Actual source code: ex35.c
petsc-3.7.5 2017-01-01
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 <petscdm.h>
58: #include <petscdmda.h>
59: #include <petscsnes.h>
61: /*
62: User-defined routines
63: */
64: extern PetscErrorCode FormMatrix(DM,Mat);
65: extern PetscErrorCode MyComputeFunction(SNES,Vec,Vec,void*);
66: extern PetscErrorCode MyComputeJacobian(SNES,Vec,Mat,Mat,void*);
67: extern PetscErrorCode NonlinearGS(SNES,Vec);
71: int main(int argc,char **argv)
72: {
73: SNES snes; /* nonlinear solver */
74: SNES psnes; /* nonlinear Gauss-Seidel approximate solver */
75: Vec x,b; /* solution vector */
76: PetscInt its; /* iterations for convergence */
78: DM da;
79: PetscBool use_ngs = PETSC_FALSE; /* use the nonlinear Gauss-Seidel approximate solver */
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Initialize program
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: PetscInitialize(&argc,&argv,(char*)0,help);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Create nonlinear solver context
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90: SNESCreate(PETSC_COMM_WORLD,&snes);
92: PetscOptionsGetBool(NULL,NULL,"-use_ngs",&use_ngs,0);
94: if (use_ngs) {
95: SNESGetNPC(snes,&psnes);
96: SNESSetType(psnes,SNESSHELL);
97: SNESShellSetSolve(psnes,NonlinearGS);
98: }
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Create distributed array (DMDA) to manage parallel grid and vectors
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
104: DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
105: SNESSetDM(snes,da);
106: if (use_ngs) {
107: SNESShellSetContext(psnes,da);
108: }
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Extract global vectors from DMDA; then duplicate for remaining
111: vectors that are the same types
112: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
113: DMCreateGlobalVector(da,&x);
114: DMCreateGlobalVector(da,&b);
115: VecSet(b,1.0);
117: SNESSetFunction(snes,NULL,MyComputeFunction,NULL);
118: SNESSetJacobian(snes,NULL,NULL,MyComputeJacobian,NULL);
120: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: Customize nonlinear solver; set runtime options
122: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: SNESSetFromOptions(snes);
125: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Solve nonlinear system
127: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128: SNESSolve(snes,b,x);
129: SNESGetIterationNumber(snes,&its);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Free work space. All PETSc objects should be destroyed when they
136: are no longer needed.
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: VecDestroy(&x);
139: VecDestroy(&b);
140: SNESDestroy(&snes);
141: DMDestroy(&da);
142: PetscFinalize();
143: return(0);
144: }
146: /* ------------------------------------------------------------------- */
149: PetscErrorCode MyComputeFunction(SNES snes,Vec x,Vec F,void *ctx)
150: {
152: Mat J;
153: DM dm;
156: SNESGetDM(snes,&dm);
157: DMGetApplicationContext(dm,&J);
158: if (!J) {
159: DMSetMatType(dm,MATAIJ);
160: DMCreateMatrix(dm,&J);
161: MatSetDM(J, NULL);
162: FormMatrix(dm,J);
163: DMSetApplicationContext(dm,J);
164: DMSetApplicationContextDestroy(dm,(PetscErrorCode (*)(void**))MatDestroy);
165: }
166: MatMult(J,x,F);
167: return(0);
168: }
172: PetscErrorCode MyComputeJacobian(SNES snes,Vec x,Mat J,Mat Jp,void *ctx)
173: {
175: DM dm;
178: SNESGetDM(snes,&dm);
179: FormMatrix(dm,Jp);
180: return(0);
181: }
185: PetscErrorCode FormMatrix(DM da,Mat jac)
186: {
188: PetscInt i,j,nrows = 0;
189: MatStencil col[5],row,*rows;
190: PetscScalar v[5],hx,hy,hxdhy,hydhx;
191: DMDALocalInfo info;
194: DMDAGetLocalInfo(da,&info);
195: hx = 1.0/(PetscReal)(info.mx-1);
196: hy = 1.0/(PetscReal)(info.my-1);
197: hxdhy = hx/hy;
198: hydhx = hy/hx;
200: PetscMalloc1(info.ym*info.xm,&rows);
201: /*
202: Compute entries for the locally owned part of the Jacobian.
