Actual source code: ex15.c petsc-3.5.4 2015-05-23
1: static const char help[] = "p-Bratu nonlinear PDE in 2d.\n\
2: We solve the p-Laplacian (nonlinear diffusion) combined with\n\
3: the Bratu (solid fuel ignition) nonlinearity in a 2D rectangular\n\
4: domain, using distributed arrays (DAs) to partition the parallel grid.\n\
5: The command line options include:\n\
6: -p <2>: `p' in p-Laplacian term\n\
7: -epsilon <1e-05>: Strain-regularization in p-Laplacian\n\
8: -lambda <6>: Bratu parameter\n\
9: -blocks <bx,by>: number of coefficient interfaces in x and y direction\n\
10: -kappa <1e-3>: diffusivity in odd regions\n\
11: \n" ;
35: /*
36: mpiexec -n 2 ./ex15 -snes_monitor -ksp_monitor log_summary
37: */
39: /*
40: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
41: Include "petscsnes.h" so that we can use SNES solvers. Note that this
42: file automatically includes:
43: petsc.h - base PETSc routines petscvec.h - vectors
44: petscsys.h - system routines petscmat.h - matrices
45: petscis.h - index sets petscksp.h - Krylov subspace methods
46: petscviewer.h - viewers petscpc.h - preconditioners
47: petscksp.h - linear solvers
48: */
49: #include <petscdm.h>
50: #include <petscdmda.h>
51: #include <petscsnes.h>
53: /* These functions _should_ be internal, but currently have a reverse dependency so cannot be set with
54: * DMDASNESSetPicardLocal . This hack needs to be fixed in PETSc. */
55: PETSC_EXTERN PetscErrorCode SNESPicardComputeFunction(SNES ,Vec ,Vec ,void*) 56: PETSC_EXTERN PetscErrorCode SNESPicardComputeJacobian(SNES ,Vec ,Mat ,Mat ,void*) 58: typedef enum {JAC_BRATU,JAC_PICARD,JAC_STAR,JAC_NEWTON} JacType;
59: static const char *const JacTypes[] = {"BRATU" ,"PICARD" ,"STAR" ,"NEWTON" ,"JacType" ,"JAC_" ,0};
61: /*
62: User-defined application context - contains data needed by the
63: application-provided call-back routines, FormJacobianLocal() and
64: FormFunctionLocal().
65: */
66: typedef struct {
67: PassiveReal lambda; /* Bratu parameter */
68: PassiveReal p; /* Exponent in p-Laplacian */
69: PassiveReal epsilon; /* Regularization */
70: PassiveReal source; /* Source term */
71: JacType jtype; /* What type of Jacobian to assemble */
72: PetscBool picard;
73: PetscInt blocks[2];
74: PetscReal kappa;
75: PetscInt initial; /* initial conditions type */
76: } AppCtx;
78: /*
79: User-defined routines
80: */
81: static PetscErrorCode FormRHS(AppCtx*,DM,Vec ) 82: static PetscErrorCode FormInitialGuess(AppCtx*,DM,Vec ) 83: static PetscErrorCode FormFunctionLocal(DMDALocalInfo *,PetscScalar **,PetscScalar **,AppCtx*) 84: static PetscErrorCode FormFunctionPicardLocal(DMDALocalInfo *,PetscScalar **,PetscScalar **,AppCtx*) 85: static PetscErrorCode FormJacobianLocal(DMDALocalInfo *,PetscScalar **,Mat ,Mat ,AppCtx*) 86: static PetscErrorCode NonlinearGS(SNES ,Vec ,Vec ,void*) 88: typedef struct _n_PreCheck *PreCheck;
89: 90: MPI_Comm comm;
91: PetscReal angle;
92: Vec Ylast;
93: PetscViewer monitor;
94: };
95: PetscErrorCode PreCheckCreate(MPI_Comm ,PreCheck*) 96: PetscErrorCode PreCheckDestroy(PreCheck*) 97: PetscErrorCode PreCheckFunction(SNESLineSearch ,Vec ,Vec ,PetscBool *,void*) 98: PetscErrorCode PreCheckSetFromOptions(PreCheck)102: 103: {
104: SNES snes; /* nonlinear solver */
105: Vec x,r,b; /* solution, residual, rhs vectors */
106: Mat A,B; /* Jacobian and preconditioning matrices */
107: AppCtx user; /* user-defined work context */
108: PetscInt its; /* iterations for convergence */
109: SNESConvergedReason reason; /* Check convergence */
110: PetscBool alloc_star; /* Only allocate for the STAR stencil */
111: PetscBool write_output;
112: char filename[PETSC_MAX_PATH_LEN] = "ex15.vts" ;
113: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
114: DM da,dastar; /* distributed array data structure */
115: PreCheck precheck = NULL; /* precheck context for version in this file */
116: PetscInt use_precheck; /* 0=none, 1=version in this file, 2=SNES -provided version */
117: PetscReal precheck_angle; /* When manually setting the SNES -provided precheck function */
118: PetscErrorCode ierr;
119: SNESLineSearch linesearch;
121: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122: Initialize program
