Actual source code: ex15.c petsc-3.4.5 2014-06-29
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 <petscdmda.h>
50: #include <petscsnes.h>
52: /* These functions _should_ be internal, but currently have a reverse dependency so cannot be set with
53: * DMDASNESSetPicardLocal . This hack needs to be fixed in PETSc. */
54: PETSC_EXTERN PetscErrorCode SNESPicardComputeFunction(SNES ,Vec ,Vec ,void*) 55: PETSC_EXTERN PetscErrorCode SNESPicardComputeJacobian(SNES ,Vec ,Mat *,Mat *,MatStructure *,void*) 57: typedef enum {JAC_BRATU,JAC_PICARD,JAC_STAR,JAC_NEWTON} JacType;
58: static const char *const JacTypes[] = {"BRATU" ,"PICARD" ,"STAR" ,"NEWTON" ,"JacType" ,"JAC_" ,0};
60: /*
61: User-defined application context - contains data needed by the
62: application-provided call-back routines, FormJacobianLocal() and
63: FormFunctionLocal().
64: */
65: typedef struct {
66: PassiveReal lambda; /* Bratu parameter */
67: PassiveReal p; /* Exponent in p-Laplacian */
68: PassiveReal epsilon; /* Regularization */
69: PassiveReal source; /* Source term */
70: JacType jtype; /* What type of Jacobian to assemble */
71: PetscBool picard;
72: PetscInt blocks[2];
73: PetscReal kappa;
74: PetscInt initial; /* initial conditions type */
75: } AppCtx;
77: /*
78: User-defined routines
79: */
80: static PetscErrorCode FormRHS(AppCtx*,DM,Vec ) 81: static PetscErrorCode FormInitialGuess(AppCtx*,DM,Vec ) 82: static PetscErrorCode FormFunctionLocal(DMDALocalInfo *,PetscScalar **,PetscScalar **,AppCtx*) 83: static PetscErrorCode FormFunctionPicardLocal(DMDALocalInfo *,PetscScalar **,PetscScalar **,AppCtx*) 84: static PetscErrorCode FormJacobianLocal(DMDALocalInfo *,PetscScalar **,Mat ,Mat ,MatStructure *,AppCtx*) 85: static PetscErrorCode NonlinearGS(SNES ,Vec ,Vec ,void*) 87: typedef struct _n_PreCheck *PreCheck;
88: 89: MPI_Comm comm;
90: PetscReal angle;
91: Vec Ylast;
92: PetscViewer monitor;
93: };
94: PetscErrorCode PreCheckCreate(MPI_Comm ,PreCheck*) 95: PetscErrorCode PreCheckDestroy(PreCheck*) 96: PetscErrorCode PreCheckFunction(SNESLineSearch ,Vec ,Vec ,PetscBool *,void*) 97: PetscErrorCode PreCheckSetFromOptions(PreCheck)101: 102: {
103: SNES snes; /* nonlinear solver */
104: Vec x,r,b; /* solution, residual, rhs vectors */
105: Mat A,B; /* Jacobian and preconditioning matrices */
106: AppCtx user; /* user-defined work context */
107: PetscInt its; /* iterations for convergence */
108: SNESConvergedReason reason; /* Check convergence */
109: PetscBool alloc_star; /* Only allocate for the STAR stencil */
110: PetscBool write_output;
111: char filename[PETSC_MAX_PATH_LEN] = "ex15.vts" ;
112: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
113: DM da,dastar; /* distributed array data structure */
114: PreCheck precheck = NULL; /* precheck context for version in this file */
115: PetscInt use_precheck; /* 0=none, 1=version in this file, 2=SNES -provided version */
116: PetscReal precheck_angle; /* When manually setting the SNES -provided precheck function */
117: PetscErrorCode ierr;
118: SNESLineSearch linesearch;
120: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: Initialize program
122: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124: PetscInitialize (&argc,&argv,(char*)0,help);
126: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127: Initialize problem parameters
128: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129: user.lambda = 0.0; user.p = 2.0; user.epsilon = 1e-5; user.source = 0.1; user.jtype = JAC_NEWTON;user.initial=-1;
