Actual source code: ex14.c
1: /*$Id: ex14.c,v 1.23 2001/08/07 21:31:17 bsmith Exp $*/
3: /* Program usage: mpirun -np <procs> ex14 [-help] [all PETSc options] */
5: static char help[] = "Bratu nonlinear PDE in 3d.\n\
6: We solve the Bratu (SFI - solid fuel ignition) problem in a 3D rectangular\n\
7: domain, using distributed arrays (DAs) to partition the parallel grid.\n\
8: The command line options include:\n\
9: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
10: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";
12: /*T
13: Concepts: SNES^parallel Bratu example
14: Concepts: DA^using distributed arrays;
15: Processors: n
16: T*/
18: /* ------------------------------------------------------------------------
20: Solid Fuel Ignition (SFI) problem. This problem is modeled by
21: the partial differential equation
22:
23: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
24:
25: with boundary conditions
26:
27: u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1
28:
29: A finite difference approximation with the usual 7-point stencil
30: is used to discretize the boundary value problem to obtain a nonlinear
31: system of equations.
34: ------------------------------------------------------------------------- */
36: /*
37: Include "petscda.h" so that we can use distributed arrays (DAs).
38: Include "petscsnes.h" so that we can use SNES solvers. Note that this
39: file automatically includes:
40: petsc.h - base PETSc routines petscvec.h - vectors
41: petscsys.h - system routines petscmat.h - matrices
42: petscis.h - index sets petscksp.h - Krylov subspace methods
43: petscviewer.h - viewers petscpc.h - preconditioners
44: petscksp.h - linear solvers
45: */
46: #include petscda.h
47: #include petscsnes.h
50: /*
51: User-defined application context - contains data needed by the
52: application-provided call-back routines, FormJacobian() and
53: FormFunction().
54: */
55: typedef struct {
56: PetscReal param; /* test problem parameter */
57: DA da; /* distributed array data structure */
58: } AppCtx;
60: /*
61: User-defined routines
62: */
63: extern int FormFunction(SNES,Vec,Vec,void*),FormInitialGuess(AppCtx*,Vec);
64: extern int FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
68: int main(int argc,char **argv)
69: {
70: SNES snes; /* nonlinear solver */
71: Vec x,r; /* solution, residual vectors */
72: Mat J; /* Jacobian matrix */
73: AppCtx user; /* user-defined work context */
74: int its; /* iterations for convergence */
75: PetscTruth matrix_free,coloring;
76: int ierr;
77: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;
78: MatFDColoring matfdcoloring;
80: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: Initialize program
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: PetscInitialize(&argc,&argv,(char *)0,help);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Initialize problem parameters
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: user.param = 6.0;
90: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
91: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
92: SETERRQ(1,"Lambda is out of range");
93: }
95: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
96: Create nonlinear solver context
97: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: SNESCreate(PETSC_COMM_WORLD,&snes);
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Create distributed array (DA) to manage parallel grid and vectors
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103: DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,4,4,4,PETSC_DECIDE,PETSC_DECIDE,
104: PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,PETSC_NULL,&user.da);
106: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107: Extract global vectors from DA; then duplicate for remaining
108: vectors that are the same types
109: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
110: DACreateGlobalVector(user.da,&x);
111: VecDuplicate(x,&r);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Set function evaluation routine and vector
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: SNESSetFunction(snes,r,FormFunction,(void*)&user);
118: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Create matrix data structure; set Jacobian evaluation routine
121: Set Jacobian matrix data structure and default Jacobian evaluation
122: routine. User can override with:
123: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
124: (unless user explicitly sets preconditioner)
125: -snes_mf_operator : form preconditioning matrix as set by the user,
126: but use matrix-free approx for Jacobian-vector
127: products within Newton-Krylov method
128: -fdcoloring : using finite differences with coloring to compute the Jacobian
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: PetscOptionsHasName(PETSC_NULL,"-snes_mf",&matrix_free);
132: PetscOptionsHasName(PETSC_NULL,"-fdcoloring",&coloring);
133: if (!matrix_free) {
134: if (coloring) {
135: ISColoring iscoloring;
137: DAGetColoring(user.da,IS_COLORING_LOCAL,&iscoloring);
138: DAGetMatrix(user.da,MATAIJ,&J);
139: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
140: ISColoringDestroy(iscoloring);
141: MatFDColoringSetFunction(matfdcoloring,(int (*)(void))FormFunction,&user);
142: MatFDColoringSetFromOptions(matfdcoloring);
143: SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor,matfdcoloring);
144: } else {
145: DAGetMatrix(user.da,MATAIJ,&J);
146: SNESSetJacobian(snes,J,J,FormJacobian,&user);
147: }
148: }
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Customize nonlinear solver; set runtime options
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: SNESSetFromOptions(snes);
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Evaluate initial guess
157: Note: The user should initialize the vector, x, with the initial guess
158: for the nonlinear solver prior to calling SNESSolve(). In particular,
159: to employ an initial guess of zero, the user should explicitly set
160: this vector to zero by calling VecSet().