123: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125: PetscInitialize (&argc,&argv,(char*)0,help);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Initialize problem parameters
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: user.lambda = 0.0; user.p = 2.0; user.epsilon = 1e-5; user.source = 0.1; user.jtype = JAC_NEWTON;user.initial=-1;
131: user.blocks[0] = 1; user.blocks[1] = 1; user.kappa = 1e-3;
132: alloc_star = PETSC_FALSE ;
133: use_precheck = 0; precheck_angle = 10.;
134: user.picard = PETSC_FALSE ;
135: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"p-Bratu options" ,__FILE__);
136: {
137: PetscInt two=2;
138: PetscOptionsReal ("-lambda" ,"Bratu parameter" ,"" ,user.lambda,&user.lambda,NULL);
139: PetscOptionsReal ("-p" ,"Exponent `p' in p-Laplacian" ,"" ,user.p,&user.p,NULL);
140: PetscOptionsReal ("-epsilon" ,"Strain-regularization in p-Laplacian" ,"" ,user.epsilon,&user.epsilon,NULL);
141: PetscOptionsReal ("-source" ,"Constant source term" ,"" ,user.source,&user.source,NULL);
142: PetscOptionsEnum ("-jtype" ,"Jacobian approximation to assemble" ,"" ,JacTypes,(PetscEnum )user.jtype,(PetscEnum *)&user.jtype,NULL);
143: PetscOptionsName ("-picard" ,"Solve with defect-correction Picard iteration" ,"" ,&user.picard);
144: if (user.picard) {user.jtype = JAC_PICARD; user.p = 3;}
145: PetscOptionsBool ("-alloc_star" ,"Allocate for STAR stencil (5-point)" ,"" ,alloc_star,&alloc_star,NULL);
146: PetscOptionsInt ("-precheck" ,"Use a pre-check correction intended for use with Picard iteration 1=this version, 2=library" ,"" ,use_precheck,&use_precheck,NULL);
147: PetscOptionsInt ("-initial" ,"Initial conditions type (-1: default, 0: zero-valued, 1: peaked guess)" ,"" ,user.initial,&user.initial,NULL);
148: if (use_precheck == 2) { /* Using library version, get the angle */
149: PetscOptionsReal ("-precheck_angle" ,"Angle in degrees between successive search directions necessary to activate step correction" ,"" ,precheck_angle,&precheck_angle,NULL);
150: }
151: PetscOptionsIntArray ("-blocks" ,"number of coefficient interfaces in x and y direction" ,"" ,user.blocks,&two,NULL);
152: PetscOptionsReal ("-kappa" ,"diffusivity in odd regions" ,"" ,user.kappa,&user.kappa,NULL);
153: PetscOptionsString ("-o" ,"Output solution in vts format" ,"" ,filename,filename,sizeof (filename),&write_output);
154: }
155: PetscOptionsEnd ();
156: if (user.lambda > bratu_lambda_max || user.lambda < bratu_lambda_min) {
157: PetscPrintf (PETSC_COMM_WORLD ,"WARNING: lambda %g out of range for p=2\n" ,user.lambda);
158: }
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Create nonlinear solver context
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: SNESCreate (PETSC_COMM_WORLD ,&snes);
165: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: Create distributed array (DMDA ) to manage parallel grid and vectors
167: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168: DMDACreate2d (PETSC_COMM_WORLD ,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX ,-4,-4,PETSC_DECIDE ,PETSC_DECIDE ,
169: 1,1,NULL,NULL,&da);
170: DMDACreate2d (PETSC_COMM_WORLD ,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR ,-4,-4,PETSC_DECIDE ,PETSC_DECIDE ,
171: 1,1,NULL,NULL,&dastar);
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Extract global vectors from DM; then duplicate for remaining
176: vectors that are the same types
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: DMCreateGlobalVector (da,&x);
179: VecDuplicate (x,&r);
180: VecDuplicate (x,&b);
182: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183: Create matrix data structure; set Jacobian evaluation routine
185: Set Jacobian matrix data structure and default Jacobian evaluation
186: routine. User can override with:
187: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
188: (unless user explicitly sets preconditioner)
189: -snes_mf_operator : form preconditioning matrix as set by the user,
190: but use matrix-free approx for Jacobian-vector
191: products within Newton-Krylov method
193: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194: /* B can be type of MATAIJ ,MATBAIJ or MATSBAIJ */
195: DMCreateMatrix (alloc_star ? dastar : da,&B);
196: A = B;
