PetscCall(DMDAVecGetArrayWrite(da, X, &x));
208 
209   /*
210      Compute initial guess over the locally owned part of the grid
211      Initial condition is motionless fluid and equilibrium temperature
212   */
213   for (j = ys; j < ys + ym; j++) {
214     for (i = xs; i < xs + xm; i++) {
215       x[j][i].u     = 0.0;
216       x[j][i].v     = 0.0;
217       x[j][i].omega = 0.0;
218       x[j][i].temp  = (grashof > 0) * i * dx;
219     }
220   }
221 
222   /*
223      Restore vector
224   */
225   PetscCall(DMDAVecRestoreArrayWrite(da, X, &x));
226   PetscFunctionReturn(0);
227 }
228 
229 PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, Field **x, Field **f, void *ptr) {
230   AppCtx     *user = (AppCtx *)ptr;
231   PetscInt    xints, xinte, yints, yinte, i, j;
232   PetscReal   hx, hy, dhx, dhy, hxdhy, hydhx;
233   PetscReal   grashof, prandtl, lid;
234   PetscScalar u, uxx, uyy, vx, vy, avx, avy, vxp, vxm, vyp, vym;
235 
236   PetscFunctionBeginUser;
237   grashof = user->grashof;
238   prandtl = user->prandtl;
239   lid     = user->lidvelocity;
240 
241   /*
242      Define mesh intervals ratios for uniform grid.
243 
244      Note: FD formulae below are normalized by multiplying through by
245      local volume element (i.e. hx*hy) to obtain coefficients O(1) in two dimensions.
246 
247   */
248   dhx   = (PetscReal)(info->mx - 1);
249   dhy   = (PetscReal)(info->my - 1);
250   hx    = 1.0 / dhx;
251   hy    = 1.0 / dhy;
252   hxdhy = hx * dhy;
253   hydhx = hy * dhx;
254 
255   xints = info->xs;
256   xinte = info->xs + info->xm;
257   yints = info->ys;
258   yinte = info->ys + info->ym;
259 
260   /* Test whether we are on the bottom edge of the global array */
261   if (yints == 0) {
262     j     = 0;
263     yints = yints + 1;
264     /* bottom edge */
265     for (i = info->xs; i < info->xs + info->xm; i++) {
266       f[j][i].u     = x[j][i].u;
267       f[j][i].v     = x[j][i].v;
268       f[j][i].omega = x[j][i].omega + (x[j + 1][i].u - x[j][i].u) * dhy;
269       f[j][i].temp  = x[j][i].temp - x[j + 1][i].temp;
270     }
271   }
272 
273   /* Test whether we are on the top edge of the global array */
274   if (yinte == info->my) {
275     j     = info->my - 1;
276     yinte = yinte - 1;
277     /* top edge */
278     for (i = info->xs; i < info->xs + info->xm; i++) {
279       f[j][i].u     = x[j][i].u - lid;
280       f[j][i].v     = x[j][i].v;
281       f[j][i].omega = x[j][i].omega + (x[j][i].u - x[j - 1][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 left edge of the global array */
287   if (xints == 0) {
288     i     = 0;
289     xints = xints + 1;
290     /* left edge */
291     for (j = info->ys; j < info->ys + info->ym; j++) {
292       f[j][i].u     = x[j][i].u;
293       f[j][i].v     = x[j][i].v;
294       f[j][i].omega = x[j][i].omega - (x[j][i + 1].v - x[j][i].v) * dhx;
295       f[j][i].temp  = x[j][i].temp;
296     }
297   }
298 
299   /* Test whether we are on the right edge of the global array */
300   if (xinte == info->mx) {
301     i     = info->mx - 1;
302     xinte = xinte - 1;
303     /* right 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].v - x[j][i - 1].v) * dhx;
308       f[j][i].temp  = x[j][i].temp - (PetscReal)(grashof > 0);
309     }
310   }
311 
312   /* Compute over the interior points */
313   for (j = yints; j < yinte; j++) {
314     for (i = xints; i < xinte; i++) {
315       /*
316        convective coefficients for upwinding
317       */
318       vx  = x[j][i].u;
319       avx = PetscAbsScalar(vx);
320       vxp = .5 * (vx + avx);
321       vxm = .5 * (vx - avx);
322       vy  = x[j][i].v;
323       avy = PetscAbsScalar(vy);
324       vyp = .5 * (vy + avy);
325       vym = .5 * (vy - avy);
326 
327       /* U velocity */
328       u         = x[j][i].u;
329       uxx       = (2.0 * u - x[j][i - 1].u - x[j][i + 1].u) * hydhx;
330       uyy       = (2.0 * u - x[j - 1][i].u - x[j + 1][i].u) * hxdhy;
331       f[j][i].u = uxx + uyy - .5 * (x[j + 1][i].omega - x[j - 1][i].omega) * hx;
332 
333       /* V velocity */
334       u         = x[j][i].v;
335       uxx       = (2.0 * u - x[j][i - 1].v - x[j][i + 1].v) * hydhx;
336       uyy       = (2.0 * u - x[j - 1][i].v - x[j + 1][i].v) * hxdhy;
337       f[j][i].v = uxx + uyy + .5 * (x[j][i + 1].omega - x[j][i - 1].omega) * hy;
338 
339       /* Omega */
340       u             = x[j][i].omega;