130: user.blocks[0] = 1; user.blocks[1] = 1; user.kappa = 1e-3;
131: alloc_star = PETSC_FALSE ;
132: use_precheck = 0; precheck_angle = 10.;
133: user.picard = PETSC_FALSE ;
134: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"p-Bratu options" ,__FILE__);
135: {
136: PetscInt two=2;
137: PetscOptionsReal ("-lambda" ,"Bratu parameter" ,"" ,user.lambda,&user.lambda,NULL);
138: PetscOptionsReal ("-p" ,"Exponent `p' in p-Laplacian" ,"" ,user.p,&user.p,NULL);
139: PetscOptionsReal ("-epsilon" ,"Strain-regularization in p-Laplacian" ,"" ,user.epsilon,&user.epsilon,NULL);
140: PetscOptionsReal ("-source" ,"Constant source term" ,"" ,user.source,&user.source,NULL);
141: PetscOptionsEnum ("-jtype" ,"Jacobian approximation to assemble" ,"" ,JacTypes,(PetscEnum )user.jtype,(PetscEnum *)&user.jtype,NULL);
142: PetscOptionsName ("-picard" ,"Solve with defect-correction Picard iteration" ,"" ,&user.picard);
143: if (user.picard) {user.jtype = JAC_PICARD; user.p = 3;}
144: PetscOptionsBool ("-alloc_star" ,"Allocate for STAR stencil (5-point)" ,"" ,alloc_star,&alloc_star,NULL);
145: PetscOptionsInt ("-precheck" ,"Use a pre-check correction intended for use with Picard iteration 1=this version, 2=library" ,"" ,use_precheck,&use_precheck,NULL);
146: PetscOptionsInt ("-initial" ,"Initial conditions type (-1: default, 0: zero-valued, 1: peaked guess)" ,"" ,user.initial,&user.initial,NULL);
147: if (use_precheck == 2) { /* Using library version, get the angle */
148: PetscOptionsReal ("-precheck_angle" ,"Angle in degrees between successive search directions necessary to activate step correction" ,"" ,precheck_angle,&precheck_angle,NULL);
149: }
150: PetscOptionsIntArray ("-blocks" ,"number of coefficient interfaces in x and y direction" ,"" ,user.blocks,&two,NULL);
151: PetscOptionsReal ("-kappa" ,"diffusivity in odd regions" ,"" ,user.kappa,&user.kappa,NULL);
152: PetscOptionsString ("-o" ,"Output solution in vts format" ,"" ,filename,filename,sizeof (filename),&write_output);
153: }
154: PetscOptionsEnd ();
155: if (user.lambda > bratu_lambda_max || user.lambda < bratu_lambda_min) {
156: PetscPrintf (PETSC_COMM_WORLD ,"WARNING: lambda %g out of range for p=2\n" ,user.lambda);
157: }
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Create nonlinear solver context
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162: SNESCreate (PETSC_COMM_WORLD ,&snes);
164: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: Create distributed array (DMDA ) to manage parallel grid and vectors
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: DMDACreate2d (PETSC_COMM_WORLD ,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX ,-4,-4,PETSC_DECIDE ,PETSC_DECIDE ,
168: 1,1,NULL,NULL,&da);
169: DMDACreate2d (PETSC_COMM_WORLD ,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR ,-4,-4,PETSC_DECIDE ,PETSC_DECIDE ,
170: 1,1,NULL,NULL,&dastar);
173: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174: Extract global vectors from DM; then duplicate for remaining
175: vectors that are the same types
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177: DMCreateGlobalVector (da,&x);
178: VecDuplicate (x,&r);
179: VecDuplicate (x,&b);
181: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: Create matrix data structure; set Jacobian evaluation routine
184: Set Jacobian matrix data structure and default Jacobian evaluation