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Set local function evaluation routine
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: DMSetApplicationContext (da, &user);
202: SNESSetDM (snes,da);
203: if (user.picard) {
204: /*
205: This is not really right requiring the user to call SNESSetFunction /Jacobian but the DMDASNESSetPicardLocal () cannot access
206: the SNES to set it
207: */
208: DMDASNESSetPicardLocal (da,INSERT_VALUES ,(PetscErrorCode (*)(DMDALocalInfo *,void*,void*,void*))FormFunctionPicardLocal,
209: (PetscErrorCode (*)(DMDALocalInfo *,void*,Mat ,Mat ,void*))FormJacobianLocal,&user);
210: SNESSetFunction (snes,NULL,SNESPicardComputeFunction,&user);
211: SNESSetJacobian (snes,NULL,NULL,SNESPicardComputeJacobian,&user);
212: } else {
213: DMDASNESSetFunctionLocal (da,INSERT_VALUES ,(PetscErrorCode (*)(DMDALocalInfo *,void*,void*,void*))FormFunctionLocal,&user);
214: DMDASNESSetJacobianLocal (da,(PetscErrorCode (*)(DMDALocalInfo *,void*,Mat ,Mat ,void*))FormJacobianLocal,&user);
215: }
218: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219: Customize nonlinear solver; set runtime options
220: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221: SNESSetFromOptions (snes);
222: SNESSetNGS (snes,NonlinearGS,&user);
223: SNESGetLineSearch (snes, &linesearch);
224: /* Set up the precheck context if requested */
225: if (use_precheck == 1) { /* Use the precheck routines in this file */
226: PreCheckCreate(PETSC_COMM_WORLD ,&precheck);
227: PreCheckSetFromOptions(precheck);
228: SNESLineSearchSetPreCheck (linesearch,PreCheckFunction,precheck);
229: } else if (use_precheck == 2) { /* Use the version provided by the library */
230: SNESLineSearchSetPreCheck (linesearch,SNESLineSearchPreCheckPicard ,&precheck_angle);
231: }
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Evaluate initial guess
235: Note: The user should initialize the vector, x, with the initial guess
236: for the nonlinear solver prior to calling SNESSolve (). In particular,
237: to employ an initial guess of zero, the user should explicitly set
238: this vector to zero by calling VecSet ().
239: */
241: FormInitialGuess(&user,da,x);
242: FormRHS(&user,da,b);
244: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
245: Solve nonlinear system
246: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
247: SNESSolve (snes,b,x);
248: SNESGetIterationNumber (snes,&its);
249: SNESGetConvergedReason (snes,&reason);
251: PetscPrintf (PETSC_COMM_WORLD ,"%s Number of nonlinear iterations = %D\n" ,SNESConvergedReasons[reason],its);
253: if (write_output) {
254: PetscViewer viewer;
255: PetscViewerVTKOpen (PETSC_COMM_WORLD ,filename,FILE_MODE_WRITE,&viewer);
256: VecView (x,viewer);
257: PetscViewerDestroy (&viewer);
258: }
260: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: Free work space. All PETSc objects should be destroyed when they
262: are no longer needed.
263: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
265: if (A != B) {
266: MatDestroy (&A);
267: }
268: MatDestroy (&B);
269: VecDestroy (&x);
270: VecDestroy (&r);
271: VecDestroy (&b);
272: SNESDestroy (&snes);
273: DMDestroy (&da);
274: DMDestroy (&dastar);
275: PreCheckDestroy(&precheck);
276: PetscFinalize ();
277: return 0;
278: }
280: /* ------------------------------------------------------------------- */
283: /*
284: FormInitialGuess - Forms initial approximation.
286: Input Parameters:
287: user - user-defined application context
288: X - vector
290: Output Parameter:
291: X - vector
292: */
293: PetscErrorCode FormInitialGuess(AppCtx *user,DM da,Vec X)294: {
295: PetscInt i,j,Mx,My,xs,ys,xm,ym;
297: PetscReal temp1,temp,hx,hy;
298: PetscScalar **x;
301: DMDAGetInfo (da,PETSC_IGNORE ,&Mx,&My,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,
302: PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE );
304: hx = 1.0/(PetscReal )(Mx-1);
305: hy = 1.0/(PetscReal )(My-1);
306: temp1 = user->lambda / (user->lambda + 1.);
308: /*
309: Get a pointer to vector data.
310: - For default PETSc vectors, VecGetArray () returns a pointer to
311: the data array. Otherwise, the routine is implementation dependent.
312: - You MUST call VecRestoreArray () when you no longer need access to
313: the array.