341       uxx           = (2.0 * u - x[j][i - 1].omega - x[j][i + 1].omega) * hydhx;
342       uyy           = (2.0 * u - x[j - 1][i].omega - x[j + 1][i].omega) * hxdhy;
343       f[j][i].omega = uxx + uyy + (vxp * (u - x[j][i - 1].omega) + vxm * (x[j][i + 1].omega - u)) * hy + (vyp * (u - x[j - 1][i].omega) + vym * (x[j + 1][i].omega - u)) * hx - .5 * grashof * (x[j][i + 1].temp - x[j][i - 1].temp) * hy;
344 
345       /* Temperature */
346       u            = x[j][i].temp;
347       uxx          = (2.0 * u - x[j][i - 1].temp - x[j][i + 1].temp) * hydhx;
348       uyy          = (2.0 * u - x[j - 1][i].temp - x[j + 1][i].temp) * hxdhy;
349       f[j][i].temp = uxx + uyy + prandtl * ((vxp * (u - x[j][i - 1].temp) + vxm * (x[j][i + 1].temp - u)) * hy + (vyp * (u - x[j - 1][i].temp) + vym * (x[j + 1][i].temp - u)) * hx);
350     }
351   }
352 
353   /*
354      Flop count (multiply-adds are counted as 2 operations)
355   */
356   PetscCall(PetscLogFlops(84.0 * info->ym * info->xm));
357   PetscFunctionReturn(0);
358 }
359 
360 /*
361     Performs sweeps of point block nonlinear Gauss-Seidel on all the local grid points
362 */
363 PetscErrorCode NonlinearGS(SNES snes, Vec X, Vec B, void *ctx) {
364   DMDALocalInfo info;
365   Field       **x, **b;
366   Vec           localX, localB;
367   DM            da;
368   PetscInt      xints, xinte, yints, yinte, i, j, k, l;
369   PetscInt      max_its, tot_its;
370   PetscInt      sweeps;
371   PetscReal     rtol, atol, stol;
372   PetscReal     hx, hy, dhx, dhy, hxdhy, hydhx;
373   PetscReal     grashof, prandtl, lid;
374   PetscScalar   u, uxx, uyy, vx, vy, avx, avy, vxp, vxm, vyp, vym;
375   PetscScalar   fu, fv, fomega, ftemp;
376   PetscScalar   dfudu;
377   PetscScalar   dfvdv;
378   PetscScalar   dfodu, dfodv, dfodo;
379   PetscScalar   dftdu, dftdv, dftdt;
380   PetscScalar   yu = 0, yv = 0, yo = 0, yt = 0;
381   PetscScalar   bjiu, bjiv, bjiomega, bjitemp;
382   PetscBool     ptconverged;
383   PetscReal     pfnorm, pfnorm0, pynorm, pxnorm;
384   AppCtx       *user = (AppCtx *)ctx;
385 
386   PetscFunctionBeginUser;
387   grashof = user->grashof;
388   prandtl = user->prandtl;
389   lid     = user->lidvelocity;
390   tot_its = 0;
391   PetscCall(SNESNGSGetTolerances(snes, &rtol, &atol, &stol, &max_its));
392   PetscCall(SNESNGSGetSweeps(snes, &sweeps));
393   PetscCall(SNESGetDM(snes, (DM *)&da));
394   PetscCall(DMGetLocalVector(da, &localX));
395   if (B) { PetscCall(DMGetLocalVector(da, &localB)); }
396   /*
397      Scatter ghost points to local vector, using the 2-step process
398         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
399   */
400   PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
401   PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
402   if (B) {
403     PetscCall(DMGlobalToLocalBegin(da, B, INSERT_VALUES, localB));
404     PetscCall(DMGlobalToLocalEnd(da, B, INSERT_VALUES, localB));
405   }
406   PetscCall(DMDAGetLocalInfo(da, &info));
407   PetscCall(DMDAVecGetArrayWrite(da, localX, &x));
408   if (B) { PetscCall(DMDAVecGetArrayRead(da, localB, &b)); }
409   /* looks like a combination of the formfunction / formjacobian routines */
410   dhx   = (PetscReal)(info.mx - 1);
411   dhy   = (PetscReal)(info.my - 1);
412   hx    = 1.0 / dhx;
413   hy    = 1.0 / dhy;
414   hxdhy = hx * dhy;
415   hydhx = hy * dhx;
416 
417   xints = info.xs;
418   xinte = info.xs + info.xm;
419   yints = info.ys;
420   yinte = info.ys + info.ym;
421 
422   /* Set the boundary conditions on the momentum equations */
423   /* Test whether we are on the bottom edge of the global array */
424   if (yints == 0) {
425     j = 0;
426     /* bottom edge */
427     for (i = info.xs; i < info.xs + info.xm; i++) {
428       if (B) {
429         bjiu = b[j][i].u;
430         bjiv = b[j][i].v;
431       } else {
432         bjiu = 0.0;
433         bjiv = 0.0;
434       }
435       x[j][i].u = 0.0 + bjiu;
436       x[j][i].v = 0.0 + bjiv;
437     }
438   }
439 
440   /* Test whether we are on the top edge of the global array */
441   if (yinte == info.my) {
442     j = info.my - 1;
443     /* top edge */
444     for (i = info.xs; i < info.xs + info.xm; i++) {
445       if (B) {
446         bjiu = b[j][i].u;
447         bjiv = b[j][i].v;
448       } else {
449         bjiu = 0.0;
450         bjiv = 0.0;
451       }
452       x[j][i].u = lid + bjiu;