185: routine. User can override with:
186: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
187: (unless user explicitly sets preconditioner)
188: -snes_mf_operator : form preconditioning matrix as set by the user,
189: but use matrix-free approx for Jacobian-vector
190: products within Newton-Krylov method
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193: /* B can be type of MATAIJ ,MATBAIJ or MATSBAIJ */
194: DMCreateMatrix (alloc_star ? dastar : da,MATAIJ ,&B);
195: A = B;
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Set local function evaluation routine
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: DMSetApplicationContext (da, &user);
201: SNESSetDM (snes,da);
202: if (user.picard) {
203: /*
204: This is not really right requiring the user to call SNESSetFunction /Jacobian but the DMDASNESSetPicardLocal () cannot access
205: the SNES to set it
206: */
207: DMDASNESSetPicardLocal (da,INSERT_VALUES ,(PetscErrorCode (*)(DMDALocalInfo *,void*,void*,void*))FormFunctionPicardLocal,
208: (PetscErrorCode (*)(DMDALocalInfo *,void*,Mat ,Mat ,MatStructure *,void*))FormJacobianLocal,&user);
209: SNESSetFunction (snes,NULL,SNESPicardComputeFunction,&user);
210: SNESSetJacobian (snes,NULL,NULL,SNESPicardComputeJacobian,&user);
211: } else {
212: DMDASNESSetFunctionLocal (da,INSERT_VALUES ,(PetscErrorCode (*)(DMDALocalInfo *,void*,void*,void*))FormFunctionLocal,&user);
213: DMDASNESSetJacobianLocal (da,(PetscErrorCode (*)(DMDALocalInfo *,void*,Mat ,Mat ,MatStructure *,void*))FormJacobianLocal,&user);
214: }
217: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218: Customize nonlinear solver; set runtime options
219: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
220: SNESSetFromOptions (snes);
221: SNESSetGS (snes,NonlinearGS,&user);
222: SNESGetLineSearch (snes, &linesearch);
223: /* Set up the precheck context if requested */
224: if (use_precheck == 1) { /* Use the precheck routines in this file */
225: PreCheckCreate(PETSC_COMM_WORLD ,&precheck);
226: PreCheckSetFromOptions(precheck);
227: SNESLineSearchSetPreCheck (linesearch,PreCheckFunction,precheck);
228: } else if (use_precheck == 2) { /* Use the version provided by the library */
229: SNESLineSearchSetPreCheck (linesearch,SNESLineSearchPreCheckPicard ,&precheck_angle);
230: }
232: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233: Evaluate initial guess
234: Note: The user should initialize the vector, x, with the initial guess
235: for the nonlinear solver prior to calling SNESSolve (). In particular,
236: to employ an initial guess of zero, the user should explicitly set
237: this vector to zero by calling VecSet ().
238: */
240: FormInitialGuess(&user,da,x);
241: FormRHS(&user,da,b);
243: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244: Solve nonlinear system
245: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
246: SNESSolve (snes,b,x);
247: SNESGetIterationNumber (snes,&its);
248: SNESGetConvergedReason (snes,&reason);
250: PetscPrintf (PETSC_COMM_WORLD ,"%s Number of nonlinear iterations = %D\n" ,SNESConvergedReasons[reason],its);
252: if (write_output) {
253: PetscViewer viewer;
254: PetscViewerVTKOpen (PETSC_COMM_WORLD ,filename,FILE_MODE_WRITE,&viewer);
255: VecView (x,viewer);
256: PetscViewerDestroy (&viewer);
257: }
259: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
260: Free work space. All PETSc objects should be destroyed when they
261: are no longer needed.