314: */
315: DMDAVecGetArray (da,X,&x);
317: /*
318: Get local grid boundaries (for 2-dimensional DA):
319: xs, ys - starting grid indices (no ghost points)
320: xm, ym - widths of local grid (no ghost points)
322: */
323: DMDAGetCorners (da,&xs,&ys,NULL,&xm,&ym,NULL);
325: /*
326: Compute initial guess over the locally owned part of the grid
327: */
328: for (j=ys; j<ys+ym; j++) {
329: temp = (PetscReal )(PetscMin(j,My-j-1))*hy;
330: for (i=xs; i<xs+xm; i++) {
331: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
332: /* boundary conditions are all zero Dirichlet */
333: x[j][i] = 0.0;
334: } else {
335: if (user->initial == -1) {
336: if (user->lambda != 0) {
337: x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
338: } else {
339: /* The solution above is an exact solution for lambda=0, this avoids "accidentally" starting
340: * with an exact solution. */
341: const PetscReal
342: xx = 2*(PetscReal )i/(Mx-1) - 1,
343: yy = 2*(PetscReal )j/(My-1) - 1;
344: x[j][i] = (1 - xx*xx) * (1-yy*yy) * xx * yy;
345: }
346: } else if (user->initial == 0) {
347: x[j][i] = 0.;
348: } else if (user->initial == 1) {
349: const PetscReal
350: xx = 2*(PetscReal )i/(Mx-1) - 1,
351: yy = 2*(PetscReal )j/(My-1) - 1;
352: x[j][i] = (1 - xx*xx) * (1-yy*yy) * xx * yy;
353: } else {
354: if (user->lambda != 0) {
355: x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
356: } else {
357: x[j][i] = 0.5*PetscSqrtReal(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
358: }
359: }
360: }
361: }
362: }
363: /*
364: Restore vector
365: */
366: DMDAVecRestoreArray (da,X,&x);
367: return (0);
368: }
372: /*
373: FormRHS - Forms constant RHS for the problem.
375: Input Parameters:
376: user - user-defined application context
377: B - RHS vector
379: Output Parameter:
380: B - vector
381: */
382: PetscErrorCode FormRHS(AppCtx *user,DM da,Vec B)383: {
384: PetscInt i,j,Mx,My,xs,ys,xm,ym;
386: PetscReal hx,hy;
387: PetscScalar **b;
390: DMDAGetInfo (da,PETSC_IGNORE ,&Mx,&My,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,
391: PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE );
393: hx = 1.0/(PetscReal )(Mx-1);
394: hy = 1.0/(PetscReal )(My-1);
395: DMDAVecGetArray (da,B,&b);
396: DMDAGetCorners (da,&xs,&ys,NULL,&xm,&ym,NULL);
397: for (j=ys; j<ys+ym; j++) {
398: for (i=xs; i<xs+xm; i++) {
399: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
400: b[j][i] = 0.0;
401: } else {
402: b[j][i] = hx*hy*user->source;
403: }
404: }
405: }
406: DMDAVecRestoreArray (da,B,&b);
407: return (0);
408: }
410: PetscReal kappa(const AppCtx *ctx,PetscReal x,PetscReal y)411: {
412: return (((PetscInt )(x*ctx->blocks[0])) + ((PetscInt )(y*ctx->blocks[1]))) % 2 ? ctx->kappa : 1.0;
413: }
414: /* p-Laplacian diffusivity */
415: PetscScalar eta(const AppCtx *ctx,PetscReal x,PetscReal y,PetscScalar ux,PetscScalar uy)416: {
417: return kappa(ctx,x,y) * PetscPowScalar(PetscSqr(ctx->epsilon)+0.5*(ux*ux + uy*uy),0.5*(ctx->p-2.));
418: }
419: PetscScalar deta(const AppCtx *ctx,PetscReal x,PetscReal y,PetscScalar ux,PetscScalar uy)420: {
421: return (ctx->p == 2)
422: ? 0
423: : kappa(ctx,x,y)*PetscPowScalar(PetscSqr(ctx->epsilon)+0.5*(ux*ux + uy*uy),0.5*(ctx->p-4)) * 0.5 * (ctx->p-2.);
424: }
427: /* ------------------------------------------------------------------- */
430: /*
431: FormFunctionLocal - Evaluates nonlinear function, F(x).