453       x[j][i].v = bjiv;
454     }
455   }
456 
457   /* Test whether we are on the left edge of the global array */
458   if (xints == 0) {
459     i = 0;
460     /* left edge */
461     for (j = info.ys; j < info.ys + info.ym; j++) {
462       if (B) {
463         bjiu = b[j][i].u;
464         bjiv = b[j][i].v;
465       } else {
466         bjiu = 0.0;
467         bjiv = 0.0;
468       }
469       x[j][i].u = 0.0 + bjiu;
470       x[j][i].v = 0.0 + bjiv;
471     }
472   }
473 
474   /* Test whether we are on the right edge of the global array */
475   if (xinte == info.mx) {
476     i = info.mx - 1;
477     /* right edge */
478     for (j = info.ys; j < info.ys + info.ym; j++) {
479       if (B) {
480         bjiu = b[j][i].u;
481         bjiv = b[j][i].v;
482       } else {
483         bjiu = 0.0;
484         bjiv = 0.0;
485       }
486       x[j][i].u = 0.0 + bjiu;
487       x[j][i].v = 0.0 + bjiv;
488     }
489   }
490 
491   for (k = 0; k < sweeps; k++) {
492     for (j = info.ys; j < info.ys + info.ym; j++) {
493       for (i = info.xs; i < info.xs + info.xm; i++) {
494         ptconverged = PETSC_FALSE;
495         pfnorm0     = 0.0;
496         fu          = 0.0;
497         fv          = 0.0;
498         fomega      = 0.0;
499         ftemp       = 0.0;
500         /*  Run Newton's method on a single grid point */
501         for (l = 0; l < max_its && !ptconverged; l++) {
502           if (B) {
503             bjiu     = b[j][i].u;
504             bjiv     = b[j][i].v;
505             bjiomega = b[j][i].omega;
506             bjitemp  = b[j][i].temp;
507           } else {
508             bjiu     = 0.0;
509             bjiv     = 0.0;
510             bjiomega = 0.0;
511             bjitemp  = 0.0;
512           }
513 
514           if (i != 0 && i != info.mx - 1 && j != 0 && j != info.my - 1) {
515             /* U velocity */
516             u      = x[j][i].u;
517             uxx    = (2.0 * u - x[j][i - 1].u - x[j][i + 1].u) * hydhx;
518             uyy    = (2.0 * u - x[j - 1][i].u - x[j + 1][i].u) * hxdhy;
519             fu     = uxx + uyy - .5 * (x[j + 1][i].omega - x[j - 1][i].omega) * hx - bjiu;
520             dfudu  = 2.0 * (hydhx + hxdhy);
521             /* V velocity */
522             u      = x[j][i].v;
523             uxx    = (2.0 * u - x[j][i - 1].v - x[j][i + 1].v) * hydhx;
524             uyy    = (2.0 * u - x[j - 1][i].v - x[j + 1][i].v) * hxdhy;
525             fv     = uxx + uyy + .5 * (x[j][i + 1].omega - x[j][i - 1].omega) * hy - bjiv;
526             dfvdv  = 2.0 * (hydhx + hxdhy);
527             /*
528              convective coefficients for upwinding
529              */
530             vx     = x[j][i].u;
531             avx    = PetscAbsScalar(vx);
532             vxp    = .5 * (vx + avx);
533             vxm    = .5 * (vx - avx);
534             vy     = x[j][i].v;
535             avy    = PetscAbsScalar(vy);
536             vyp    = .5 * (vy + avy);
537             vym    = .5 * (vy - avy);
538             /* Omega */
539             u      = x[j][i].omega;
540             uxx    = (2.0 * u - x[j][i - 1].omega - x[j][i + 1].omega) * hydhx;
541             uyy    = (2.0 * u - x[j - 1][i].omega - x[j + 1][i].omega) * hxdhy;
542             fomega = uxx + uyy + (vxp * (u - x[j][i - 1].omega) + vxm * (x[j][i + 1].omega - u)) * hy + (vyp * (u - x[j - 1][i].omega) + vym * (x[j + 1][i].omega - u)) * hx - .5 * grashof * (x[j][i + 1].temp - x[j][i - 1].temp) * hy - bjiomega;
543             /* convective coefficient derivatives */
544             dfodo  = 2.0 * (hydhx + hxdhy) + ((vxp - vxm) * hy + (vyp - vym) * hx);
545             if (PetscRealPart(vx) > 0.0) dfodu = (u - x[j][i - 1].omega) * hy;
546             else dfodu = (x[j][i + 1].omega - u) * hy;
547 
548             if (PetscRealPart(vy) > 0.0) dfodv = (u - x[j - 1][i].omega) * hx;
549             else dfodv = (x[j + 1][i].omega - u) * hx;
550 
551             /* Temperature */
552             u     = x[j][i].temp;
553             uxx   = (2.0 * u - x[j][i - 1].temp - x[j][i + 1].temp) * hydhx;
554             uyy   = (2.0 * u - x[j - 1][i].temp - x[j + 1][i].temp) * hxdhy;
555             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;
556             dftdt = 2.0 * (hydhx + hxdhy) + prandtl * ((vxp - vxm) * hy + (vyp - vym) * hx);
557             if (PetscRealPart(vx) > 0.0) dftdu = prandtl * (u - x[j][i - 1].temp) * hy;
