Actual source code: ex14.c
petsc-3.4.5 2014-06-29
2: static char help[] = "Bratu nonlinear PDE in 3d.\n\
3: We solve the Bratu (SFI - solid fuel ignition) problem in a 3D rectangular\n\
4: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
5: The command line options include:\n\
6: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
7: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";
9: /*T
10: Concepts: SNES^parallel Bratu example
11: Concepts: DMDA^using distributed arrays;
12: Processors: n
13: T*/
15: /* ------------------------------------------------------------------------
17: Solid Fuel Ignition (SFI) problem. This problem is modeled by
18: the partial differential equation
20: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
22: with boundary conditions
24: u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1
26: A finite difference approximation with the usual 7-point stencil
27: is used to discretize the boundary value problem to obtain a nonlinear
28: system of equations.
31: ------------------------------------------------------------------------- */
33: /*
34: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
35: Include "petscsnes.h" so that we can use SNES solvers. Note that this
36: file automatically includes:
37: petscsys.h - base PETSc routines petscvec.h - vectors
38: petscmat.h - matrices
39: petscis.h - index sets petscksp.h - Krylov subspace methods
40: petscviewer.h - viewers petscpc.h - preconditioners
41: petscksp.h - linear solvers
42: */
43: #include <petscdmda.h>
44: #include <petscsnes.h>
47: /*
48: User-defined application context - contains data needed by the
49: application-provided call-back routines, FormJacobian() and
50: FormFunction().
51: */
52: typedef struct {
53: PetscReal param; /* test problem parameter */
54: DM da; /* distributed array data structure */
55: } AppCtx;
57: /*
58: User-defined routines
59: */
60: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*),FormInitialGuess(AppCtx*,Vec);
61: extern PetscErrorCode FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
65: int main(int argc,char **argv)
66: {
67: SNES snes; /* nonlinear solver */
68: Vec x,r; /* solution, residual vectors */
69: Mat J; /* Jacobian matrix */
70: AppCtx user; /* user-defined work context */
71: PetscInt its; /* iterations for convergence */
72: MatFDColoring matfdcoloring;
73: PetscBool matrix_free = PETSC_FALSE,coloring = PETSC_FALSE;
75: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;
77: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
78: Initialize program
79: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
81: PetscInitialize(&argc,&argv,(char*)0,help);
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Initialize problem parameters
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: user.param = 6.0;
87: PetscOptionsGetReal(NULL,"-par",&user.param,NULL);
88: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) SETERRQ(PETSC_COMM_SELF,1,"Lambda is out of range");
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Create nonlinear solver context
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: SNESCreate(PETSC_COMM_WORLD,&snes);
95: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
96: Create distributed array (DMDA) to manage parallel grid and vectors
97: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: DMDACreate3d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,-4,PETSC_DECIDE,PETSC_DECIDE,
99: PETSC_DECIDE,1,1,NULL,NULL,NULL,&user.da);
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Extract global vectors from DMDA; then duplicate for remaining
103: vectors that are the same types
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: DMCreateGlobalVector(user.da,&x);
106: VecDuplicate(x,&r);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Set function evaluation routine and vector
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: SNESSetFunction(snes,r,FormFunction,(void*)&user);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Create matrix data structure; set Jacobian evaluation routine
116: Set Jacobian matrix data structure and default Jacobian evaluation
117: routine. User can override with:
118: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
119: (unless user explicitly sets preconditioner)
120: -snes_mf_operator : form preconditioning matrix as set by the user,
121: but use matrix-free approx for Jacobian-vector
122: products within Newton-Krylov method
123: -fdcoloring : using finite differences with coloring to compute the Jacobian
125: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126: PetscOptionsGetBool(NULL,"-snes_mf",&matrix_free,NULL);
127: PetscOptionsGetBool(NULL,"-fdcoloring",&coloring,NULL);
128: if (!matrix_free) {
129: DMCreateMatrix(user.da,MATAIJ,&J);
130: if (coloring) {
131: ISColoring iscoloring;
132: DMCreateColoring(user.da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);
133: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
134: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
135: MatFDColoringSetFromOptions(matfdcoloring);
136: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
137: ISColoringDestroy(&iscoloring);
138: } else {
139: SNESSetJacobian(snes,J,J,FormJacobian,&user);
140: }
141: }
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Customize nonlinear solver; set runtime options
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: SNESSetFromOptions(snes);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Evaluate initial guess
150: Note: The user should initialize the vector, x, with the initial guess
151: for the nonlinear solver prior to calling SNESSolve(). In particular,
152: to employ an initial guess of zero, the user should explicitly set
153: this vector to zero by calling VecSet().