432: */
433: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)434: {
435: PetscReal hx,hy,dhx,dhy,sc;
436: PetscInt i,j;
437: PetscScalar eu;
442: hx = 1.0/(PetscReal )(info->mx-1);
443: hy = 1.0/(PetscReal )(info->my-1);
444: sc = hx*hy*user->lambda;
445: dhx = 1/hx;
446: dhy = 1/hy;
447: /*
448: Compute function over the locally owned part of the grid
449: */
450: for (j=info->ys; j<info->ys+info->ym; j++) {
451: for (i=info->xs; i<info->xs+info->xm; i++) {
452: PetscReal xx = i*hx,yy = j*hy;
453: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
454: f[j][i] = x[j][i];
455: } else {
456: const PetscScalar
457: u = x[j][i],
458: ux_E = dhx*(x[j][i+1]-x[j][i]),
459: uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
460: ux_W = dhx*(x[j][i]-x[j][i-1]),
461: uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
462: ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
463: uy_N = dhy*(x[j+1][i]-x[j][i]),
464: ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]),
465: uy_S = dhy*(x[j][i]-x[j-1][i]),
466: e_E = eta(user,xx,yy,ux_E,uy_E),
467: e_W = eta(user,xx,yy,ux_W,uy_W),
468: e_N = eta(user,xx,yy,ux_N,uy_N),
469: e_S = eta(user,xx,yy,ux_S,uy_S),
470: uxx = -hy * (e_E*ux_E - e_W*ux_W),
471: uyy = -hx * (e_N*uy_N - e_S*uy_S);
472: if (sc) eu = PetscExpScalar(u);
473: else eu = 0.;
474: /** For p=2, these terms decay to:
475: * uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx
476: * uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy
477: **/
478: f[j][i] = uxx + uyy - sc*eu;
479: }
480: }
481: }
482: PetscLogFlops (info->xm*info->ym*(72.0));
483: return (0);
484: }
488: /*
489: This is the opposite sign of the part of FormFunctionLocal that excludes the A(x) x part of the operation,
490: that is FormFunction applies A(x) x - b(x) while this applies b(x) because for Picard we think of it as solving A(x) x = b(x)
492: */
493: PetscErrorCode FormFunctionPicardLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)494: {
495: PetscReal hx,hy,sc;
496: PetscInt i,j;
500: hx = 1.0/(PetscReal )(info->mx-1);
501: hy = 1.0/(PetscReal )(info->my-1);
502: sc = hx*hy*user->lambda;
503: /*
504: Compute function over the locally owned part of the grid
505: */
506: for (j=info->ys; j<info->ys+info->ym; j++) {
507: for (i=info->xs; i<info->xs+info->xm; i++) {
508: if (!(i == 0 || j == 0 || i == info->mx-1 || j == info->my-1)) {
509: const PetscScalar u = x[j][i];
510: f[j][i] = sc*PetscExpScalar(u);
511: }
512: }
513: }
514: PetscLogFlops (info->xm*info->ym*2.0);
515: return (0);
516: }
520: /*
521: FormJacobianLocal - Evaluates Jacobian matrix.
522: */
523: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat J,Mat B,AppCtx *user)524: {
526: PetscInt i,j;
527: MatStencil col[9],row;
528: PetscScalar v[9];
529: PetscReal hx,hy,hxdhy,hydhx,dhx,dhy,sc;
532: hx = 1.0/(PetscReal )(info->mx-1);
533: hy = 1.0/(PetscReal )(info->my-1);
534: sc = hx*hy*user->lambda;
535: dhx = 1/hx;
536: dhy = 1/hy;
537: hxdhy = hx/hy;
538: hydhx = hy/hx;
540: /*
541: Compute entries for the locally owned part of the Jacobian.
542: - PETSc parallel matrix formats are partitioned by
543: contiguous chunks of rows across the processors.
544: - Each processor needs to insert only elements that it owns
545: locally (but any non-local elements will be sent to the
546: appropriate processor during matrix assembly).
547: - Here, we set all entries for a particular row at once.