203: - Currently, all PETSc parallel matrix formats are partitioned by
204: contiguous chunks of rows across the processors.
205: - Each processor needs to insert only elements that it owns
206: locally (but any non-local elements will be sent to the
207: appropriate processor during matrix assembly).
208: - Here, we set all entries for a particular row at once.
209: - We can set matrix entries either using either
210: MatSetValuesLocal() or MatSetValues(), as discussed above.
211: */
212: for (j=info.ys; j<info.ys+info.ym; j++) {
213: for (i=info.xs; i<info.xs+info.xm; i++) {
214: row.j = j; row.i = i;
215: /* boundary points */
216: if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
217: v[0] = 2.0*(hydhx + hxdhy);
218: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
219: rows[nrows].i = i;
220: rows[nrows++].j = j;
221: } else {
222: /* interior grid points */
223: v[0] = -hxdhy; col[0].j = j - 1; col[0].i = i;
224: v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
225: v[2] = 2.0*(hydhx + hxdhy); col[2].j = row.j; col[2].i = row.i;
226: v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
227: v[4] = -hxdhy; col[4].j = j + 1; col[4].i = i;
228: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
229: }
230: }
231: }
233: /*
234: Assemble matrix, using the 2-step process:
235: MatAssemblyBegin(), MatAssemblyEnd().
236: */
237: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
238: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
239: MatZeroRowsColumnsStencil(jac,nrows,rows,2.0*(hydhx + hxdhy),NULL,NULL);
240: PetscFree(rows);
241: /*
242: Tell the matrix we will never add a new nonzero location to the
243: matrix. If we do, it will generate an error.
244: */
245: MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
246: return(0);
247: }
251: /* ------------------------------------------------------------------- */
254: /*
255: Applies some sweeps on nonlinear Gauss-Seidel on each process
257: */
258: PetscErrorCode NonlinearGS(SNES snes,Vec X)
259: {
260: PetscInt i,j,Mx,My,xs,ys,xm,ym,its,l;
262: PetscReal hx,hy,hxdhy,hydhx;
263: PetscScalar **x,F,J,u,uxx,uyy;
264: DM da;
265: Vec localX;
268: SNESGetTolerances(snes,NULL,NULL,NULL,&its,NULL);
269: SNESShellGetContext(snes,(void**)&da);
271: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
272: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
274: hx = 1.0/(PetscReal)(Mx-1);
275: hy = 1.0/(PetscReal)(My-1);
276: hxdhy = hx/hy;
277: hydhx = hy/hx;
280: DMGetLocalVector(da,&localX);
282: for (l=0; l<its; l++) {
284: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
285: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
286: /*
287: Get a pointer to vector data.
288: - For default PETSc vectors, VecGetArray() returns a pointer to
289: the data array. Otherwise, the routine is implementation dependent.
290: - You MUST call VecRestoreArray() when you no longer need access to
291: the array.
292: */
293: DMDAVecGetArray(da,localX,&x);
295: /*
296: Get local grid boundaries (for 2-dimensional DMDA):
297: xs, ys - starting grid indices (no ghost points)
298: xm, ym - widths of local grid (no ghost points)
300: */
301: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
303: for (j=ys; j<ys+ym; j++) {
304: for (i=xs; i<xs+xm; i++) {
305: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
306: /* boundary conditions are all zero Dirichlet */
307: x[j][i] = 0.0;
308: } else {
309: u = x[j][i];
310: uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
311: uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
312: F = uxx + uyy;
313: J = 2.0*(hydhx + hxdhy);
314: u = u - F/J;
316: x[j][i] = u;
317: }
318: }
319: }
321: /*
322: Restore vector
323: */
324: DMDAVecRestoreArray(da,localX,&x);
325: DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);
326: DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);
327: }
328: DMRestoreLocalVector(da,&localX);
329: return(0);
330: }