Actual source code: ex35.c
petsc-3.4.5 2014-06-29
1: static const char help[] = "-Laplacian u = b as a nonlinear problem.\n\n";
3: /*T
4: Concepts: SNES^parallel Bratu example
5: Concepts: DMDA^using distributed arrays;
6: Concepts: IS coloirng types;
7: Processors: n
8: T*/
10: /*
12: The linear and nonlinear versions of these should give almost identical results on this problem
14: Richardson
15: Nonlinear:
16: -snes_rtol 1.e-12 -snes_monitor -snes_type nrichardson -snes_linesearch_monitor
18: Linear:
19: -snes_rtol 1.e-12 -snes_monitor -ksp_rtol 1.e-12 -ksp_monitor -ksp_type richardson -pc_type none -ksp_richardson_self_scale -info
21: GMRES
22: Nonlinear:
23: -snes_rtol 1.e-12 -snes_monitor -snes_type ngmres
25: Linear:
26: -snes_rtol 1.e-12 -snes_monitor -ksp_type gmres -ksp_monitor -ksp_rtol 1.e-12 -pc_type none
28: CG
29: Nonlinear:
30: -snes_rtol 1.e-12 -snes_monitor -snes_type ncg -snes_linesearch_monitor
32: Linear:
33: -snes_rtol 1.e-12 -snes_monitor -ksp_type cg -ksp_monitor -ksp_rtol 1.e-12 -pc_type none
35: Multigrid
36: Linear:
37: 1 level:
38: -snes_rtol 1.e-12 -snes_monitor -pc_type mg -mg_levels_ksp_type richardson -mg_levels_pc_type none -mg_levels_ksp_monitor
39: -mg_levels_ksp_richardson_self_scale -ksp_type richardson -ksp_monitor -ksp_rtol 1.e-12 -ksp_monitor_true_residual
41: n levels:
42: -da_refine n
44: Nonlinear:
45: 1 level:
46: -snes_rtol 1.e-12 -snes_monitor -snes_type fas -fas_levels_snes_monitor
48: n levels:
49: -da_refine n -fas_coarse_snes_type newtonls -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly
51: */
53: /*
54: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
55: Include "petscsnes.h" so that we can use SNES solvers. Note that this
56: */
57: #include <petscdmda.h>
58: #include <petscsnes.h>
60: /*
61: User-defined routines
62: */
63: extern PetscErrorCode FormMatrix(DM,Mat);
64: extern PetscErrorCode MyComputeFunction(SNES,Vec,Vec,void*);
65: extern PetscErrorCode MyComputeJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
66: extern PetscErrorCode NonlinearGS(SNES,Vec);
70: int main(int argc,char **argv)
71: {
72: SNES snes; /* nonlinear solver */
73: SNES psnes; /* nonlinear Gauss-Seidel approximate solver */
74: Vec x,b; /* solution vector */
75: PetscInt its; /* iterations for convergence */
77: DM da;
78: PetscBool use_ngs = PETSC_FALSE; /* use the nonlinear Gauss-Seidel approximate solver */
80: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: Initialize program
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: PetscInitialize(&argc,&argv,(char*)0,help);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Create nonlinear solver context
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: SNESCreate(PETSC_COMM_WORLD,&snes);
91: PetscOptionsGetBool(NULL,"-use_ngs",&use_ngs,0);
93: if (use_ngs) {
94: SNESGetPC(snes,&psnes);
95: SNESSetType(psnes,SNESSHELL);
96: SNESShellSetSolve(psnes,NonlinearGS);
97: }
99: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: Create distributed array (DMDA) to manage parallel grid and vectors
101: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
102: DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
103: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
104: SNESSetDM(snes,da);
105: if (use_ngs) {
106: SNESShellSetContext(psnes,da);
107: }
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Extract global vectors from DMDA; then duplicate for remaining
110: vectors that are the same types
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: DMCreateGlobalVector(da,&x);
113: DMCreateGlobalVector(da,&b);
114: VecSetRandom(b,NULL);
116: SNESSetFunction(snes,NULL,MyComputeFunction,NULL);
117: SNESSetJacobian(snes,NULL,NULL,MyComputeJacobian,NULL);
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Customize nonlinear solver; set runtime options
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: SNESSetFromOptions(snes);
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Solve nonlinear system
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: SNESSolve(snes,b,x);
128: SNESGetIterationNumber(snes,&its);
130: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Free work space. All PETSc objects should be destroyed when they
135: are no longer needed.