548: */
549: for (j=info->ys; j<info->ys+info->ym; j++) {
550: for (i=info->xs; i<info->xs+info->xm; i++) {
551: PetscReal xx = i*hx,yy = j*hy;
552: row.j = j; row.i = i;
553: /* boundary points */
554: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
555: v[0] = 1.0;
556: MatSetValuesStencil (B,1,&row,1,&row,v,INSERT_VALUES );
557: } else {
558: /* interior grid points */
559: const PetscScalar
560: ux_E = dhx*(x[j][i+1]-x[j][i]),
561: uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
562: ux_W = dhx*(x[j][i]-x[j][i-1]),
563: uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
564: ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
565: uy_N = dhy*(x[j+1][i]-x[j][i]),
566: ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]),
567: uy_S = dhy*(x[j][i]-x[j-1][i]),
568: u = x[j][i],
569: e_E = eta(user,xx,yy,ux_E,uy_E),
570: e_W = eta(user,xx,yy,ux_W,uy_W),
571: e_N = eta(user,xx,yy,ux_N,uy_N),
572: e_S = eta(user,xx,yy,ux_S,uy_S),
573: de_E = deta(user,xx,yy,ux_E,uy_E),
574: de_W = deta(user,xx,yy,ux_W,uy_W),
575: de_N = deta(user,xx,yy,ux_N,uy_N),
576: de_S = deta(user,xx,yy,ux_S,uy_S),
577: skew_E = de_E*ux_E*uy_E,
578: skew_W = de_W*ux_W*uy_W,
579: skew_N = de_N*ux_N*uy_N,
580: skew_S = de_S*ux_S*uy_S,
581: cross_EW = 0.25*(skew_E - skew_W),
582: cross_NS = 0.25*(skew_N - skew_S),
583: newt_E = e_E+de_E*PetscSqr(ux_E),
584: newt_W = e_W+de_W*PetscSqr(ux_W),
585: newt_N = e_N+de_N*PetscSqr(uy_N),
586: newt_S = e_S+de_S*PetscSqr(uy_S);
587: /* interior grid points */
588: switch (user->jtype) {
589: case JAC_BRATU:
590: /* Jacobian from p=2 */
591: v[0] = -hxdhy; col[0].j = j-1; col[0].i = i;
592: v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
593: v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(u); col[2].j = row.j; col[2].i = row.i;
594: v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
595: v[4] = -hxdhy; col[4].j = j+1; col[4].i = i;
596: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
597: break ;
598: case JAC_PICARD:
599: /* Jacobian arising from Picard linearization */
600: v[0] = -hxdhy*e_S; col[0].j = j-1; col[0].i = i;
601: v[1] = -hydhx*e_W; col[1].j = j; col[1].i = i-1;
602: v[2] = (e_W+e_E)*hydhx + (e_S+e_N)*hxdhy; col[2].j = row.j; col[2].i = row.i;
603: v[3] = -hydhx*e_E; col[3].j = j; col[3].i = i+1;
604: v[4] = -hxdhy*e_N; col[4].j = j+1; col[4].i = i;
605: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
606: break ;
607: case JAC_STAR:
608: /* Full Jacobian, but only a star stencil */
609: col[0].j = j-1; col[0].i = i;
610: col[1].j = j; col[1].i = i-1;
611: col[2].j = j; col[2].i = i;
612: col[3].j = j; col[3].i = i+1;
613: col[4].j = j+1; col[4].i = i;
614: v[0] = -hxdhy*newt_S + cross_EW;
615: v[1] = -hydhx*newt_W + cross_NS;
616: v[2] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
617: v[3] = -hydhx*newt_E - cross_NS;
618: v[4] = -hxdhy*newt_N - cross_EW;
619: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
620: break ;
621: case JAC_NEWTON:
622: /** The Jacobian is
623: *
624: * -div [ eta (grad u) + deta (grad u0 . grad u) grad u0 ] - (eE u0) u
625: *
626: **/
627: col[0].j = j-1; col[0].i = i-1;
628: col[1].j = j-1; col[1].i = i;
629: col[2].j = j-1; col[2].i = i+1;
630: col[3].j = j; col[3].i = i-1;
631: col[4].j = j; col[4].i = i;
632: col[5].j = j; col[5].i = i+1;
633: col[6].j = j+1; col[6].i = i-1;
634: col[7].j = j+1; col[7].i = i;
635: col[8].j = j+1; col[8].i = i+1;
636: v[0] = -0.25*(skew_S + skew_W);
637: v[1] = -hxdhy*newt_S + cross_EW;
638: v[2] = 0.25*(skew_S + skew_E);
639: v[3] = -hydhx*newt_W + cross_NS;
640: v[4] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
641: v[5] = -hydhx*newt_E - cross_NS;
642: v[6] = 0.25*(skew_N + skew_W);
643: v[7] = -hxdhy*newt_N - cross_EW;
644: v[8] = -0.25*(skew_N + skew_E);
645: MatSetValuesStencil (B,1,&row,9,col,v,INSERT_VALUES );
646: break ;
647: default: 648: SETERRQ1 (PetscObjectComm ((PetscObject )info->da),PETSC_ERR_SUP,"Jacobian type %d not implemented" ,user->jtype);
649: }
650: }
651: }
652: }
654: /*
655: Assemble matrix, using the 2-step process:
656: MatAssemblyBegin (), MatAssemblyEnd ().
657: */
658: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
659: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
661: if (J != B) {
662: MatAssemblyBegin (J,MAT_FINAL_ASSEMBLY);
663: MatAssemblyEnd (J,MAT_FINAL_ASSEMBLY);
664: }
666: /*
667: Tell the matrix we will never add a new nonzero location to the
668: matrix. If we do, it will generate an error.