558             else dftdu = prandtl * (x[j][i + 1].temp - u) * hy;
559 
560             if (PetscRealPart(vy) > 0.0) dftdv = prandtl * (u - x[j - 1][i].temp) * hx;
561             else dftdv = prandtl * (x[j + 1][i].temp - u) * hx;
562 
563             /* invert the system:
564              [ dfu / du     0        0        0    ][yu] = [fu]
565              [     0    dfv / dv     0        0    ][yv]   [fv]
566              [ dfo / du dfo / dv dfo / do     0    ][yo]   [fo]
567              [ dft / du dft / dv     0    dft / dt ][yt]   [ft]
568              by simple back-substitution
569            */
570             yu = fu / dfudu;
571             yv = fv / dfvdv;
572             yo = (fomega - (dfodu * yu + dfodv * yv)) / dfodo;
573             yt = (ftemp - (dftdu * yu + dftdv * yv)) / dftdt;
574 
575             x[j][i].u     = x[j][i].u - yu;
576             x[j][i].v     = x[j][i].v - yv;
577             x[j][i].temp  = x[j][i].temp - yt;
578             x[j][i].omega = x[j][i].omega - yo;
579           }
580           if (i == 0) {
581             fomega        = x[j][i].omega - (x[j][i + 1].v - x[j][i].v) * dhx - bjiomega;
582             ftemp         = x[j][i].temp - bjitemp;
583             yo            = fomega;
584             yt            = ftemp;
585             x[j][i].omega = x[j][i].omega - fomega;
586             x[j][i].temp  = x[j][i].temp - ftemp;
587           }
588           if (i == info.mx - 1) {
589             fomega        = x[j][i].omega - (x[j][i].v - x[j][i - 1].v) * dhx - bjiomega;
590             ftemp         = x[j][i].temp - (PetscReal)(grashof > 0) - bjitemp;
591             yo            = fomega;
592             yt            = ftemp;
593             x[j][i].omega = x[j][i].omega - fomega;
594             x[j][i].temp  = x[j][i].temp - ftemp;
595           }
596           if (j == 0) {
597             fomega        = x[j][i].omega + (x[j + 1][i].u - x[j][i].u) * dhy - bjiomega;
598             ftemp         = x[j][i].temp - x[j + 1][i].temp - bjitemp;
599             yo            = fomega;
600             yt            = ftemp;
601             x[j][i].omega = x[j][i].omega - fomega;
602             x[j][i].temp  = x[j][i].temp - ftemp;
603           }
604           if (j == info.my - 1) {
605             fomega        = x[j][i].omega + (x[j][i].u - x[j - 1][i].u) * dhy - bjiomega;
606             ftemp         = x[j][i].temp - x[j - 1][i].temp - bjitemp;
607             yo            = fomega;
608             yt            = ftemp;
609             x[j][i].omega = x[j][i].omega - fomega;
610             x[j][i].temp  = x[j][i].temp - ftemp;
611           }
612           tot_its++;
613           pfnorm = PetscRealPart(fu * fu + fv * fv + fomega * fomega + ftemp * ftemp);
614           pfnorm = PetscSqrtReal(pfnorm);
615           pynorm = PetscRealPart(yu * yu + yv * yv + yo * yo + yt * yt);
616           pynorm = PetscSqrtReal(pynorm);
617           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);
618           pxnorm = PetscSqrtReal(pxnorm);
619           if (l == 0) pfnorm0 = pfnorm;
620           if (rtol * pfnorm0 > pfnorm || atol > pfnorm || pxnorm * stol > pynorm) ptconverged = PETSC_TRUE;
621         }
622       }
623     }
624   }
625   PetscCall(DMDAVecRestoreArrayWrite(da, localX, &x));
626   if (B) { PetscCall(DMDAVecRestoreArrayRead(da, localB, &b)); }
627   PetscCall(DMLocalToGlobalBegin(da, localX, INSERT_VALUES, X));
628   PetscCall(DMLocalToGlobalEnd(da, localX, INSERT_VALUES, X));
629   PetscCall(PetscLogFlops(tot_its * (84.0 + 41.0 + 26.0)));
630   PetscCall(DMRestoreLocalVector(da, &localX));
631   if (B) { PetscCall(DMRestoreLocalVector(da, &localB)); }
632   PetscFunctionReturn(0);
633 }
634 
635 /*TEST
636 
637    test:
638       nsize: 2
639       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full
640       requires: !single
641 
642    test:
643       suffix: 10
644       nsize: 3
645       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type symmetric_multiplicative -snes_view -da_refine 1 -ksp_type fgmres
646       requires: !single
647 
648    test:
649       suffix: 11
650       nsize: 4
651       requires: pastix
652       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
653 
654    test:
655       suffix: 12
656       nsize: 12
657       requires: pastix
