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*/
9: /*
10: Laplacian in 3D. Modeled by the partial differential equation
12: div grad u = f, 0 < x,y,z < 1,
14: with pure Neumann boundary conditions
16: u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
18: The functions are cell-centered
20: This uses multigrid to solve the linear system
22: Contributed by Jianming Yang <jianming-yang@uiowa.edu>
23: */
25: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";
27: #include <petscdm.h>
28: #include <petscdmda.h>
29: #include <petscksp.h>
31: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
32: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
34: int main(int argc,char **argv)
35: {
36: KSP ksp;
37: DM da;
38: PetscReal norm;
40: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,d,dof;
41: PetscScalar Hx,Hy,Hz;
42: PetscScalar ****array;
43: Vec x,b,r;
44: Mat J;
46: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
47: dof = 1;
48: PetscOptionsGetInt(NULL,NULL,"-da_dof",&dof,NULL);
49: KSPCreate(PETSC_COMM_WORLD,&ksp);
50: 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);
51: DMSetFromOptions(da);
52: DMSetUp(da);
53: DMDASetInterpolationType(da, DMDA_Q0);
55: KSPSetDM(ksp,da);
57: KSPSetComputeRHS(ksp,ComputeRHS,NULL);
58: KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
59: KSPSetFromOptions(ksp);
60: KSPSolve(ksp,NULL,NULL);
61: KSPGetSolution(ksp,&x);
62: KSPGetRhs(ksp,&b);
63: KSPGetOperators(ksp,NULL,&J);
64: VecDuplicate(b,&r);
66: MatMult(J,x,r);
67: VecAXPY(r,-1.0,b);
68: VecNorm(r,NORM_2,&norm);
69: PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);
71: DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);
72: Hx = 1.0 / (PetscReal)(mx);
73: Hy = 1.0 / (PetscReal)(my);
74: Hz = 1.0 / (PetscReal)(mz);
75: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
76: DMDAVecGetArrayDOF(da, x, &array);
78: for (k=zs; k<zs+zm; k++) {
79: for (j=ys; j<ys+ym; j++) {
80: for (i=xs; i<xs+xm; i++) {
81: for (d=0; d<dof; d++) {
82: array[k][j][i][d] -=
83: PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
84: PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
85: PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
86: }
87: }
88: }
89: }
90: DMDAVecRestoreArrayDOF(da, x, &array);
91: VecAssemblyBegin(x);
92: VecAssemblyEnd(x);
94: VecNorm(x,NORM_INFINITY,&norm);
95: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)norm);
96: VecNorm(x,NORM_1,&norm);
97: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
98: VecNorm(x,NORM_2,&norm);
99: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
101: VecDestroy(&r);
102: KSPDestroy(&ksp);
103: DMDestroy(&da);
104: PetscFinalize();
105: return ierr;
106: }
108: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
109: {
111: PetscInt d,dof,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
112: PetscScalar Hx,Hy,Hz;
113: PetscScalar ****array;
114: DM da;
115: MatNullSpace nullspace;
118: KSPGetDM(ksp,&da);
119: DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,&dof,0,0,0,0,0);
120: Hx = 1.0 / (PetscReal)(mx);
121: Hy = 1.0 / (PetscReal)(my);
122: Hz = 1.0 / (PetscReal)(mz);
123: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
124: DMDAVecGetArrayDOF(da, b, &array);
125: for (k=zs; k<zs+zm; k++) {
126: for (j=ys; j<ys+ym; j++) {
127: for (i=xs; i<xs+xm; i++) {
128: for (d=0; d<dof; d++) {
129: array[k][j][i][d] = 12 * PETSC_PI * PETSC_PI
130: * PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))
131: * PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))
132: * PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz))
133: * Hx * Hy * Hz;
134: }
135: }
136: }
137: }
138: DMDAVecRestoreArrayDOF(da, b, &array);
139: VecAssemblyBegin(b);
140: VecAssemblyEnd(b);
142: /* force right hand side to be consistent for singular matrix */
143: /* note this is really a hack, normally the model would provide you with a consistent right handside */
145: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
146: MatNullSpaceRemove(nullspace,b);
147: MatNullSpaceDestroy(&nullspace);
148: return(0);
149: }
152: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
153: {
155: PetscInt dof,i,j,k,d,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
156: PetscScalar v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