669: */
670: if (user->jtype == JAC_NEWTON) {
671: PetscLogFlops (info->xm*info->ym*(131.0));
672: }
673: MatSetOption (B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE );
674: return (0);
675: }
677: /***********************************************************
678: * PreCheck implementation
679: ***********************************************************/
682: PetscErrorCode PreCheckSetFromOptions(PreCheck precheck)683: {
685: PetscBool flg;
688: PetscOptionsBegin (precheck->comm,NULL,"PreCheck Options" ,"none" );
689: PetscOptionsReal ("-precheck_angle" ,"Angle in degrees between successive search directions necessary to activate step correction" ,"" ,precheck->angle,&precheck->angle,NULL);
690: flg = PETSC_FALSE ;
691: PetscOptionsBool ("-precheck_monitor" ,"Monitor choices made by precheck routine" ,"" ,flg,&flg,NULL);
692: if (flg) {
693: PetscViewerASCIIOpen (precheck->comm,"stdout" ,&precheck->monitor);
694: }
695: PetscOptionsEnd ();
696: return (0);
697: }
701: /*
702: Compare the direction of the current and previous step, modify the current step accordingly
703: */
704: PetscErrorCode PreCheckFunction(SNESLineSearch linesearch,Vec X,Vec Y,PetscBool *changed, void *ctx)705: {
707: PreCheck precheck;
708: Vec Ylast;
709: PetscScalar dot;
710: PetscInt iter;
711: PetscReal ynorm,ylastnorm,theta,angle_radians;
712: SNES snes;
715: SNESLineSearchGetSNES (linesearch, &snes);
716: precheck = (PreCheck)ctx;
717: if (!precheck->Ylast) {VecDuplicate (Y,&precheck->Ylast);}
718: Ylast = precheck->Ylast;
719: SNESGetIterationNumber (snes,&iter);
720: if (iter < 1) {
721: VecCopy (Y,Ylast);
722: *changed = PETSC_FALSE ;
723: return (0);
724: }
726: VecDot (Y,Ylast,&dot);
727: VecNorm (Y,NORM_2 ,&ynorm);
728: VecNorm (Ylast,NORM_2 ,&ylastnorm);
729: /* Compute the angle between the vectors Y and Ylast, clip to keep inside the domain of acos() */
730: theta = PetscAcosReal((PetscReal )PetscClipInterval(PetscAbsScalar(dot) / (ynorm * ylastnorm),-1.0,1.0));
731: angle_radians = precheck->angle * PETSC_PI / 180.;
732: if (PetscAbsReal(theta) < angle_radians || PetscAbsReal(theta - PETSC_PI) < angle_radians) {
733: /* Modify the step Y */
734: PetscReal alpha,ydiffnorm;
735: VecAXPY (Ylast,-1.0,Y);
736: VecNorm (Ylast,NORM_2 ,&ydiffnorm);
737: alpha = ylastnorm / ydiffnorm;
738: VecCopy (Y,Ylast);
739: VecScale (Y,alpha);
740: if (precheck->monitor) {
741: PetscViewerASCIIPrintf (precheck->monitor,"Angle %E degrees less than threshold %g, corrected step by alpha=%g\n" ,(double)(theta*180./PETSC_PI),(double)precheck->angle,(double)alpha);
742: }
743: } else {
744: VecCopy (Y,Ylast);
745: *changed = PETSC_FALSE ;
746: if (precheck->monitor) {
747: PetscViewerASCIIPrintf (precheck->monitor,"Angle %E degrees exceeds threshold %g, no correction applied\n" ,(double)(theta*180./PETSC_PI),(double)precheck->angle);
748: }
749: }
750: return (0);
751: }
755: PetscErrorCode PreCheckDestroy(PreCheck *precheck)756: {
760: if (!*precheck) return (0);
761: VecDestroy (&(*precheck)->Ylast);
762: PetscViewerDestroy (&(*precheck)->monitor);
763: PetscFree (*precheck);
764: return (0);
765: }
769: PetscErrorCode PreCheckCreate(MPI_Comm comm,PreCheck *precheck)770: {
774: PetscMalloc (sizeof (struct _n_PreCheck ),precheck);
775: PetscMemzero (*precheck,sizeof (struct _n_PreCheck ));
777: (*precheck)->comm = comm;
778: (*precheck)->angle = 10.; /* only active if angle is less than 10 degrees */
779: return (0);
780: }
784: /*
785: Applies some sweeps on nonlinear Gauss-Seidel on each process
787: */
788: PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx)789: {