658       args: -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_pc_factor_mat_solver_type pastix -pc_redundant_number 5 -da_refine 4 -ksp_type fgmres
659 
660    test:
661       suffix: 13
662       nsize: 3
663       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
664       requires: !single
665 
666    test:
667       suffix: 14
668       nsize: 4
669       args: -snes_monitor_short -pc_type mg -dm_mat_type baij -mg_coarse_pc_type bjacobi -da_refine 3 -ksp_type fgmres
670       requires: !single
671 
672    test:
673       suffix: 14_ds
674       nsize: 4
675       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
676       output_file: output/ex19_2.out
677       requires: !single
678 
679    test:
680       suffix: 17
681       args: -snes_monitor_short -ksp_pc_side right
682       requires: !single
683 
684    test:
685       suffix: 18
686       args: -snes_monitor_ksp draw::draw_lg -ksp_pc_side right
687       requires: x !single
688 
689    test:
690       suffix: 19
691       nsize: 2
692       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -snes_type newtontrdc
693       requires: !single
694 
695    test:
696       suffix: 20
697       nsize: 2
698       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -snes_type newtontrdc -snes_trdc_use_cauchy false
699       requires: !single
700 
701    test:
702       suffix: 2
703       nsize: 4
704       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
705       requires: !single
706 
707    test:
708       suffix: 2_bcols1
709       nsize: 4
710       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols
711       output_file: output/ex19_2.out
712       requires: !single
713 
714    test:
715       suffix: 3
716       nsize: 4
717       requires: mumps
718       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
719 
720    test:
721       suffix: 4
722       nsize: 12
723       requires: mumps
724       args: -da_refine 3 -snes_monitor_short -pc_type redundant -dm_mat_type mpiaij -redundant_ksp_type preonly -redundant_pc_factor_mat_solver_type mumps -pc_redundant_number 5
725       output_file: output/ex19_3.out
726 
727    test:
728       suffix: 6
729       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -ksp_type fgmres -da_refine 1
730       requires: !single
731 
732    test:
733       suffix: 7
734       nsize: 3
735       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -snes_view -da_refine 1 -ksp_type fgmres
736 
737       requires: !single
738    test:
739       suffix: 8
740       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
741       requires: !single
742 
743    test:
744       suffix: 9
745       nsize: 3
746       args: -snes_monitor_short -ksp_monitor_short -pc_type fieldsplit -pc_fieldsplit_type multiplicative -snes_view -da_refine 1 -ksp_type fgmres
747       requires: !single
748 
749    test:
750       suffix: aspin
751       nsize: 4
752       args: -da_refine 3 -da_overlap 2 -snes_monitor_short -snes_type aspin -grashof 4e4 -lidvelocity 100 -ksp_monitor_short
753       requires: !single
754 
755    test:
756       suffix: bcgsl
757       nsize: 2
758       args: -ksp_type bcgsl -ksp_monitor_short -da_refine 2 -ksp_bcgsl_ell 3 -snes_view
759       requires: !single
760 
761    test:
762       suffix: bcols1
763       nsize: 2
764       args: -da_refine 3 -snes_monitor_short -pc_type mg -ksp_type fgmres -pc_mg_type full -mat_fd_coloring_bcols 1
765       output_file: output/ex19_1.out
766       requires: !single
767 
768    test:
769       suffix: bjacobi
770       nsize: 4
771       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
772       requires: !single
773 
774    test:
775       suffix: cgne
776       args: -da_refine 2 -pc_type lu -ksp_type cgne -ksp_monitor_short -ksp_converged_reason -ksp_view -ksp_norm_type unpreconditioned
777       filter: grep -v HERMITIAN
778       requires: !single
779 
780    test:
781       suffix: cgs
782       args: -da_refine 1 -ksp_monitor_short -ksp_type cgs
783       requires: !single
784 
785    test:
786       suffix: composite_fieldsplit
787       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
788       requires: !single
789 
790    test:
791       suffix: composite_fieldsplit_bjacobi
792       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
793       requires: !single
794 
795    test:
796       suffix: composite_fieldsplit_bjacobi_2
797       nsize: 4
