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 rectangularn
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 nonlinearityn
10: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)nn";
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: petscsles.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*);
66: #undef __FUNCT__
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,MATMPIAIJ,&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,MATMPIAIJ,&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,&its);
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Explicitly check norm of the residual of the solution
171: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
172: FormFunction(snes,x,r,(void *)&user);
173: VecNorm(r,NORM_2,&fnorm);
174: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %d fnorm %gn",its,fnorm);
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Free work space. All PETSc objects should be destroyed when they
178: are no longer needed.
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: if (!matrix_free) {
182: MatDestroy(J);
183: }
184: if (coloring) {
185: MatFDColoringDestroy(matfdcoloring);
186: }
187: VecDestroy(x);
188: VecDestroy(r);
189: SNESDestroy(snes);
190: DADestroy(user.da);
191: PetscFinalize();
193: return(0);
194: }
195: /* ------------------------------------------------------------------- */
196: #undef __FUNCT__
198: /*
199: FormInitialGuess - Forms initial approximation.
201: Input Parameters:
202: user - user-defined application context
203: X - vector
205: Output Parameter:
206: X - vector
207: */
208: int FormInitialGuess(AppCtx *user,Vec X)
209: {
210: int i,j,k,Mx,My,Mz,ierr,xs,ys,zs,xm,ym,zm;
211: PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
212: PetscScalar ***x;
215: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
216: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
218: lambda = user->param;
219: hx = 1.0/(PetscReal)(Mx-1);
220: hy = 1.0/(PetscReal)(My-1);
221: hz = 1.0/(PetscReal)(Mz-1);
222: temp1 = lambda/(lambda + 1.0);
224: /*
225: Get a pointer to vector data.
226: - For default PETSc vectors, VecGetArray() returns a pointer to
227: the data array. Otherwise, the routine is implementation dependent.
228: - You MUST call VecRestoreArray() when you no longer need access to
229: the array.
230: */
231: DAVecGetArray(user->da,X,(void**)&x);
233: /*
234: Get local grid boundaries (for 3-dimensional DA):
235: xs, ys, zs - starting grid indices (no ghost points)
236: xm, ym, zm - widths of local grid (no ghost points)
238: */
239: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
241: /*
242: Compute initial guess over the locally owned part of the grid
243: */
244: for (k=zs; k<zs+zm; k++) {
245: tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
246: for (j=ys; j<ys+ym; j++) {
247: tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
248: for (i=xs; i<xs+xm; i++) {
249: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
250: /* boundary conditions are all zero Dirichlet */
251: x[k][j][i] = 0.0;
252: } else {
253: x[k][j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
254: }
255: }
256: }
257: }
259: /*
260: Restore vector
261: */
262: DAVecRestoreArray(user->da,X,(void**)&x);
263: return(0);
264: }
265: /* ------------------------------------------------------------------- */
266: #undef __FUNCT__
268: /*
269: FormFunction - Evaluates nonlinear function, F(x).
271: Input Parameters:
272: . snes - the SNES context
273: . X - input vector
274: . ptr - optional user-defined context, as set by SNESSetFunction()
276: Output Parameter:
277: . F - function vector
278: */
279: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
280: {
281: AppCtx *user = (AppCtx*)ptr;
282: int ierr,i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
283: PetscReal two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
284: PetscScalar u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
285: Vec localX;
288: DAGetLocalVector(user->da,&localX);
289: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
290: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
292: lambda = user->param;
293: hx = 1.0/(PetscReal)(Mx-1);
294: hy = 1.0/(PetscReal)(My-1);
295: hz = 1.0/(PetscReal)(Mz-1);
296: sc = hx*hy*hz*lambda;
297: hxhzdhy = hx*hz/hy;
298: hyhzdhx = hy*hz/hx;
299: hxhydhz = hx*hy/hz;
301: /*
302: Scatter ghost points to local vector,using the 2-step process
303: DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
304: By placing code between these two statements, computations can be
305: done while messages are in transition.
