Actual source code: ex5.c
2: /* Program usage: mpirun -np <procs> ex5 [-help] [all PETSc options] */
4: static char help[] = "Bratu nonlinear PDE in 2d.\n\
5: We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
6: domain, using distributed arrays (DAs) to partition the parallel grid.\n\
7: The command line options include:\n\
8: -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
9: problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";
11: /*T
12: Concepts: SNES^parallel Bratu example
13: Concepts: DA^using distributed arrays;
14: Processors: n
15: T*/
17: /* ------------------------------------------------------------------------
19: Solid Fuel Ignition (SFI) problem. This problem is modeled by
20: the partial differential equation
21:
22: -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
23:
24: with boundary conditions
25:
26: u = 0 for x = 0, x = 1, y = 0, y = 1.
27:
28: A finite difference approximation with the usual 5-point stencil
29: is used to discretize the boundary value problem to obtain a nonlinear
30: system of equations.
33: ------------------------------------------------------------------------- */
35: /*
36: Include "petscda.h" so that we can use distributed arrays (DAs).
37: Include "petscsnes.h" so that we can use SNES solvers. Note that this
38: file automatically includes:
39: petsc.h - base PETSc routines petscvec.h - vectors
40: petscsys.h - system routines petscmat.h - matrices
41: petscis.h - index sets petscksp.h - Krylov subspace methods
42: petscviewer.h - viewers petscpc.h - preconditioners
43: petscksp.h - linear solvers
44: */
45: #include petscda.h
46: #include petscsnes.h
48: /*
49: User-defined application context - contains data needed by the
50: application-provided call-back routines, FormJacobianLocal() and
51: FormFunctionLocal().
52: */
53: typedef struct {
54: DA da; /* distributed array data structure */
55: PassiveReal param; /* test problem parameter */
56: } AppCtx;
58: /*
59: User-defined routines
60: */
67: int main(int argc,char **argv)
68: {
69: SNES snes; /* nonlinear solver */
70: Vec x,r; /* solution, residual vectors */
71: Mat A,J; /* Jacobian matrix */
72: AppCtx user; /* user-defined work context */
73: PetscInt its; /* iterations for convergence */
74: PetscTruth matlab_function = PETSC_FALSE;
75: PetscTruth fd_jacobian = PETSC_FALSE,adic_jacobian=PETSC_FALSE;
76: PetscTruth adicmf_jacobian = PETSC_FALSE;
77: PetscErrorCode ierr;
78: PetscReal bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
79: MatFDColoring matfdcoloring = 0;
80: ISColoring iscoloring;
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Initialize program
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: PetscInitialize(&argc,&argv,(char *)0,help);
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Initialize problem parameters
90: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
91: user.param = 6.0;
92: PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
93: if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
94: SETERRQ(1,"Lambda is out of range");
95: }
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Create nonlinear solver context
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: SNESCreate(PETSC_COMM_WORLD,&snes);
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Create distributed array (DA) to manage parallel grid and vectors
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,
106: 1,1,PETSC_NULL,PETSC_NULL,&user.da);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Extract global vectors from DA; then duplicate for remaining
110: vectors that are the same types
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: DACreateGlobalVector(user.da,&x);
113: VecDuplicate(x,&r);
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Create matrix data structure; set Jacobian evaluation routine
118: Set Jacobian matrix data structure and default Jacobian evaluation
119: routine. User can override with:
120: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
121: (unless user explicitly sets preconditioner)
122: -snes_mf_operator : form preconditioning matrix as set by the user,
123: but use matrix-free approx for Jacobian-vector
124: products within Newton-Krylov method
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: /* J can be type of MATAIJ,MATBAIJ or MATSBAIJ */
128: DAGetMatrix(user.da,MATAIJ,&J);
129:
130: A = J;
131: PetscOptionsGetTruth(PETSC_NULL,"-fd_jacobian",&fd_jacobian,0);
132: PetscOptionsGetTruth(PETSC_NULL,"-adic_jacobian",&adic_jacobian,0);
133: PetscOptionsGetTruth(PETSC_NULL,"-adicmf_jacobian",&adicmf_jacobian,0);
134: #if defined(PETSC_HAVE_ADIC)
135: if (adicmf_jacobian) {
136: DASetLocalAdicMFFunction(user.da,admf_FormFunctionLocal);