161: */
162: FormInitialGuess(&user,x);
164: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: Solve nonlinear system
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: SNESSolve(snes,x);
168: SNESGetIterationNumber(snes,&its);
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Explicitly check norm of the residual of the solution
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: FormFunction(snes,x,r,(void *)&user);
174: VecNorm(r,NORM_2,&fnorm);
175: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %d fnorm %g\n",its,fnorm);
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Free work space. All PETSc objects should be destroyed when they
179: are no longer needed.
180: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182: if (!matrix_free) {
183: MatDestroy(J);
184: }
185: if (coloring) {
186: MatFDColoringDestroy(matfdcoloring);
187: }
188: VecDestroy(x);
189: VecDestroy(r);
190: SNESDestroy(snes);
191: DADestroy(user.da);
192: PetscFinalize();
194: return(0);
195: }
196: /* ------------------------------------------------------------------- */
199: /*
200: FormInitialGuess - Forms initial approximation.
202: Input Parameters:
203: user - user-defined application context
204: X - vector
206: Output Parameter:
207: X - vector
208: */
209: int FormInitialGuess(AppCtx *user,Vec X)
210: {
211: int i,j,k,Mx,My,Mz,ierr,xs,ys,zs,xm,ym,zm;
212: PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
213: PetscScalar ***x;
216: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
217: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
219: lambda = user->param;
220: hx = 1.0/(PetscReal)(Mx-1);
221: hy = 1.0/(PetscReal)(My-1);
222: hz = 1.0/(PetscReal)(Mz-1);
223: temp1 = lambda/(lambda + 1.0);
225: /*
226: Get a pointer to vector data.
227: - For default PETSc vectors, VecGetArray() returns a pointer to
228: the data array. Otherwise, the routine is implementation dependent.
229: - You MUST call VecRestoreArray() when you no longer need access to
230: the array.
231: */
232: DAVecGetArray(user->da,X,&x);
234: /*
235: Get local grid boundaries (for 3-dimensional DA):
236: xs, ys, zs - starting grid indices (no ghost points)
237: xm, ym, zm - widths of local grid (no ghost points)
239: */
240: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
242: /*
243: Compute initial guess over the locally owned part of the grid
244: */
245: for (k=zs; k<zs+zm; k++) {
246: tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
247: for (j=ys; j<ys+ym; j++) {
248: tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
249: for (i=xs; i<xs+xm; i++) {
250: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
251: /* boundary conditions are all zero Dirichlet */
252: x[k][j][i] = 0.0;
253: } else {
254: x[k][j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
255: }
256: }
257: }
258: }
260: /*
261: Restore vector
262: */
263: DAVecRestoreArray(user->da,X,&x);
264: return(0);
265: }
266: /* ------------------------------------------------------------------- */
269: /*
270: FormFunction - Evaluates nonlinear function, F(x).
272: Input Parameters:
273: . snes - the SNES context
274: . X - input vector
275: . ptr - optional user-defined context, as set by SNESSetFunction()
277: Output Parameter:
278: . F - function vector
279: */
280: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
281: {
282: AppCtx *user = (AppCtx*)ptr;
283: int ierr,i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
284: PetscReal two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
285: PetscScalar u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
286: Vec localX;
289: DAGetLocalVector(user->da,&localX);
290: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
291: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
293: lambda = user->param;
294: hx = 1.0/(PetscReal)(Mx-1);
295: hy = 1.0/(PetscReal)(My-1);
296: hz = 1.0/(PetscReal)(Mz-1);
297: sc = hx*hy*hz*lambda;
298: hxhzdhy = hx*hz/hy;
299: hyhzdhx = hy*hz/hx;
300: hxhydhz = hx*hy/hz;
302: /*
303: Scatter ghost points to local vector,using the 2-step process
304: DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
305: By placing code between these two statements, computations can be
306: done while messages are in transition.
307: */
308: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
309: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
311: /*
312: Get pointers to vector data
313: */
314: DAVecGetArray(user->da,localX,&x);
315: DAVecGetArray(user->da,F,&f);
317: /*
318: Get local grid boundaries
319: */
320: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
322: /*
323: Compute function over the locally owned part of the grid
324: */
325: for (k=zs; k<zs+zm; k++) {
326: for (j=ys; j<ys+ym; j++) {
327: for (i=xs; i<xs+xm; i++) {
328: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
329: f[k][j][i] = x[k][j][i];
330: } else {
331: u = x[k][j][i];
332: u_east = x[k][j][i+1];
333: u_west = x[k][j][i-1];
334: u_north = x[k][j+1][i];
335: u_south = x[k][j-1][i];
336: u_up = x[k+1][j][i];
337: u_down = x[k-1][j][i];
338: u_xx = (-u_east + two*u - u_west)*hyhzdhx;
339: u_yy = (-u_north + two*u - u_south)*hxhzdhy;
340: u_zz = (-u_up + two*u - u_down)*hxhydhz;
341: f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
342: }
343: }
344: }
345: }
347: /*
348: Restore vectors
349: */
350: DAVecRestoreArray(user->da,localX,&x);
351: DAVecRestoreArray(user->da,F,&f);
352: DARestoreLocalVector(user->da,&localX);
353: PetscLogFlops(11*ym*xm);
354: return(0);
355: }
356: /* ------------------------------------------------------------------- */
359: /*
360: FormJacobian - Evaluates Jacobian matrix.