798       args: -ksp_type fgmres -pc_type composite -pc_composite_type MULTIPLICATIVE -pc_composite_pcs fieldsplit,bjacobi -sub_0_pc_fieldsplit_block_size 4 -sub_0_pc_fieldsplit_type additive -sub_0_pc_fieldsplit_0_fields 0,1,2 -sub_0_pc_fieldsplit_1_fields 3 -sub_1_pc_bjacobi_blocks 16 -sub_1_sub_pc_type lu -snes_monitor_short -ksp_monitor_short
799       requires: !single
800 
801    test:
802       suffix: composite_gs_newton
803       nsize: 2
804       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
805       requires: !single
806 
807    test:
808       suffix: cuda
809       requires: cuda !single
810       args: -dm_vec_type cuda -dm_mat_type aijcusparse -pc_type none -ksp_type fgmres -snes_monitor_short -snes_rtol 1.e-5
811 
812    test:
813       suffix: draw
814       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
815       requires: x !single
816 
817    test:
818       suffix: drawports
819       args: -snes_monitor_solution draw::draw_ports -da_refine 1
820       output_file: output/ex19_draw.out
821       requires: x !single
822 
823    test:
824       suffix: fas
825       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
826       requires: !single
827 
828    test:
829       suffix: fas_full
830       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
831       requires: !single
832 
833    test:
834       suffix: fdcoloring_ds
835       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds
836       output_file: output/ex19_2.out
837       requires: !single
838 
839    test:
840       suffix: fdcoloring_ds_baij
841       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -dm_mat_type baij
842       output_file: output/ex19_2.out
843       requires: !single
844 
845    test:
846       suffix: fdcoloring_ds_bcols1
847       args: -da_refine 3 -snes_converged_reason -pc_type mg -mat_fd_type ds -mat_fd_coloring_bcols 1
848       output_file: output/ex19_2.out
849       requires: !single
850 
851    test:
852       suffix: fdcoloring_wp
853       args: -da_refine 3 -snes_monitor_short -pc_type mg
854       requires: !single
855 
856    test:
857       suffix: fdcoloring_wp_baij
858       args: -da_refine 3 -snes_monitor_short -pc_type mg -dm_mat_type baij
859       output_file: output/ex19_fdcoloring_wp.out
860       requires: !single
861 
862    test:
863       suffix: fdcoloring_wp_bcols1
864       args: -da_refine 3 -snes_monitor_short -pc_type mg -mat_fd_coloring_bcols 1
865       output_file: output/ex19_fdcoloring_wp.out
866       requires: !single
867 
868    test:
869       suffix: fieldsplit_2
870       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
871       requires: !single
872 
873    test:
874       suffix: fieldsplit_3
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 -fieldsplit_0_pc_type lu -fieldsplit_1_pc_type lu -snes_monitor_short -ksp_monitor_short
876       requires: !single
877 
878    test:
879       suffix: fieldsplit_4
880       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
881       requires: !single
882 
883    # HYPRE PtAP broken with complex numbers
884    test:
885       suffix: fieldsplit_hypre
886       nsize: 2
887       requires: hypre mumps !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
888       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
889 
890    test:
891       suffix: fieldsplit_mumps
892       nsize: 2
893       requires: mumps
894       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
895       output_file: output/ex19_fieldsplit_5.out
896 
897    test:
898       suffix: greedy_coloring
899       nsize: 2
900       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
901       requires: !single
902 
903    # HYPRE PtAP broken with complex numbers
904    test:
905       suffix: hypre
906       nsize: 2
907       requires: hypre !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
908       args: -da_refine 3 -snes_monitor_short -pc_type hypre -ksp_norm_type unpreconditioned
909 
910    # ibcgs is broken when using device vectors
911    test:
912       suffix: ibcgs
913       nsize: 2
914       args: -ksp_type ibcgs -ksp_monitor_short -da_refine 2 -snes_view
915       requires: !complex !single
916 
917    test:
918       suffix: kaczmarz
919       nsize: 2
920       args: -pc_type kaczmarz -ksp_monitor_short -snes_monitor_short -snes_view
921       requires: !single
922 
923    test:
924       suffix: klu
925       requires: suitesparse
