Actual source code: ex14.c
petsc-3.6.4 2016-04-12
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 <petscdm.h>
44: #include <petscdmda.h>
45: #include <petscsnes.h>
48: /*
49: User-defined application context - contains data needed by the
50: application-provided call-back routines, FormJacobian() and
51: FormFunction().
52: */
53: typedef struct {
54: PetscReal param; /* test problem parameter */
55: DM da; /* distributed array data structure */
56: } AppCtx;
58: /*
59: User-defined routines
60: */
61: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*),FormInitialGuess(AppCtx*,Vec);
62: extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
66: int main(int argc,char **argv)
67: {
68: SNES snes; /* nonlinear solver */
69: Vec x,r; /* solution, residual vectors */
70: Mat J; /* Jacobian matrix */
71: AppCtx user; /* user-defined work context */
72: PetscInt its; /* iterations for convergence */
73: MatFDColoring matfdcoloring;
74: PetscBool matrix_free = PETSC_FALSE,coloring = PETSC_FALSE;
76: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;
78: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
79: Initialize program
80: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
82: PetscInitialize(&argc,&argv,(char*)0,help);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Initialize problem parameters
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: user.param = 6.0;
88: PetscOptionsGetReal(NULL,"-par",&user.param,NULL);
89: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) SETERRQ(PETSC_COMM_SELF,1,"Lambda is out of range");
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Create nonlinear solver context
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: SNESCreate(PETSC_COMM_WORLD,&snes);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Create distributed array (DMDA) to manage parallel grid and vectors
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
99: DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,-4,PETSC_DECIDE,PETSC_DECIDE,
100: PETSC_DECIDE,1,1,NULL,NULL,NULL,&user.da);
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Extract global vectors from DMDA; then duplicate for remaining
104: vectors that are the same types
105: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: DMCreateGlobalVector(user.da,&x);
107: VecDuplicate(x,&r);
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Set function evaluation routine and vector
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: SNESSetFunction(snes,r,FormFunction,(void*)&user);
114: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115: Create matrix data structure; set Jacobian evaluation routine
117: Set Jacobian matrix data structure and default Jacobian evaluation
118: routine. User can override with:
119: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
120: (unless user explicitly sets preconditioner)
121: -snes_mf_operator : form preconditioning matrix as set by the user,
122: but use matrix-free approx for Jacobian-vector
123: products within Newton-Krylov method
124: -fdcoloring : using finite differences with coloring to compute the Jacobian
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: PetscOptionsGetBool(NULL,"-snes_mf",&matrix_free,NULL);
128: PetscOptionsGetBool(NULL,"-fdcoloring",&coloring,NULL);
129: if (!matrix_free) {
130: DMSetMatType(user.da,MATAIJ);
131: DMCreateMatrix(user.da,&J);
132: if (coloring) {
133: ISColoring iscoloring;
134: DMCreateColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);
135: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
136: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
137: MatFDColoringSetFromOptions(matfdcoloring);
138: MatFDColoringSetUp(J,iscoloring,matfdcoloring);
139: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
140: ISColoringDestroy(&iscoloring);
141: } else {
142: SNESSetJacobian(snes,J,J,FormJacobian,&user);
143: }
144: }
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Customize nonlinear solver; set runtime options
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: SNESSetDM(snes,user.da);
150: SNESSetFromOptions(snes);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Evaluate initial guess
154: Note: The user should initialize the vector, x, with the initial guess
155: for the nonlinear solver prior to calling SNESSolve(). In particular,
156: to employ an initial guess of zero, the user should explicitly set
157: this vector to zero by calling VecSet().
158: */
159: FormInitialGuess(&user,x);
161: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: Solve nonlinear system
163: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: SNESSolve(snes,NULL,x);
165: SNESGetIterationNumber(snes,&its);
167: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: Explicitly check norm of the residual of the solution
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: FormFunction(snes,x,r,(void*)&user);
171: VecNorm(r,NORM_2,&fnorm);
172: PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D fnorm %g\n",its,(double)fnorm);
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Free work space. All PETSc objects should be destroyed when they
176: are no longer needed.