262: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
264: if (A != B) {
265: MatDestroy (&A);
266: }
267: MatDestroy (&B);
268: VecDestroy (&x);
269: VecDestroy (&r);
270: VecDestroy (&b);
271: SNESDestroy (&snes);
272: DMDestroy (&da);
273: DMDestroy (&dastar);
274: PreCheckDestroy(&precheck);
275: PetscFinalize ();
276: return 0;
277: }
279: /* ------------------------------------------------------------------- */
282: /*
283: FormInitialGuess - Forms initial approximation.
285: Input Parameters:
286: user - user-defined application context
287: X - vector
289: Output Parameter:
290: X - vector
291: */
292: PetscErrorCode FormInitialGuess(AppCtx *user,DM da,Vec X)293: {
294: PetscInt i,j,Mx,My,xs,ys,xm,ym;
296: PetscReal temp1,temp,hx,hy;
297: PetscScalar **x;
300: DMDAGetInfo (da,PETSC_IGNORE ,&Mx,&My,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,
301: PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE );
303: hx = 1.0/(PetscReal )(Mx-1);
304: hy = 1.0/(PetscReal )(My-1);
305: temp1 = user->lambda / (user->lambda + 1.);
307: /*
308: Get a pointer to vector data.
309: - For default PETSc vectors, VecGetArray () returns a pointer to
310: the data array. Otherwise, the routine is implementation dependent.
311: - You MUST call VecRestoreArray () when you no longer need access to
312: the array.
313: */
314: DMDAVecGetArray (da,X,&x);
316: /*
317: Get local grid boundaries (for 2-dimensional DA):
318: xs, ys - starting grid indices (no ghost points)
319: xm, ym - widths of local grid (no ghost points)
321: */
322: DMDAGetCorners (da,&xs,&ys,NULL,&xm,&ym,NULL);
324: /*
325: Compute initial guess over the locally owned part of the grid
326: */
327: for (j=ys; j<ys+ym; j++) {
328: temp = (PetscReal )(PetscMin(j,My-j-1))*hy;
329: for (i=xs; i<xs+xm; i++) {
330: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
331: /* boundary conditions are all zero Dirichlet */
332: x[j][i] = 0.0;
333: } else {
334: if (user->initial == -1) {
335: if (user->lambda != 0) {
336: x[j][i] = temp1*sqrt(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
337: } else {
338: /* The solution above is an exact solution for lambda=0, this avoids "accidentally" starting
339: * with an exact solution. */
340: const PetscReal
341: xx = 2*(PetscReal )i/(Mx-1) - 1,
342: yy = 2*(PetscReal )j/(My-1) - 1;
343: x[j][i] = (1 - xx*xx) * (1-yy*yy) * xx * yy;
344: }
345: } else if (user->initial == 0) {
346: x[j][i] = 0.;
347: } else if (user->initial == 1) {
348: const PetscReal
349: xx = 2*(PetscReal )i/(Mx-1) - 1,
350: yy = 2*(PetscReal )j/(My-1) - 1;
351: x[j][i] = (1 - xx*xx) * (1-yy*yy) * xx * yy;
352: } else {
353: if (user->lambda != 0) {
354: x[j][i] = temp1*sqrt(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
355: } else {
356: x[j][i] = 0.5*sqrt(PetscMin((PetscReal )(PetscMin(i,Mx-i-1))*hx,temp));
357: }
358: }
359: }
360: }
361: }
362: /*
363: Restore vector
364: */
365: DMDAVecRestoreArray (da,X,&x);
366: return (0);
367: }
371: /*
372: FormRHS - Forms constant RHS for the problem.