362: Input Parameters:
363: . snes - the SNES context
364: . x - input vector
365: . ptr - optional user-defined context, as set by SNESSetJacobian()
367: Output Parameters:
368: . A - Jacobian matrix
369: . B - optionally different preconditioning matrix
370: . flag - flag indicating matrix structure
372: */
373: int FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
374: {
375: AppCtx *user = (AppCtx*)ptr; /* user-defined application context */
376: Mat jac = *B; /* Jacobian matrix */
377: Vec localX;
378: int ierr,i,j,k,Mx,My,Mz;
379: MatStencil col[7],row;
380: int xs,ys,zs,xm,ym,zm;
381: PetscScalar lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
385: DAGetLocalVector(user->da,&localX);
386: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
387: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
389: lambda = user->param;
390: hx = 1.0/(PetscReal)(Mx-1);
391: hy = 1.0/(PetscReal)(My-1);
392: hz = 1.0/(PetscReal)(Mz-1);
393: sc = hx*hy*hz*lambda;
394: hxhzdhy = hx*hz/hy;
395: hyhzdhx = hy*hz/hx;
396: hxhydhz = hx*hy/hz;
398: /*
399: Scatter ghost points to local vector, using the 2-step process
400: DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
401: By placing code between these two statements, computations can be
402: done while messages are in transition.
403: */
404: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
405: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
407: /*
408: Get pointer to vector data
409: */
410: DAVecGetArray(user->da,localX,&x);
412: /*
413: Get local grid boundaries
414: */
415: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
417: /*
418: Compute entries for the locally owned part of the Jacobian.
419: - Currently, all PETSc parallel matrix formats are partitioned by
420: contiguous chunks of rows across the processors.
421: - Each processor needs to insert only elements that it owns
422: locally (but any non-local elements will be sent to the
423: appropriate processor during matrix assembly).
424: - Here, we set all entries for a particular row at once.
425: - We can set matrix entries either using either
426: MatSetValuesLocal() or MatSetValues(), as discussed above.
427: */
428: for (k=zs; k<zs+zm; k++) {
429: for (j=ys; j<ys+ym; j++) {
430: for (i=xs; i<xs+xm; i++) {
431: row.k = k; row.j = j; row.i = i;
432: /* boundary points */
433: if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
434: v[0] = 1.0;
435: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
436: } else {
437: /* interior grid points */
438: v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
439: v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
440: v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
441: v[3] = 2.0*(hyhzdhx+hxhzdhy+hxhydhz)-sc*PetscExpScalar(x[k][j][i]);col[3].k=row.k;col[3].j=row.j;col[3].i = row.i;
442: v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
443: v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
444: v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
445: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
446: }
447: }
448: }
449: }
450: DAVecRestoreArray(user->da,localX,&x);
451: DARestoreLocalVector(user->da,&localX);
453: /*
454: Assemble matrix, using the 2-step process:
455: MatAssemblyBegin(), MatAssemblyEnd().
456: */
457: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
458: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
460: /*
461: Normally since the matrix has already been assembled above; this
462: would do nothing. But in the matrix free mode -snes_mf_operator
463: this tells the "matrix-free" matrix that a new linear system solve
464: is about to be done.
465: */
467: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
468: MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
470: /*
471: Set flag to indicate that the Jacobian matrix retains an identical
472: nonzero structure throughout all nonlinear iterations (although the
473: values of the entries change). Thus, we can save some work in setting
474: up the preconditioner (e.g., no need to redo symbolic factorization for
475: ILU/ICC preconditioners).
476: - If the nonzero structure of the matrix is different during
477: successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
478: must be used instead. If you are unsure whether the matrix
479: structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
480: - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
481: believes your assertion and does not check the structure
482: of the matrix. If you erroneously claim that the structure
483: is the same when it actually is not, the new preconditioner
484: will not function correctly. Thus, use this optimization
485: feature with caution!
486: */
487: *flag = SAME_NONZERO_PATTERN;
490: /*
491: Tell the matrix we will never add a new nonzero location to the
492: matrix. If we do, it will generate an error.
493: */
494: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR);
495: return(0);
496: }