926       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu
927       output_file: output/ex19_superlu.out
928 
929    test:
930       suffix: klu_2
931       requires: suitesparse
932       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -pc_factor_mat_ordering_type nd
933       output_file: output/ex19_superlu.out
934 
935    test:
936       suffix: klu_3
937       requires: suitesparse
938       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type klu -mat_klu_use_btf 0
939       output_file: output/ex19_superlu.out
940 
941    test:
942       suffix: ml
943       nsize: 2
944       requires: ml
945       args: -da_refine 3 -snes_monitor_short -pc_type ml
946 
947    test:
948       suffix: ngmres_fas
949       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
950       requires: !single
951 
952    test:
953       suffix: ngmres_fas_gssecant
954       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
955       requires: !single
956 
957    test:
958       suffix: ngmres_fas_ms
959       nsize: 2
960       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
961       requires: !single
962 
963    test:
964       suffix: ngmres_nasm
965       nsize: 4
966       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
967       requires: !single
968 
969    test:
970       suffix: ngs
971       args: -snes_type ngs -snes_view -snes_monitor -snes_rtol 1e-4
972       requires: !single
973 
974    test:
975       suffix: ngs_fd
976       args: -snes_type ngs -snes_ngs_secant -snes_view -snes_monitor -snes_rtol 1e-4
977       requires: !single
978 
979    test:
980       suffix: parms
981       nsize: 2
982       requires: parms
983       args: -pc_type parms -ksp_monitor_short -snes_view
984 
985    test:
986       suffix: superlu
987       requires: superlu
988       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu
989 
990    test:
991       suffix: superlu_sell
992       requires: superlu
993       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
994       output_file: output/ex19_superlu.out
995 
996    test:
997       suffix: superlu_dist
998       requires: superlu_dist
999       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1000       output_file: output/ex19_superlu.out
1001 
1002    test:
1003       suffix: superlu_dist_2
1004       nsize: 2
1005       requires: superlu_dist
1006       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist
1007       output_file: output/ex19_superlu.out
1008 
1009    test:
1010       suffix: superlu_dist_3d
1011       nsize: 4
1012       requires: superlu_dist !defined(PETSCTEST_VALGRIND)
1013       filter: grep -v iam | grep -v openMP
1014       args: -da_grid_x 20 -da_grid_y 20 -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_3d -mat_superlu_dist_d 2 -snes_view -snes_monitor -ksp_monitor
1015 
1016    test:
1017       suffix: superlu_equil
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
1020 
1021    test:
1022       suffix: superlu_equil_sell
1023       requires: superlu
1024       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
1025       output_file: output/ex19_superlu_equil.out
1026 
1027    test:
1028       suffix: tcqmr
1029       args: -da_refine 1 -ksp_monitor_short -ksp_type tcqmr
1030       requires: !single
1031 
1032    test:
1033       suffix: tfqmr
1034       args: -da_refine 1 -ksp_monitor_short -ksp_type tfqmr
1035       requires: !single
1036 
1037    test:
1038       suffix: umfpack
1039       requires: suitesparse
1040       args: -da_refine 2 -pc_type lu -pc_factor_mat_solver_type umfpack -snes_view -snes_monitor_short -ksp_monitor_short -pc_factor_mat_ordering_type external
1041 
1042    test:
1043       suffix: tut_1
1044       nsize: 4
1045       requires: !single
1046       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view
1047 
1048    test:
1049       suffix: tut_2
1050       nsize: 4
1051       requires: !single
1052       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg
1053 
1054    # HYPRE PtAP broken with complex numbers
1055    test:
1056       suffix: tut_3
1057       nsize: 4
1058       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
1059       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre
1060 
1061    test:
1062       suffix: tut_8
1063       nsize: 4
1064       requires: ml !single
1065       args: -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml
