Actual source code: ex34.c

```  1: /*T
2:    Concepts: KSP^solving a system of linear equations
3:    Concepts: KSP^Laplacian, 3d
4:    Processors: n
5: T*/

7: /*
8: Laplacian in 3D. Modeled by the partial differential equation

10:    div  grad u = f,  0 < x,y,z < 1,

12: with pure Neumann boundary conditions

14:    u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.

16: The functions are cell-centered

18: This uses multigrid to solve the linear system

20:        Contributed by Jianming Yang <jianming-yang@uiowa.edu>
21: */

23: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";

25: #include <petscdm.h>
26: #include <petscdmda.h>
27: #include <petscksp.h>

29: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
30: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

32: int main(int argc,char **argv)
33: {
34:   KSP            ksp;
35:   DM             da;
36:   PetscReal      norm;
38:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,d,dof;
39:   PetscScalar    Hx,Hy,Hz;
40:   PetscScalar    ****array;
41:   Vec            x,b,r;
42:   Mat            J;

44:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
45:   dof  = 1;
46:   PetscOptionsGetInt(NULL,NULL,"-da_dof",&dof,NULL);
47:   KSPCreate(PETSC_COMM_WORLD,&ksp);
48:   DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,12,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,1,0,0,0,&da);
49:   DMSetFromOptions(da);
50:   DMSetUp(da);
51:   DMDASetInterpolationType(da, DMDA_Q0);

53:   KSPSetDM(ksp,da);

55:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
56:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
57:   KSPSetFromOptions(ksp);
58:   KSPSolve(ksp,NULL,NULL);
59:   KSPGetSolution(ksp,&x);
60:   KSPGetRhs(ksp,&b);
61:   KSPGetOperators(ksp,NULL,&J);
62:   VecDuplicate(b,&r);

64:   MatMult(J,x,r);
65:   VecAXPY(r,-1.0,b);
66:   VecNorm(r,NORM_2,&norm);
67:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);

69:   DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);
70:   Hx   = 1.0 / (PetscReal)(mx);
71:   Hy   = 1.0 / (PetscReal)(my);
72:   Hz   = 1.0 / (PetscReal)(mz);
73:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
74:   DMDAVecGetArrayDOF(da, x, &array);

76:   for (k=zs; k<zs+zm; k++) {
77:     for (j=ys; j<ys+ym; j++) {
78:       for (i=xs; i<xs+xm; i++) {
79:         for (d=0; d<dof; d++) {
80:           array[k][j][i][d] -=
81:             PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
82:             PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
83:             PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
84:         }
85:       }
86:     }
87:   }
88:   DMDAVecRestoreArrayDOF(da, x, &array);
89:   VecAssemblyBegin(x);
90:   VecAssemblyEnd(x);

92:   VecNorm(x,NORM_INFINITY,&norm);
93:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)norm);
94:   VecNorm(x,NORM_1,&norm);
95:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
96:   VecNorm(x,NORM_2,&norm);
97:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));

99:   VecDestroy(&r);
100:   KSPDestroy(&ksp);
101:   DMDestroy(&da);
102:   PetscFinalize();
103:   return ierr;
104: }

106: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
107: {
109:   PetscInt       d,dof,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
110:   PetscScalar    Hx,Hy,Hz;
111:   PetscScalar    ****array;
112:   DM             da;
113:   MatNullSpace   nullspace;

116:   KSPGetDM(ksp,&da);
117:   DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,&dof,0,0,0,0,0);
118:   Hx   = 1.0 / (PetscReal)(mx);
119:   Hy   = 1.0 / (PetscReal)(my);
120:   Hz   = 1.0 / (PetscReal)(mz);
121:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
122:   DMDAVecGetArrayDOFWrite(da, b, &array);
123:   for (k=zs; k<zs+zm; k++) {
124:     for (j=ys; j<ys+ym; j++) {
125:       for (i=xs; i<xs+xm; i++) {
126:         for (d=0; d<dof; d++) {
127:           array[k][j][i][d] = 12 * PETSC_PI * PETSC_PI
128:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))
129:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))
130:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz))
131:                            * Hx * Hy * Hz;
132:         }
133:       }
134:     }
135:   }
136:   DMDAVecRestoreArrayDOFWrite(da, b, &array);
137:   VecAssemblyBegin(b);
138:   VecAssemblyEnd(b);

140:   /* force right hand side to be consistent for singular matrix */
141:   /* note this is really a hack, normally the model would provide you with a consistent right handside */

143:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
144:   MatNullSpaceRemove(nullspace,b);
145:   MatNullSpaceDestroy(&nullspace);
146:   return(0);
147: }

149: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
150: {
152:   PetscInt       dof,i,j,k,d,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
153:   PetscScalar    v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
154:   MatStencil     row, col[7];
155:   DM             da;
156:   MatNullSpace   nullspace;
157:   PetscBool      dump_mat = PETSC_FALSE, check_matis = PETSC_FALSE;

160:   KSPGetDM(ksp,&da);
161:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
162:   Hx      = 1.0 / (PetscReal)(mx);
163:   Hy      = 1.0 / (PetscReal)(my);
164:   Hz      = 1.0 / (PetscReal)(mz);
165:   HyHzdHx = Hy*Hz/Hx;
166:   HxHzdHy = Hx*Hz/Hy;
167:   HxHydHz = Hx*Hy/Hz;
168:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