374: Input Parameters:
375: user - user-defined application context
376: B - RHS vector
378: Output Parameter:
379: B - vector
380: */
381: PetscErrorCode FormRHS(AppCtx *user,DM da,Vec B)382: {
383: PetscInt i,j,Mx,My,xs,ys,xm,ym;
385: PetscReal hx,hy;
386: PetscScalar **b;
389: DMDAGetInfo (da,PETSC_IGNORE ,&Mx,&My,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,
390: PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE ,PETSC_IGNORE );
392: hx = 1.0/(PetscReal )(Mx-1);
393: hy = 1.0/(PetscReal )(My-1);
394: DMDAVecGetArray (da,B,&b);
395: DMDAGetCorners (da,&xs,&ys,NULL,&xm,&ym,NULL);
396: for (j=ys; j<ys+ym; j++) {
397: for (i=xs; i<xs+xm; i++) {
398: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
399: b[j][i] = 0.0;
400: } else {
401: b[j][i] = hx*hy*user->source;
402: }
403: }
404: }
405: DMDAVecRestoreArray (da,B,&b);
406: return (0);
407: }
409: PetscReal kappa(const AppCtx *ctx,PetscReal x,PetscReal y)410: {
411: return (((PetscInt )(x*ctx->blocks[0])) + ((PetscInt )(y*ctx->blocks[1]))) % 2 ? ctx->kappa : 1.0;
412: }
413: /* p-Laplacian diffusivity */
414: PetscScalar eta(const AppCtx *ctx,PetscReal x,PetscReal y,PetscScalar ux,PetscScalar uy)415: {
416: return kappa(ctx,x,y) * PetscPowScalar(PetscSqr(ctx->epsilon)+0.5*(ux*ux + uy*uy),0.5*(ctx->p-2.));
417: }
418: PetscScalar deta(const AppCtx *ctx,PetscReal x,PetscReal y,PetscScalar ux,PetscScalar uy)419: {
420: return (ctx->p == 2)
421: ? 0
422: : kappa(ctx,x,y)*PetscPowScalar(PetscSqr(ctx->epsilon)+0.5*(ux*ux + uy*uy),0.5*(ctx->p-4)) * 0.5 * (ctx->p-2.);
423: }
426: /* ------------------------------------------------------------------- */
429: /*
430: FormFunctionLocal - Evaluates nonlinear function, F(x).
431: */
432: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)433: {
434: PetscReal hx,hy,dhx,dhy,sc;
435: PetscInt i,j;
436: PetscScalar eu;
441: hx = 1.0/(PetscReal )(info->mx-1);
442: hy = 1.0/(PetscReal )(info->my-1);
443: sc = hx*hy*user->lambda;
444: dhx = 1/hx;
445: dhy = 1/hy;
446: /*
447: Compute function over the locally owned part of the grid
448: */
449: for (j=info->ys; j<info->ys+info->ym; j++) {
450: for (i=info->xs; i<info->xs+info->xm; i++) {
451: PetscReal xx = i*hx,yy = j*hy;
452: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
453: f[j][i] = x[j][i];
454: } else {
455: const PetscScalar
456: u = x[j][i],
457: ux_E = dhx*(x[j][i+1]-x[j][i]),
458: uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
459: ux_W = dhx*(x[j][i]-x[j][i-1]),
460: uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
461: ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
462: uy_N = dhy*(x[j+1][i]-x[j][i]),
463: ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]),
464: uy_S = dhy*(x[j][i]-x[j-1][i]),
465: e_E = eta(user,xx,yy,ux_E,uy_E),
466: e_W = eta(user,xx,yy,ux_W,uy_W),
467: e_N = eta(user,xx,yy,ux_N,uy_N),
468: e_S = eta(user,xx,yy,ux_S,uy_S),
469: uxx = -hy * (e_E*ux_E - e_W*ux_W),
470: uyy = -hx * (e_N*uy_N - e_S*uy_S);
471: if (sc) eu = PetscExpScalar(u);
472: else eu = 0.;
473: /** For p=2, these terms decay to:
474: * uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx
475: * uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy
476: **/
477: f[j][i] = uxx + uyy - sc*eu;
478: }
479: }
480: }
481: PetscLogFlops (info->xm*info->ym*(72.0));
482: return (0);
483: }
487: /*
488: This is the opposite sign of the part of FormFunctionLocal that excludes the A(x) x part of the operation,
489: 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)
491: */
492: PetscErrorCode FormFunctionPicardLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)493: {
494: PetscReal hx,hy,sc;
495: PetscInt i,j;
499: hx = 1.0/(PetscReal )(info->mx-1);
500: hy = 1.0/(PetscReal )(info->my-1);
501: sc = hx*hy*user->lambda;
502: /*
503: Compute function over the locally owned part of the grid
504: */
505: for (j=info->ys; j<info->ys+info->ym; j++) {
506: for (i=info->xs; i<info->xs+info->xm; i++) {
507: if (!(i == 0 || j == 0 || i == info->mx-1 || j == info->my-1)) {
508: const PetscScalar u = x[j][i];
509: f[j][i] = sc*PetscExpScalar(u);
510: }
511: }
512: }
513: PetscLogFlops (info->xm*info->ym*2.0);
514: return (0);
515: }
519: /*
520: FormJacobianLocal - Evaluates Jacobian matrix.