154: */
155: FormInitialGuess(&user,x);
157: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: Solve nonlinear system
159: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: SNESSolve(snes,NULL,x);
161: SNESGetIterationNumber(snes,&its);
163: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: Explicitly check norm of the residual of the solution
165: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166: FormFunction(snes,x,r,(void*)&user);
167: VecNorm(r,NORM_2,&fnorm);
168: PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D fnorm %G\n",its,fnorm);
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: Free work space. All PETSc objects should be destroyed when they
172: are no longer needed.
173: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
175: if (!matrix_free) {
176: MatDestroy(&J);
177: }
178: VecDestroy(&x);
179: VecDestroy(&r);
180: SNESDestroy(&snes);
181: DMDestroy(&user.da);
182: if (coloring) {MatFDColoringDestroy(&matfdcoloring);}
183: PetscFinalize();
184: return(0);
185: }
186: /* ------------------------------------------------------------------- */
189: /*
190: FormInitialGuess - Forms initial approximation.
192: Input Parameters:
193: user - user-defined application context
194: X - vector
196: Output Parameter:
197: X - vector
198: */
199: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
200: {
201: PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
203: PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
204: PetscScalar ***x;
207: DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
209: lambda = user->param;
210: hx = 1.0/(PetscReal)(Mx-1);
211: hy = 1.0/(PetscReal)(My-1);
212: hz = 1.0/(PetscReal)(Mz-1);
213: temp1 = lambda/(lambda + 1.0);
215: /*
216: Get a pointer to vector data.
217: - For default PETSc vectors, VecGetArray() returns a pointer to
218: the data array. Otherwise, the routine is implementation dependent.
219: - You MUST call VecRestoreArray() when you no longer need access to
220: the array.
221: */
222: DMDAVecGetArray(user->da,X,&x);
224: /*
225: Get local grid boundaries (for 3-dimensional DMDA):
226: xs, ys, zs - starting grid indices (no ghost points)
227: xm, ym, zm - widths of local grid (no ghost points)
229: */
230: DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
232: /*
233: Compute initial guess over the locally owned part of the grid
234: */
235: for (k=zs; k<zs+zm; k++) {
236: tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
237: for (j=ys; j<ys+ym; j++) {
238: tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
239: for (i=xs; i<xs+xm; i++) {
240: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
241: /* boundary conditions are all zero Dirichlet */
242: x[k][j][i] = 0.0;
243: } else {
244: x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
245: }
246: }
247: }
248: }
250: /*
251: Restore vector
252: */
253: DMDAVecRestoreArray(user->da,X,&x);
254: return(0);
255: }
256: /* ------------------------------------------------------------------- */
259: /*
260: FormFunction - Evaluates nonlinear function, F(x).
262: Input Parameters:
263: . snes - the SNES context
264: . X - input vector
265: . ptr - optional user-defined context, as set by SNESSetFunction()
267: Output Parameter:
268: . F - function vector
269: */
270: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
271: {
272: AppCtx *user = (AppCtx*)ptr;
274: PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
275: PetscReal two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
276: PetscScalar u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
277: Vec localX;
280: DMGetLocalVector(user->da,&localX);
281: DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
282: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
284: lambda = user->param;
285: hx = 1.0/(PetscReal)(Mx-1);
286: hy = 1.0/(PetscReal)(My-1);
287: hz = 1.0/(PetscReal)(Mz-1);
288: sc = hx*hy*hz*lambda;
289: hxhzdhy = hx*hz/hy;
290: hyhzdhx = hy*hz/hx;
291: hxhydhz = hx*hy/hz;
293: /*
294: Scatter ghost points to local vector,using the 2-step process
295: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
296: By placing code between these two statements, computations can be
297: done while messages are in transition.
298: */
299: DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
300: DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
302: /*
303: Get pointers to vector data
304: */
305: DMDAVecGetArray(user->da,localX,&x);
306: DMDAVecGetArray(user->da,F,&f);
308: /*
309: Get local grid boundaries
310: */
311: DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
313: /*
314: Compute function over the locally owned part of the grid
315: */
316: for (k=zs; k<zs+zm; k++) {
317: for (j=ys; j<ys+ym; j++) {
318: for (i=xs; i<xs+xm; i++) {
319: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
320: f[k][j][i] = x[k][j][i];
321: } else {
322: u = x[k][j][i];
323: u_east = x[k][j][i+1];
324: u_west = x[k][j][i-1];
325: u_north = x[k][j+1][i];
326: u_south = x[k][j-1][i];
327: u_up = x[k+1][j][i];
328: u_down = x[k-1][j][i];
329: u_xx = (-u_east + two*u - u_west)*hyhzdhx;
330: u_yy = (-u_north + two*u - u_south)*hxhzdhy;
331: u_zz = (-u_up + two*u - u_down)*hxhydhz;
332: f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
333: }
334: }
335: }
336: }
338: /*
339: Restore vectors
340: */
341: DMDAVecRestoreArray(user->da,localX,&x);
342: DMDAVecRestoreArray(user->da,F,&f);
343: DMRestoreLocalVector(user->da,&localX);
344: PetscLogFlops(11.0*ym*xm);
345: return(0);
346: }
347: /* ------------------------------------------------------------------- */
350: /*
351: FormJacobian - Evaluates Jacobian matrix.