1066 
1067    test:
1068       suffix: tut_4
1069       nsize: 1
1070       requires: !single
1071       args: -da_refine 5 -log_view
1072       filter: head -n 2
1073       filter_output: head -n 2
1074 
1075    test:
1076       suffix: tut_5
1077       nsize: 1
1078       requires: !single
1079       args: -da_refine 5 -log_view -pc_type mg
1080       filter: head -n 2
1081       filter_output: head -n 2
1082 
1083    test:
1084       suffix: tut_6
1085       nsize: 4
1086       requires: !single
1087       args: -da_refine 5 -log_view
1088       filter: head -n 2
1089       filter_output: head -n 2
1090 
1091    test:
1092       suffix: tut_7
1093       nsize: 4
1094       requires: !single
1095       args: -da_refine 5 -log_view -pc_type mg
1096       filter: head -n 2
1097       filter_output: head -n 2
1098 
1099    test:
1100       suffix: cuda_1
1101       nsize: 1
1102       requires: cuda
1103       args: -snes_monitor -dm_mat_type seqaijcusparse -dm_vec_type seqcuda -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor -mg_levels_ksp_max_it 3
1104 
1105    test:
1106       suffix: cuda_2
1107       nsize: 3
1108       requires: cuda !single
1109       args: -snes_monitor -dm_mat_type mpiaijcusparse -dm_vec_type mpicuda -pc_type gamg -pc_gamg_esteig_ksp_max_it 10 -ksp_monitor  -mg_levels_ksp_max_it 3
1110 
1111    test:
1112       suffix: cuda_dm_bind_below
1113       nsize: 2
1114       requires: cuda
1115       args: -dm_mat_type aijcusparse -dm_vec_type cuda -da_refine 3 -pc_type mg -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -log_view -pc_mg_log -dm_bind_below 10000
1116       filter: awk "/Level/ {print \$NF}"
1117 
1118    test:
1119       suffix: viennacl_dm_bind_below
1120       nsize: 2
1121       requires: viennacl
1122       args: -dm_mat_type aijviennacl -dm_vec_type viennacl -da_refine 3 -pc_type mg -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -log_view -pc_mg_log -dm_bind_below 10000
1123       filter: awk "/Level/ {print \$NF}"
1124 
1125    test:
1126       suffix: seqbaijmkl
1127       nsize: 1
1128       requires: defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1129       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view
1130 
1131    test:
1132       suffix: mpibaijmkl
1133       nsize: 2
1134       requires:  defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
1135       args: -dm_mat_type baij -snes_monitor -ksp_monitor -snes_view
1136 
1137    test:
1138      suffix: cpardiso
1139      nsize: 4
1140      requires: mkl_cpardiso
1141      args: -pc_type lu -pc_factor_mat_solver_type mkl_cpardiso -ksp_monitor
1142 
1143    test:
1144      suffix: logviewmemory
1145      requires: defined(PETSC_USE_LOG) !defined(PETSCTEST_VALGRIND)
1146      args: -log_view -log_view_memory -da_refine 4
1147      filter: grep MatFDColorSetUp | wc -w | xargs  -I % sh -c "expr % \> 21"
1148 
1149    test:
1150      suffix: fs
1151      args: -pc_type fieldsplit -da_refine 3  -all_ksp_monitor -fieldsplit_y_velocity_pc_type lu  -fieldsplit_temperature_pc_type lu -fieldsplit_x_velocity_pc_type lu  -snes_view
1152 
1153    test:
1154      suffix: asm_matconvert
1155      args: -mat_type aij -pc_type asm -pc_asm_sub_mat_type dense -snes_view
1156 
1157    test:
1158       suffix: euclid
1159       nsize: 2
1160       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1161       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid
1162 
1163    test:
1164       suffix: euclid_bj
1165       nsize: 2
1166       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1167       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_bj
1168 
1169    test:
1170       suffix: euclid_droptolerance
1171       nsize: 1
1172       requires: hypre !single !complex !defined(PETSC_HAVE_HYPRE_MIXEDINT) !defined(PETSC_HAVE_HYPRE_DEVICE)
1173       args: -da_refine 2 -ksp_monitor -snes_monitor -snes_view -pc_type hypre -pc_hypre_type euclid -pc_hypre_euclid_droptolerance .1
1174 
1175    test:
1176       suffix: failure_size
1177       nsize: 1
1178       requires: !defined(PETSC_USE_64BIT_INDICES) !defined(PETSCTEST_VALGRIND)
1179       args: -da_refine 100 -petsc_ci_portable_error_output -error_output_stdout
1180       filter: egrep -v "(options_left|memory block|leaked context|is not freed before MPI_Finalize|Could be the program crashed)"
1181 
1182 TEST*/
1183