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: if (!matrix_free) {
180: MatDestroy(&J);
181: }
182: VecDestroy(&x);
183: VecDestroy(&r);
184: SNESDestroy(&snes);
185: DMDestroy(&user.da);
186: if (coloring) {MatFDColoringDestroy(&matfdcoloring);}
187: PetscFinalize();
188: return(0);
189: }
190: /* ------------------------------------------------------------------- */
193: /*
194: FormInitialGuess - Forms initial approximation.
196: Input Parameters:
197: user - user-defined application context
198: X - vector
200: Output Parameter:
201: X - vector
202: */
203: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
204: {
205: PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
207: PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
208: PetscScalar ***x;
211: 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);
213: lambda = user->param;
214: hx = 1.0/(PetscReal)(Mx-1);
215: hy = 1.0/(PetscReal)(My-1);
216: hz = 1.0/(PetscReal)(Mz-1);
217: temp1 = lambda/(lambda + 1.0);
219: /*
220: Get a pointer to vector data.
221: - For default PETSc vectors, VecGetArray() returns a pointer to
222: the data array. Otherwise, the routine is implementation dependent.
223: - You MUST call VecRestoreArray() when you no longer need access to
224: the array.
225: */
226: DMDAVecGetArray(user->da,X,&x);
228: /*
229: Get local grid boundaries (for 3-dimensional DMDA):
230: xs, ys, zs - starting grid indices (no ghost points)
231: xm, ym, zm - widths of local grid (no ghost points)
233: */
234: DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);
236: /*
237: Compute initial guess over the locally owned part of the grid
238: */
239: for (k=zs; k<zs+zm; k++) {
240: tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
241: for (j=ys; j<ys+ym; j++) {
242: tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
243: for (i=xs; i<xs+xm; i++) {
244: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
245: /* boundary conditions are all zero Dirichlet */
246: x[k][j][i] = 0.0;
247: } else {
248: x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
249: }
250: }
251: }
252: }
254: /*
255: Restore vector
256: */
257: DMDAVecRestoreArray(user->da,X,&x);
258: return(0);
259: }
260: /* ------------------------------------------------------------------- */
263: /*
264: FormFunction - Evaluates nonlinear function, F(x).
266: Input Parameters:
267: . snes - the SNES context
268: . X - input vector
269: . ptr - optional user-defined context, as set by SNESSetFunction()
271: Output Parameter:
272: . F - function vector
273: */
274: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
275: {
276: AppCtx *user = (AppCtx*)ptr;
278: PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
279: PetscReal two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
280: PetscScalar u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
281: Vec localX;
282: DM da;
285: SNESGetDM(snes,&da);
286: DMGetLocalVector(da,&localX);
287: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
288: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
290: lambda = user->param;
291: hx = 1.0/(PetscReal)(Mx-1);
292: hy = 1.0/(PetscReal)(My-1);
293: hz = 1.0/(PetscReal)(Mz-1);
294: sc = hx*hy*hz*lambda;
295: hxhzdhy = hx*hz/hy;
296: hyhzdhx = hy*hz/hx;
297: hxhydhz = hx*hy/hz;
299: /*
300: Scatter ghost points to local vector,using the 2-step process
301: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
302: By placing code between these two statements, computations can be
303: done while messages are in transition.