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: VecDestroy(&x);
138: VecDestroy(&b);
139: SNESDestroy(&snes);
140: DMDestroy(&da);
141: PetscFinalize();
142: return(0);
143: }
145: /* ------------------------------------------------------------------- */
148: PetscErrorCode MyComputeFunction(SNES snes,Vec x,Vec F,void *ctx)
149: {
151: Mat J;
152: DM dm;
155: SNESGetDM(snes,&dm);
156: DMGetApplicationContext(dm,&J);
157: if (!J) {
158: DMCreateMatrix(dm,MATAIJ,&J);
159: MatSetDM(J, NULL);
160: FormMatrix(dm,J);
161: DMSetApplicationContext(dm,J);
162: DMSetApplicationContextDestroy(dm,(PetscErrorCode (*)(void**))MatDestroy);
163: }
164: MatMult(J,x,F);
165: return(0);
166: }
170: PetscErrorCode MyComputeJacobian(SNES snes,Vec x,Mat *J,Mat *Jp,MatStructure *str,void *ctx)
171: {
173: DM dm;
176: SNESGetDM(snes,&dm);
177: FormMatrix(dm,*Jp);
178: *str = SAME_NONZERO_PATTERN;
179: return(0);
180: }
184: PetscErrorCode FormMatrix(DM da,Mat jac)
185: {
187: PetscInt i,j,nrows = 0;
188: MatStencil col[5],row,*rows;
189: PetscScalar v[5],hx,hy,hxdhy,hydhx;
190: DMDALocalInfo info;
193: DMDAGetLocalInfo(da,&info);
194: hx = 1.0/(PetscReal)(info.mx-1);
195: hy = 1.0/(PetscReal)(info.my-1);
196: hxdhy = hx/hy;
197: hydhx = hy/hx;
199: PetscMalloc(info.ym*info.xm*sizeof(MatStencil),&rows);
200: /*
201: Compute entries for the locally owned part of the Jacobian.
202: - Currently, all PETSc parallel matrix formats are partitioned by
203: contiguous chunks of rows across the processors.
204: - Each processor needs to insert only elements that it owns
205: locally (but any non-local elements will be sent to the
206: appropriate processor during matrix assembly).
207: - Here, we set all entries for a particular row at once.
208: - We can set matrix entries either using either
209: MatSetValuesLocal() or MatSetValues(), as discussed above.
210: */
211: for (j=info.ys; j<info.ys+info.ym; j++) {
212: for (i=info.xs; i<info.xs+info.xm; i++) {
213: row.j = j; row.i = i;
214: /* boundary points */
215: if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
216: v[0] = 2.0*(hydhx + hxdhy);
217: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
218: rows[nrows].i = i;
219: rows[nrows++].j = j;
220: } else {
221: /* interior grid points */
222: v[0] = -hxdhy; col[0].j = j - 1; col[0].i = i;
223: v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
224: v[2] = 2.0*(hydhx + hxdhy); col[2].j = row.j; col[2].i = row.i;
225: v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
226: v[4] = -hxdhy; col[4].j = j + 1; col[4].i = i;
227: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
228: }
229: }
230: }
232: /*
233: Assemble matrix, using the 2-step process:
234: MatAssemblyBegin(), MatAssemblyEnd().
235: */
236: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
237: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
238: MatZeroRowsColumnsStencil(jac,nrows,rows,2.0*(hydhx + hxdhy),NULL,NULL);
239: PetscFree(rows);
240: /*
241: Tell the matrix we will never add a new nonzero location to the
242: matrix. If we do, it will generate an error.
243: */
244: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
245: return(0);
246: }
250: /* ------------------------------------------------------------------- */
253: /*
254: Applies some sweeps on nonlinear Gauss-Seidel on each process
256: */
257: PetscErrorCode NonlinearGS(SNES snes,Vec X)
258: {
259: PetscInt i,j,Mx,My,xs,ys,xm,ym,its,l;
261: PetscReal hx,hy,hxdhy,hydhx;
262: PetscScalar **x,F,J,u,uxx,uyy;
263: DM da;
264: Vec localX;
267: SNESGetTolerances(snes,NULL,NULL,NULL,&its,NULL);
268: SNESShellGetContext(snes,(void**)&da);
270: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
271: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
273: hx = 1.0/(PetscReal)(Mx-1);
274: hy = 1.0/(PetscReal)(My-1);
275: hxdhy = hx/hy;
276: hydhx = hy/hx;
279: DMGetLocalVector(da,&localX);
281: for (l=0; l<its; l++) {
283: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
284: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
285: /*
286: Get a pointer to vector data.
287: - For default PETSc vectors, VecGetArray() returns a pointer to
288: the data array. Otherwise, the routine is implementation dependent.
289: - You MUST call VecRestoreArray() when you no longer need access to
290: the array.
291: */
292: DMDAVecGetArray(da,localX,&x);
294: /*
295: Get local grid boundaries (for 2-dimensional DMDA):
296: xs, ys - starting grid indices (no ghost points)
297: xm, ym - widths of local grid (no ghost points)
299: */
300: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
302: for (j=ys; j<ys+ym; j++) {
303: for (i=xs; i<xs+xm; i++) {
304: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
305: /* boundary conditions are all zero Dirichlet */
306: x[j][i] = 0.0;
307: } else {
308: u = x[j][i];
309: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
310: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
311: F = uxx + uyy;
312: J = 2.0*(hydhx + hxdhy);
313: u = u - F/J;
315: x[j][i] = u;
316: }
317: }
318: }
320: /*
321: Restore vector
322: */
323: DMDAVecRestoreArray(da,localX,&x);
324: DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
325: DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
326: }
327: DMRestoreLocalVector(da,&localX);
328: return(0);
329: }