521: */
522: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat J,Mat B,MatStructure *str,AppCtx *user)523: {
525: PetscInt i,j;
526: MatStencil col[9],row;
527: PetscScalar v[9];
528: PetscReal hx,hy,hxdhy,hydhx,dhx,dhy,sc;
531: hx = 1.0/(PetscReal )(info->mx-1);
532: hy = 1.0/(PetscReal )(info->my-1);
533: sc = hx*hy*user->lambda;
534: dhx = 1/hx;
535: dhy = 1/hy;
536: hxdhy = hx/hy;
537: hydhx = hy/hx;
539: /*
540: Compute entries for the locally owned part of the Jacobian.
541: - PETSc parallel matrix formats are partitioned by
542: contiguous chunks of rows across the processors.
543: - Each processor needs to insert only elements that it owns
544: locally (but any non-local elements will be sent to the
545: appropriate processor during matrix assembly).
546: - Here, we set all entries for a particular row at once.
547: */
548: for (j=info->ys; j<info->ys+info->ym; j++) {
549: for (i=info->xs; i<info->xs+info->xm; i++) {
550: PetscReal xx = i*hx,yy = j*hy;
551: row.j = j; row.i = i;
552: /* boundary points */
553: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
554: v[0] = 1.0;
555: MatSetValuesStencil (B,1,&row,1,&row,v,INSERT_VALUES );
556: } else {
557: /* interior grid points */
558: const PetscScalar
559: ux_E = dhx*(x[j][i+1]-x[j][i]),
560: uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
561: ux_W = dhx*(x[j][i]-x[j][i-1]),
562: uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
563: ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
564: uy_N = dhy*(x[j+1][i]-x[j][i]),
565: ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]),
566: uy_S = dhy*(x[j][i]-x[j-1][i]),
567: u = x[j][i],
568: e_E = eta(user,xx,yy,ux_E,uy_E),
569: e_W = eta(user,xx,yy,ux_W,uy_W),
570: e_N = eta(user,xx,yy,ux_N,uy_N),
571: e_S = eta(user,xx,yy,ux_S,uy_S),
572: de_E = deta(user,xx,yy,ux_E,uy_E),
573: de_W = deta(user,xx,yy,ux_W,uy_W),
574: de_N = deta(user,xx,yy,ux_N,uy_N),
575: de_S = deta(user,xx,yy,ux_S,uy_S),
576: skew_E = de_E*ux_E*uy_E,
577: skew_W = de_W*ux_W*uy_W,
578: skew_N = de_N*ux_N*uy_N,
579: skew_S = de_S*ux_S*uy_S,
580: cross_EW = 0.25*(skew_E - skew_W),
581: cross_NS = 0.25*(skew_N - skew_S),
582: newt_E = e_E+de_E*PetscSqr(ux_E),
583: newt_W = e_W+de_W*PetscSqr(ux_W),
584: newt_N = e_N+de_N*PetscSqr(uy_N),
585: newt_S = e_S+de_S*PetscSqr(uy_S);
586: /* interior grid points */
587: switch (user->jtype) {
588: case JAC_BRATU:
589: /* Jacobian from p=2 */
590: v[0] = -hxdhy; col[0].j = j-1; col[0].i = i;
591: v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
592: v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(u); col[2].j = row.j; col[2].i = row.i;
593: v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
594: v[4] = -hxdhy; col[4].j = j+1; col[4].i = i;
595: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
596: break ;