169:   for (k=zs; k<zs+zm; k++) {
170:     for (j=ys; j<ys+ym; j++) {
171:       for (i=xs; i<xs+xm; i++) {
172:         for (d=0; d<dof; d++) {
173:           row.i = i; row.j = j; row.k = k; row.c = d;
174:           if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
175:             num = 0; numi=0; numj=0; numk=0;
176:             if (k!=0) {
177:               v[num]     = -HxHydHz;
178:               col[num].i = i;
179:               col[num].j = j;
180:               col[num].k = k-1;
181:               col[num].c = d;
182:               num++; numk++;
183:             }
184:             if (j!=0) {
185:               v[num]     = -HxHzdHy;
186:               col[num].i = i;
187:               col[num].j = j-1;
188:               col[num].k = k;
189:               col[num].c = d;
190:               num++; numj++;
191:               }
192:             if (i!=0) {
193:               v[num]     = -HyHzdHx;
194:               col[num].i = i-1;
195:               col[num].j = j;
196:               col[num].k = k;
197:               col[num].c = d;
198:               num++; numi++;
199:             }
200:             if (i!=mx-1) {
201:               v[num]     = -HyHzdHx;
202:               col[num].i = i+1;
203:               col[num].j = j;
204:               col[num].k = k;
205:               col[num].c = d;
206:               num++; numi++;
207:             }
208:             if (j!=my-1) {
209:               v[num]     = -HxHzdHy;
210:               col[num].i = i;
211:               col[num].j = j+1;
212:               col[num].k = k;
213:               col[num].c = d;
214:               num++; numj++;
215:             }
216:             if (k!=mz-1) {
217:               v[num]     = -HxHydHz;
218:               col[num].i = i;
219:               col[num].j = j;
220:               col[num].k = k+1;
221:               col[num].c = d;
222:               num++; numk++;
223:             }
224:             v[num]     = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
225:             col[num].i = i;   col[num].j = j;   col[num].k = k; col[num].c = d;
226:             num++;
227:             MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
228:           } else {
229:             v[0] = -HxHydHz;                          col[0].i = i;   col[0].j = j;   col[0].k = k-1; col[0].c = d;
230:             v[1] = -HxHzdHy;                          col[1].i = i;   col[1].j = j-1; col[1].k = k;   col[1].c = d;
231:             v[2] = -HyHzdHx;                          col[2].i = i-1; col[2].j = j;   col[2].k = k;   col[2].c = d;
232:             v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i;   col[3].j = j;   col[3].k = k;   col[3].c = d;
233:             v[4] = -HyHzdHx;                          col[4].i = i+1; col[4].j = j;   col[4].k = k;   col[4].c = d;
234:             v[5] = -HxHzdHy;                          col[5].i = i;   col[5].j = j+1; col[5].k = k;   col[5].c = d;
235:             v[6] = -HxHydHz;                          col[6].i = i;   col[6].j = j;   col[6].k = k+1; col[6].c = d;
236:             MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
237:           }
238:         }
239:       }
240:     }
241:   }
242:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
243:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
244:   PetscOptionsGetBool(NULL,NULL,"-dump_mat",&dump_mat,NULL);
245:   if (dump_mat) {
246:     Mat JJ;

248:     MatComputeOperator(jac,MATAIJ,&JJ);
249:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_MATLAB);
250:     MatView(JJ,PETSC_VIEWER_STDOUT_WORLD);
251:     MatDestroy(&JJ);
252:   }
253:   MatViewFromOptions(jac,NULL,"-view_mat");
254:   PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
255:   if (check_matis) {
256:     void      (*f)(void);
257:     Mat       J2;
258:     MatType   jtype;
259:     PetscReal nrm;

261:     MatGetType(jac,&jtype);
262:     MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
263:     MatViewFromOptions(J2,NULL,"-view_conv");
264:     MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
265:     MatGetOperation(jac,MATOP_VIEW,&f);
266:     MatSetOperation(J2,MATOP_VIEW,f);
267:     MatSetDM(J2,da);
268:     MatViewFromOptions(J2,NULL,"-view_conv_assembled");
269:     MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
270:     MatNorm(J2,NORM_FROBENIUS,&nrm);
271:     PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
272:     MatViewFromOptions(J2,NULL,"-view_conv_err");
273:     MatDestroy(&J2);
274:   }
275:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
276:   MatSetNullSpace(J,nullspace);
277:   MatNullSpaceDestroy(&nullspace);
278:   return(0);
279: }

281: /*TEST

283:    build:
284:       requires: !complex !single

286:    test:
287:       args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -pc_mg_levels 3 -mg_coarse_pc_factor_shift_type nonzero -ksp_view

289:    test:
290:       suffix: 2
291:       nsize: 2
292:       args: -ksp_monitor_short -da_grid_x 50 -da_grid_y 50 -pc_type ksp -ksp_ksp_type cg -ksp_pc_type bjacobi -ksp_ksp_rtol 1e-1 -ksp_ksp_monitor -ksp_type pipefgmres -ksp_gmres_restart 5

294:    test:
295:       suffix: hyprestruct
296:       nsize: 3
297:       requires: hypre !defined(PETSC_HAVE_HYPRE_DEVICE)
298:       args: -ksp_type gmres -pc_type pfmg -dm_mat_type hyprestruct -ksp_monitor -da_refine 3

300: TEST*/
```