137: MatRegisterDAAD();
138: MatCreateDAAD(user.da,&A);
139: MatDAADSetSNES(A,snes);
140: MatDAADSetCtx(A,&user);
141: }
142: #endif
144: if (fd_jacobian) {
145: DAGetColoring(user.da,IS_COLORING_LOCAL,&iscoloring);
146: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
147: ISColoringDestroy(iscoloring);
148: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESDAFormFunction,&user);
149: MatFDColoringSetFromOptions(matfdcoloring);
150: SNESSetJacobian(snes,A,J,SNESDefaultComputeJacobianColor,matfdcoloring);
151: #if defined(PETSC_HAVE_ADIC)
152: } else if (adic_jacobian) {
153: DAGetColoring(user.da,IS_COLORING_GHOSTED,&iscoloring);
154: MatSetColoring(J,iscoloring);
155: ISColoringDestroy(iscoloring);
156: SNESSetJacobian(snes,A,J,SNESDAComputeJacobianWithAdic,&user);
157: #endif
158: } else {
159: SNESSetJacobian(snes,A,J,SNESDAComputeJacobian,&user);
160: }
162: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: Set local function evaluation routine
164: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165: DASetLocalFunction(user.da,(DALocalFunction1)FormFunctionLocal);
166: DASetLocalJacobian(user.da,(DALocalFunction1)FormJacobianLocal);
167: DASetLocalAdicFunction(user.da,ad_FormFunctionLocal);
169: /* Decide which FormFunction to use */
170: PetscOptionsGetTruth(PETSC_NULL,"-matlab_function",&matlab_function,0);
172: SNESSetFunction(snes,r,SNESDAFormFunction,&user);
173: #if defined(PETSC_HAVE_MATLAB)
174: if (matlab_function) {
175: SNESSetFunction(snes,r,FormFunctionMatlab,&user);
176: }
177: #endif
179: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: Customize nonlinear solver; set runtime options
181: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182: SNESSetFromOptions(snes);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Evaluate initial guess
186: Note: The user should initialize the vector, x, with the initial guess
187: for the nonlinear solver prior to calling SNESSolve(). In particular,
188: to employ an initial guess of zero, the user should explicitly set
189: this vector to zero by calling VecSet().
190: */
191: FormInitialGuess(&user,x);
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Solve nonlinear system
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: SNESSolve(snes,PETSC_NULL,x);
197: SNESGetIterationNumber(snes,&its);
199: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Free work space. All PETSc objects should be destroyed when they
205: are no longer needed.
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
208: if (A != J) {
209: MatDestroy(A);
210: }
211: MatDestroy(J);
212: if (matfdcoloring) {
213: MatFDColoringDestroy(matfdcoloring);
214: }
215: VecDestroy(x);
216: VecDestroy(r);
217: SNESDestroy(snes);
218: DADestroy(user.da);
219: PetscFinalize();
221: return(0);
222: }
223: /* ------------------------------------------------------------------- */
226: /*
227: FormInitialGuess - Forms initial approximation.
229: Input Parameters:
230: user - user-defined application context
231: X - vector
233: Output Parameter:
234: X - vector
235: */
236: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
237: {
238: PetscInt i,j,Mx,My,xs,ys,xm,ym;
240: PetscReal lambda,temp1,temp,hx,hy;
241: PetscScalar **x;
244: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
245: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
247: lambda = user->param;
248: hx = 1.0/(PetscReal)(Mx-1);
249: hy = 1.0/(PetscReal)(My-1);
250: temp1 = lambda/(lambda + 1.0);
252: /*
253: Get a pointer to vector data.
254: - For default PETSc vectors, VecGetArray() returns a pointer to
255: the data array. Otherwise, the routine is implementation dependent.
256: - You MUST call VecRestoreArray() when you no longer need access to
257: the array.
258: */
259: DAVecGetArray(user->da,X,&x);
261: /*
262: Get local grid boundaries (for 2-dimensional DA):
263: xs, ys - starting grid indices (no ghost points)
264: xm, ym - widths of local grid (no ghost points)
266: */
267: DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);
269: /*
270: Compute initial guess over the locally owned part of the grid
271: */
272: for (j=ys; j<ys+ym; j++) {
273: temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
274: for (i=xs; i<xs+xm; i++) {
276: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
277: /* boundary conditions are all zero Dirichlet */
278: x[j][i] = 0.0;
279: } else {
280: x[j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
281: }
282: }
283: }
285: /*
286: Restore vector
287: */
288: DAVecRestoreArray(user->da,X,&x);
290: return(0);
291: }
292: /* ------------------------------------------------------------------- */
295: /*
296: FormFunctionLocal - Evaluates nonlinear function, F(x).