597: case JAC_PICARD:
598: /* Jacobian arising from Picard linearization */
599: v[0] = -hxdhy*e_S; col[0].j = j-1; col[0].i = i;
600: v[1] = -hydhx*e_W; col[1].j = j; col[1].i = i-1;
601: v[2] = (e_W+e_E)*hydhx + (e_S+e_N)*hxdhy; col[2].j = row.j; col[2].i = row.i;
602: v[3] = -hydhx*e_E; col[3].j = j; col[3].i = i+1;
603: v[4] = -hxdhy*e_N; col[4].j = j+1; col[4].i = i;
604: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
605: break ;
606: case JAC_STAR:
607: /* Full Jacobian, but only a star stencil */
608: col[0].j = j-1; col[0].i = i;
609: col[1].j = j; col[1].i = i-1;
610: col[2].j = j; col[2].i = i;
611: col[3].j = j; col[3].i = i+1;
612: col[4].j = j+1; col[4].i = i;
613: v[0] = -hxdhy*newt_S + cross_EW;
614: v[1] = -hydhx*newt_W + cross_NS;
615: v[2] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
616: v[3] = -hydhx*newt_E - cross_NS;
617: v[4] = -hxdhy*newt_N - cross_EW;
618: MatSetValuesStencil (B,1,&row,5,col,v,INSERT_VALUES );
619: break ;
620: case JAC_NEWTON:
621: /** The Jacobian is
622: *
623: * -div [ eta (grad u) + deta (grad u0 . grad u) grad u0 ] - (eE u0) u
624: *
625: **/
626: col[0].j = j-1; col[0].i = i-1;
627: col[1].j = j-1; col[1].i = i;
628: col[2].j = j-1; col[2].i = i+1;
629: col[3].j = j; col[3].i = i-1;
630: col[4].j = j; col[4].i = i;
631: col[5].j = j; col[5].i = i+1;
632: col[6].j = j+1; col[6].i = i-1;
633: col[7].j = j+1; col[7].i = i;
634: col[8].j = j+1; col[8].i = i+1;
635: v[0] = -0.25*(skew_S + skew_W);
636: v[1] = -hxdhy*newt_S + cross_EW;
637: v[2] = 0.25*(skew_S + skew_E);
638: v[3] = -hydhx*newt_W + cross_NS;
639: v[4] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
640: v[5] = -hydhx*newt_E - cross_NS;
641: v[6] = 0.25*(skew_N + skew_W);
642: v[7] = -hxdhy*newt_N - cross_EW;
643: v[8] = -0.25*(skew_N + skew_E);
644: MatSetValuesStencil (B,1,&row,9,col,v,INSERT_VALUES );
645: break ;
646: default: 647: SETERRQ1 (PetscObjectComm ((PetscObject )info->da),PETSC_ERR_SUP,"Jacobian type %d not implemented" ,user->jtype);
648: }
649: }
650: }
651: }
653: /*
654: Assemble matrix, using the 2-step process:
655: MatAssemblyBegin (), MatAssemblyEnd ().
656: */
657: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
658: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
660: if (J != B) {
661: MatAssemblyBegin (J,MAT_FINAL_ASSEMBLY);
662: MatAssemblyEnd (J,MAT_FINAL_ASSEMBLY);
663: }
664: *str = SAME_NONZERO_PATTERN;
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 = acos((double)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" ,theta*180./PETSC_PI,precheck->angle,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" ,theta*180./PETSC_PI,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: SNESGSGetSweeps (snes,&sweeps);
814: SNESGSGetTolerances (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: }