304: */
305: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
306: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
308: /*
309: Get pointers to vector data
310: */
311: DMDAVecGetArrayRead(da,localX,&x);
312: DMDAVecGetArray(da,F,&f);
314: /*
315: Get local grid boundaries
316: */
317: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
319: /*
320: Compute function over the locally owned part of the grid
321: */
322: for (k=zs; k<zs+zm; k++) {
323: for (j=ys; j<ys+ym; j++) {
324: for (i=xs; i<xs+xm; i++) {
325: if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
326: f[k][j][i] = x[k][j][i];
327: } else {
328: u = x[k][j][i];
329: u_east = x[k][j][i+1];
330: u_west = x[k][j][i-1];
331: u_north = x[k][j+1][i];
332: u_south = x[k][j-1][i];
333: u_up = x[k+1][j][i];
334: u_down = x[k-1][j][i];
335: u_xx = (-u_east + two*u - u_west)*hyhzdhx;
336: u_yy = (-u_north + two*u - u_south)*hxhzdhy;
337: u_zz = (-u_up + two*u - u_down)*hxhydhz;
338: f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
339: }
340: }
341: }
342: }
344: /*
345: Restore vectors
346: */
347: DMDAVecRestoreArrayRead(da,localX,&x);
348: DMDAVecRestoreArray(da,F,&f);
349: DMRestoreLocalVector(da,&localX);
350: PetscLogFlops(11.0*ym*xm);
351: return(0);
352: }
353: /* ------------------------------------------------------------------- */
356: /*
357: FormJacobian - Evaluates Jacobian matrix.
359: Input Parameters:
360: . snes - the SNES context
361: . x - input vector
362: . ptr - optional user-defined context, as set by SNESSetJacobian()
364: Output Parameters:
365: . A - Jacobian matrix
366: . B - optionally different preconditioning matrix
368: */
369: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
370: {
371: AppCtx *user = (AppCtx*)ptr; /* user-defined application context */
372: Vec localX;
374: PetscInt i,j,k,Mx,My,Mz;
375: MatStencil col[7],row;
376: PetscInt xs,ys,zs,xm,ym,zm;
377: PetscScalar lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
378: DM da;
381: SNESGetDM(snes,&da);
382: DMGetLocalVector(da,&localX);
383: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
384: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
386: lambda = user->param;
387: hx = 1.0/(PetscReal)(Mx-1);
388: hy = 1.0/(PetscReal)(My-1);
389: hz = 1.0/(PetscReal)(Mz-1);
390: sc = hx*hy*hz*lambda;
391: hxhzdhy = hx*hz/hy;
392: hyhzdhx = hy*hz/hx;
393: hxhydhz = hx*hy/hz;
395: /*
396: Scatter ghost points to local vector, using the 2-step process
397: DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
398: By placing code between these two statements, computations can be
399: done while messages are in transition.
400: */
401: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
402: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
404: /*
405: Get pointer to vector data
406: */
407: DMDAVecGetArrayRead(da,localX,&x);
409: /*
410: Get local grid boundaries
411: */
412: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
414: /*
415: Compute entries for the locally owned part of the Jacobian.
416: - Currently, all PETSc parallel matrix formats are partitioned by
417: contiguous chunks of rows across the processors.
418: - Each processor needs to insert only elements that it owns
419: locally (but any non-local elements will be sent to the
420: appropriate processor during matrix assembly).
421: - Here, we set all entries for a particular row at once.
422: - We can set matrix entries either using either
423: MatSetValuesLocal() or MatSetValues(), as discussed above.
424: */
425: for (k=zs; k<zs+zm; k++) {
426: for (j=ys; j<ys+ym; j++) {
427: for (i=xs; i<xs+xm; i++) {
428: row.k = k; row.j = j; row.i = i;
429: /* boundary points */
430: if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
431: v[0] = 1.0;
432: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
433: } else {
434: /* interior grid points */
435: v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
436: v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
437: v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
438: 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;
439: v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
440: v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
441: v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
442: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
443: }
444: }
445: }
446: }
447: DMDAVecRestoreArrayRead(da,localX,&x);
448: DMRestoreLocalVector(da,&localX);
450: /*
451: Assemble matrix, using the 2-step process:
452: MatAssemblyBegin(), MatAssemblyEnd().
453: */
454: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
455: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
457: /*
458: Normally since the matrix has already been assembled above; this
459: would do nothing. But in the matrix free mode -snes_mf_operator
460: this tells the "matrix-free" matrix that a new linear system solve
461: is about to be done.
462: */
464: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
465: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
467: /*
468: Tell the matrix we will never add a new nonzero location to the
469: matrix. If we do, it will generate an error.
470: */
471: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
472: return(0);
473: }