298: Process adiC(36): FormFunctionLocal
300: */
301: PetscErrorCode FormFunctionLocal(DALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
302: {
304: PetscInt i,j;
305: PetscReal lambda,hx,hy,hxdhy,hydhx,sc;
306: PetscScalar u,uxx,uyy;
310: lambda = user->param;
311: hx = 1.0/(PetscReal)(info->mx-1);
312: hy = 1.0/(PetscReal)(info->my-1);
313: sc = hx*hy*lambda;
314: hxdhy = hx/hy;
315: hydhx = hy/hx;
316: /*
317: Compute function over the locally owned part of the grid
318: */
319: for (j=info->ys; j<info->ys+info->ym; j++) {
320: for (i=info->xs; i<info->xs+info->xm; i++) {
321: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
322: f[j][i] = x[j][i];
323: } else {
324: u = x[j][i];
325: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
326: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
327: f[j][i] = uxx + uyy - sc*PetscExpScalar(u);
328: }
329: }
330: }
332: PetscLogFlops(11*info->ym*info->xm);
333: return(0);
334: }
338: /*
339: FormJacobianLocal - Evaluates Jacobian matrix.
340: */
341: PetscErrorCode FormJacobianLocal(DALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
342: {
344: PetscInt i,j;
345: MatStencil col[5],row;
346: PetscScalar lambda,v[5],hx,hy,hxdhy,hydhx,sc;
349: lambda = user->param;
350: hx = 1.0/(PetscReal)(info->mx-1);
351: hy = 1.0/(PetscReal)(info->my-1);
352: sc = hx*hy*lambda;
353: hxdhy = hx/hy;
354: hydhx = hy/hx;
357: /*
358: Compute entries for the locally owned part of the Jacobian.
359: - Currently, all PETSc parallel matrix formats are partitioned by
360: contiguous chunks of rows across the processors.
361: - Each processor needs to insert only elements that it owns
362: locally (but any non-local elements will be sent to the
363: appropriate processor during matrix assembly).
364: - Here, we set all entries for a particular row at once.
365: - We can set matrix entries either using either
366: MatSetValuesLocal() or MatSetValues(), as discussed above.
367: */
368: for (j=info->ys; j<info->ys+info->ym; j++) {
369: for (i=info->xs; i<info->xs+info->xm; i++) {
370: row.j = j; row.i = i;
371: /* boundary points */
372: if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
373: v[0] = 1.0;
374: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
375: } else {
376: /* interior grid points */
377: v[0] = -hxdhy; col[0].j = j - 1; col[0].i = i;
378: v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
379: v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[2].j = row.j; col[2].i = row.i;
380: v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
381: v[4] = -hxdhy; col[4].j = j + 1; col[4].i = i;
382: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
383: }
384: }
385: }
387: /*
388: Assemble matrix, using the 2-step process:
389: MatAssemblyBegin(), MatAssemblyEnd().
390: */
391: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
392: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
393: /*
394: Tell the matrix we will never add a new nonzero location to the
395: matrix. If we do, it will generate an error.
396: */
397: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR);
398: return(0);
399: }
402: /*
403: Variant of FormFunction() that computes the function in Matlab
404: */
405: #if defined(PETSC_HAVE_MATLAB)
406: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
407: {
408: AppCtx *user = (AppCtx*)ptr;
410: PetscInt Mx,My;
411: PetscReal lambda,hx,hy;
412: Vec localX,localF;
413: MPI_Comm comm;
416: DAGetLocalVector(user->da,&localX);
417: DAGetLocalVector(user->da,&localF);
418: PetscObjectSetName((PetscObject)localX,"localX");
419: PetscObjectSetName((PetscObject)localF,"localF");
420: DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
421: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
423: lambda = user->param;
424: hx = 1.0/(PetscReal)(Mx-1);
425: hy = 1.0/(PetscReal)(My-1);
427: PetscObjectGetComm((PetscObject)snes,&comm);
428: /*
429: Scatter ghost points to local vector,using the 2-step process
430: DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
431: By placing code between these two statements, computations can be
432: done while messages are in transition.
433: */
434: DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
435: DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
436: PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
437: PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
438: PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);
440: /*
441: Insert values into global vector
442: */
443: DALocalToGlobal(user->da,localF,INSERT_VALUES,F);
444: DARestoreLocalVector(user->da,&localX);
445: DARestoreLocalVector(user->da,&localF);
446: return(0);
447: }
448: #endif