353: Input Parameters:
354: . snes - the SNES context
355: . x - input vector
356: . ptr - optional user-defined context, as set by SNESSetJacobian()
358: Output Parameters:
359: . A - Jacobian matrix
360: . B - optionally different preconditioning matrix
361: . flag - flag indicating matrix structure
363: */
364: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
365: {
366: AppCtx *user = (AppCtx*)ptr; /* user-defined application context */
367: Mat jac = *B; /* Jacobian matrix */
368: Vec localX;
370: PetscInt i,j,k,Mx,My,Mz;
371: MatStencil col[7],row;
372: PetscInt xs,ys,zs,xm,ym,zm;
373: PetscScalar lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
376: DMGetLocalVector(user->da,&localX);
377: DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
378: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
380: lambda = user->param;
381: hx = 1.0/(PetscReal)(Mx-1);
382: hy = 1.0/(PetscReal)(My-1);
383: hz = 1.0/(PetscReal)(Mz-1);
384: sc = hx*hy*hz*lambda;
385: hxhzdhy = hx*hz/hy;
386: hyhzdhx = hy*hz/hx;
387: hxhydhz = hx*hy/hz;
389: /*
390: Scatter ghost points to local vector, using the 2-step process
391: DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
392: By placing code between these two statements, computations can be
393: done while messages are in transition.
394: */
395: DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
396: DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
398: /*
399: Get pointer to vector data
400: */
401: DMDAVecGetArray(user->da,localX,&x);
403: /*
404: Get local grid boundaries
405: */
406: DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
408: /*
409: Compute entries for the locally owned part of the Jacobian.
410: - Currently, all PETSc parallel matrix formats are partitioned by
411: contiguous chunks of rows across the processors.
412: - Each processor needs to insert only elements that it owns
413: locally (but any non-local elements will be sent to the
414: appropriate processor during matrix assembly).
415: - Here, we set all entries for a particular row at once.
416: - We can set matrix entries either using either
417: MatSetValuesLocal() or MatSetValues(), as discussed above.
418: */
419: for (k=zs; k<zs+zm; k++) {
420: for (j=ys; j<ys+ym; j++) {
421: for (i=xs; i<xs+xm; i++) {
422: row.k = k; row.j = j; row.i = i;
423: /* boundary points */
424: if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
425: v[0] = 1.0;
426: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
427: } else {
428: /* interior grid points */
429: v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
430: v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
431: v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
432: 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;
433: v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
434: v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
435: v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
436: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
437: }
438: }
439: }
440: }
441: DMDAVecRestoreArray(user->da,localX,&x);
442: DMRestoreLocalVector(user->da,&localX);
444: /*
445: Assemble matrix, using the 2-step process:
446: MatAssemblyBegin(), MatAssemblyEnd().
447: */
448: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
449: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
451: /*
452: Normally since the matrix has already been assembled above; this
453: would do nothing. But in the matrix free mode -snes_mf_operator
454: this tells the "matrix-free" matrix that a new linear system solve
455: is about to be done.
456: */
458: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
459: MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
461: /*
462: Set flag to indicate that the Jacobian matrix retains an identical
463: nonzero structure throughout all nonlinear iterations (although the
464: values of the entries change). Thus, we can save some work in setting
465: up the preconditioner (e.g., no need to redo symbolic factorization for
466: ILU/ICC preconditioners).
467: - If the nonzero structure of the matrix is different during
468: successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
469: must be used instead. If you are unsure whether the matrix
470: structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
471: - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
472: believes your assertion and does not check the structure
473: of the matrix. If you erroneously claim that the structure
474: is the same when it actually is not, the new preconditioner
475: will not function correctly. Thus, use this optimization
476: feature with caution!
477: */
478: *flag = SAME_NONZERO_PATTERN;
481: /*
482: Tell the matrix we will never add a new nonzero location to the
483: matrix. If we do, it will generate an error.
484: */
485: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
486: return(0);
487: }