306: */
307: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
308: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
310: /*
311: Get pointers to vector data
312: */
313: DAVecGetArray(user->da,localX,(void**)&x);
314: DAVecGetArray(user->da,F,(void**)&f);
316: /*
317: Get local grid boundaries
318: */
319: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
321: /*
322: Compute function over the locally owned part of the grid
323: */
324: for (k=zs; k<zs+zm; k++) {
325: for (j=ys; j<ys+ym; j++) {
326: for (i=xs; i<xs+xm; i++) {
327: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
328: f[k][j][i] = x[k][j][i];
329: } else {
330: u = x[k][j][i];
331: u_east = x[k][j][i+1];
332: u_west = x[k][j][i-1];
333: u_north = x[k][j+1][i];
334: u_south = x[k][j-1][i];
335: u_up = x[k+1][j][i];
336: u_down = x[k-1][j][i];
337: u_xx = (-u_east + two*u - u_west)*hyhzdhx;
338: u_yy = (-u_north + two*u - u_south)*hxhzdhy;
339: u_zz = (-u_up + two*u - u_down)*hxhydhz;
340: f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
341: }
342: }
343: }
344: }
346: /*
347: Restore vectors
348: */
349: DAVecRestoreArray(user->da,localX,(void**)&x);
350: DAVecRestoreArray(user->da,F,(void**)&f);
351: DARestoreLocalVector(user->da,&localX);
352: PetscLogFlops(11*ym*xm);
353: return(0);
354: }
355: /* ------------------------------------------------------------------- */
356: #undef __FUNCT__
358: /*
359: FormJacobian - Evaluates Jacobian matrix.
361: Input Parameters:
362: . snes - the SNES context
363: . x - input vector
364: . ptr - optional user-defined context, as set by SNESSetJacobian()
366: Output Parameters:
367: . A - Jacobian matrix
368: . B - optionally different preconditioning matrix
369: . flag - flag indicating matrix structure
371: */
372: int FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
373: {
374: AppCtx *user = (AppCtx*)ptr; /* user-defined application context */
375: Mat jac = *B; /* Jacobian matrix */
376: Vec localX;
377: int ierr,i,j,k,Mx,My,Mz;
378: MatStencil col[7],row;
379: int xs,ys,zs,xm,ym,zm;
380: PetscScalar lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
384: DAGetLocalVector(user->da,&localX);
385: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
386: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
388: lambda = user->param;
389: hx = 1.0/(PetscReal)(Mx-1);
390: hy = 1.0/(PetscReal)(My-1);
391: hz = 1.0/(PetscReal)(Mz-1);
392: sc = hx*hy*hz*lambda;
393: hxhzdhy = hx*hz/hy;
394: hyhzdhx = hy*hz/hx;
395: hxhydhz = hx*hy/hz;
397: /*
398: Scatter ghost points to local vector, using the 2-step process
399: DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
400: By placing code between these two statements, computations can be
401: done while messages are in transition.
402: */
403: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
404: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
406: /*
407: Get pointer to vector data
408: */
409: DAVecGetArray(user->da,localX,(void**)&x);
411: /*
412: Get local grid boundaries
413: */
414: DAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
416: /*
417: Compute entries for the locally owned part of the Jacobian.
418: - Currently, all PETSc parallel matrix formats are partitioned by
419: contiguous chunks of rows across the processors.
420: - Each processor needs to insert only elements that it owns
421: locally (but any non-local elements will be sent to the
422: appropriate processor during matrix assembly).
423: - Here, we set all entries for a particular row at once.
424: - We can set matrix entries either using either
425: MatSetValuesLocal() or MatSetValues(), as discussed above.
426: */
427: for (k=zs; k<zs+zm; k++) {
428: for (j=ys; j<ys+ym; j++) {
429: for (i=xs; i<xs+xm; i++) {
430: row.k = k; row.j = j; row.i = i;
431: /* boundary points */
432: if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
433: v[0] = 1.0;
434: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
435: } else {
436: /* interior grid points */
437: v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
438: v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
439: v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
440: 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;
441: v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
442: v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
443: v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
444: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
445: }
446: }
447: }
448: }
449: DAVecRestoreArray(user->da,localX,(void**)&x);
450: DARestoreLocalVector(user->da,&localX);
452: /*
453: Assemble matrix, using the 2-step process:
454: MatAssemblyBegin(), MatAssemblyEnd().
455: */
456: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
457: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
459: /*
460: Normally since the matrix has already been assembled above; this
461: would do nothing. But in the matrix free mode -snes_mf_operator
462: this tells the "matrix-free" matrix that a new linear system solve
463: is about to be done.
464: */
466: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
467: MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
469: /*
470: Set flag to indicate that the Jacobian matrix retains an identical
471: nonzero structure throughout all nonlinear iterations (although the
472: values of the entries change). Thus, we can save some work in setting
473: up the preconditioner (e.g., no need to redo symbolic factorization for
474: ILU/ICC preconditioners).
475: - If the nonzero structure of the matrix is different during
476: successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
477: must be used instead. If you are unsure whether the matrix
478: structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
479: - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
480: believes your assertion and does not check the structure
481: of the matrix. If you erroneously claim that the structure
482: is the same when it actually is not, the new preconditioner
483: will not function correctly. Thus, use this optimization
484: feature with caution!
485: */
486: *flag = SAME_NONZERO_PATTERN;
489: /*
490: Tell the matrix we will never add a new nonzero location to the
491: matrix. If we do, it will generate an error.
492: */
493: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR);
494: return(0);
495: }