790: PetscInt i,j,k,xs,ys,xm,ym,its,tot_its,sweeps,l,m;
792: PetscReal hx,hy,hxdhy,hydhx,dhx,dhy,sc;
793: PetscScalar **x,**b,bij,F,F0=0,J,y,u,eu;
794: PetscReal atol,rtol,stol;
795: DM da;
796: AppCtx *user = (AppCtx*)ctx;
797: Vec localX,localB;
798: DMDALocalInfo info;
801: SNESGetDM (snes,&da);
802: DMDAGetLocalInfo (da,&info);
804: hx = 1.0/(PetscReal )(info.mx-1);
805: hy = 1.0/(PetscReal )(info.my-1);
806: sc = hx*hy*user->lambda;
807: dhx = 1/hx;
808: dhy = 1/hy;
809: hxdhy = hx/hy;
810: hydhx = hy/hx;
812: tot_its = 0;
813: SNESNGSGetSweeps (snes,&sweeps);
814: SNESNGSGetTolerances (snes,&atol,&rtol,&stol,&its);
815: DMGetLocalVector (da,&localX);
816: if (B) {
817: DMGetLocalVector (da,&localB);
818: }
819: if (B) {
820: DMGlobalToLocalBegin (da,B,INSERT_VALUES ,localB);
821: DMGlobalToLocalEnd (da,B,INSERT_VALUES ,localB);
822: }
823: if (B) DMDAVecGetArray (da,localB,&b);
824: DMGlobalToLocalBegin (da,X,INSERT_VALUES ,localX);
825: DMGlobalToLocalEnd (da,X,INSERT_VALUES ,localX);
826: DMDAVecGetArray (da,localX,&x);
827: for (l=0; l<sweeps; l++) {
828: /*
829: Get local grid boundaries (for 2-dimensional DMDA ):
830: xs, ys - starting grid indices (no ghost points)
831: xm, ym - widths of local grid (no ghost points)
832: */
833: DMDAGetCorners (da,&xs,&ys,NULL,&xm,&ym,NULL);
834: for (m=0; m<2; m++) {
835: for (j=ys; j<ys+ym; j++) {
836: for (i=xs+(m+j)%2; i<xs+xm; i+=2) {
837: PetscReal xx = i*hx,yy = j*hy;
838: if (B) bij = b[j][i];
839: else bij = 0.;
841: if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
842: /* boundary conditions are all zero Dirichlet */
843: x[j][i] = 0.0 + bij;
844: } else {
845: const PetscScalar
846: u_E = x[j][i+1],
847: u_W = x[j][i-1],
848: u_N = x[j+1][i],
849: u_S = x[j-1][i];
850: const PetscScalar
851: uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
852: uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
853: ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
854: ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]);
855: u = x[j][i];
856: for (k=0; k<its; k++) {
857: const PetscScalar
858: ux_E = dhx*(u_E-u),
859: ux_W = dhx*(u-u_W),
860: uy_N = dhy*(u_N-u),
861: uy_S = dhy*(u-u_S),
862: e_E = eta(user,xx,yy,ux_E,uy_E),
863: e_W = eta(user,xx,yy,ux_W,uy_W),
864: e_N = eta(user,xx,yy,ux_N,uy_N),
865: e_S = eta(user,xx,yy,ux_S,uy_S),
866: de_E = deta(user,xx,yy,ux_E,uy_E),
867: de_W = deta(user,xx,yy,ux_W,uy_W),
868: de_N = deta(user,xx,yy,ux_N,uy_N),
869: de_S = deta(user,xx,yy,ux_S,uy_S),
870: newt_E = e_E+de_E*PetscSqr(ux_E),
871: newt_W = e_W+de_W*PetscSqr(ux_W),
872: newt_N = e_N+de_N*PetscSqr(uy_N),
873: newt_S = e_S+de_S*PetscSqr(uy_S),
874: uxx = -hy * (e_E*ux_E - e_W*ux_W),
875: uyy = -hx * (e_N*uy_N - e_S*uy_S);
877: if (sc) eu = PetscExpScalar(u);
878: else eu = 0;
880: F = uxx + uyy - sc*eu - bij;
881: if (k == 0) F0 = F;
882: J = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*eu;
883: y = F/J;
884: u -= y;
885: tot_its++;
886: if (atol > PetscAbsReal(PetscRealPart(F)) ||
887: rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) ||
888: stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) {
889: break ;
890: }
891: }
892: x[j][i] = u;
893: }
894: }
895: }
896: }
897: /*
898: x Restore vector
899: */
900: }
901: DMDAVecRestoreArray (da,localX,&x);
902: DMLocalToGlobalBegin (da,localX,INSERT_VALUES ,X);
903: DMLocalToGlobalEnd (da,localX,INSERT_VALUES ,X);
904: PetscLogFlops (tot_its*(118.0));
905: DMRestoreLocalVector (da,&localX);
906: if (B) {
907: DMDAVecRestoreArray (da,localB,&b);
908: DMRestoreLocalVector (da,&localB);
909: }
910: return (0);
911: }