157: MatStencil row, col[7];
158: DM da;
159: MatNullSpace nullspace;
160: PetscBool dump_mat = PETSC_FALSE, check_matis = PETSC_FALSE;
163: KSPGetDM(ksp,&da);
164: DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
165: Hx = 1.0 / (PetscReal)(mx);
166: Hy = 1.0 / (PetscReal)(my);
167: Hz = 1.0 / (PetscReal)(mz);
168: HyHzdHx = Hy*Hz/Hx;
169: HxHzdHy = Hx*Hz/Hy;
170: HxHydHz = Hx*Hy/Hz;
171: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
172: for (k=zs; k<zs+zm; k++) {
173: for (j=ys; j<ys+ym; j++) {
174: for (i=xs; i<xs+xm; i++) {
175: for (d=0; d<dof; d++) {
176: row.i = i; row.j = j; row.k = k; row.c = d;
177: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
178: num = 0; numi=0; numj=0; numk=0;
179: if (k!=0) {
180: v[num] = -HxHydHz;
181: col[num].i = i;
182: col[num].j = j;
183: col[num].k = k-1;
184: col[num].c = d;
185: num++; numk++;
186: }
187: if (j!=0) {
188: v[num] = -HxHzdHy;
189: col[num].i = i;
190: col[num].j = j-1;
191: col[num].k = k;
192: col[num].c = d;
193: num++; numj++;
194: }
195: if (i!=0) {
196: v[num] = -HyHzdHx;
197: col[num].i = i-1;
198: col[num].j = j;
199: col[num].k = k;
200: col[num].c = d;
201: num++; numi++;
202: }
203: if (i!=mx-1) {
204: v[num] = -HyHzdHx;
205: col[num].i = i+1;
206: col[num].j = j;
207: col[num].k = k;
208: col[num].c = d;
209: num++; numi++;
210: }
211: if (j!=my-1) {
212: v[num] = -HxHzdHy;
213: col[num].i = i;
214: col[num].j = j+1;
215: col[num].k = k;
216: col[num].c = d;
217: num++; numj++;
218: }
219: if (k!=mz-1) {
220: v[num] = -HxHydHz;
221: col[num].i = i;
222: col[num].j = j;
223: col[num].k = k+1;
224: col[num].c = d;
225: num++; numk++;
226: }
227: v[num] = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
228: col[num].i = i; col[num].j = j; col[num].k = k; col[num].c = d;
229: num++;
230: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
231: } else {
232: v[0] = -HxHydHz; col[0].i = i; col[0].j = j; col[0].k = k-1; col[0].c = d;
233: v[1] = -HxHzdHy; col[1].i = i; col[1].j = j-1; col[1].k = k; col[1].c = d;
234: v[2] = -HyHzdHx; col[2].i = i-1; col[2].j = j; col[2].k = k; col[2].c = d;
235: v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i; col[3].j = j; col[3].k = k; col[3].c = d;
236: v[4] = -HyHzdHx; col[4].i = i+1; col[4].j = j; col[4].k = k; col[4].c = d;
237: v[5] = -HxHzdHy; col[5].i = i; col[5].j = j+1; col[5].k = k; col[5].c = d;
238: v[6] = -HxHydHz; col[6].i = i; col[6].j = j; col[6].k = k+1; col[6].c = d;
239: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
240: }
241: }
242: }
243: }
244: }
245: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
246: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
247: PetscOptionsGetBool(NULL,NULL,"-dump_mat",&dump_mat,NULL);
248: if (dump_mat) {
249: Mat JJ;
251: MatComputeOperator(jac,MATAIJ,&JJ);
252: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_MATLAB);
253: MatView(JJ,PETSC_VIEWER_STDOUT_WORLD);
254: MatDestroy(&JJ);
255: }
256: MatViewFromOptions(jac,NULL,"-view_mat");
257: PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
258: if (check_matis) {
259: void (*f)(void);
260: Mat J2;
261: MatType jtype;
262: PetscReal nrm;
264: MatGetType(jac,&jtype);
265: MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
266: MatViewFromOptions(J2,NULL,"-view_conv");
267: MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
268: MatGetOperation(jac,MATOP_VIEW,&f);
269: MatSetOperation(J2,MATOP_VIEW,f);
270: MatSetDM(J2,da);
271: MatViewFromOptions(J2,NULL,"-view_conv_assembled");
272: MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
273: MatNorm(J2,NORM_FROBENIUS,&nrm);
274: PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
275: MatViewFromOptions(J2,NULL,"-view_conv_err");
276: MatDestroy(&J2);
277: }
278: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
279: MatSetNullSpace(J,nullspace);
280: MatNullSpaceDestroy(&nullspace);
281: return(0);
282: }
286: /*TEST
288: build:
289: requires: !complex !single
291: test:
292: 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
294: test:
295: suffix: 2
296: nsize: 2
297: 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
299: test:
300: suffix: hyprestruct
301: nsize: 3
302: requires: hypre
303: args: -ksp_type gmres -pc_type pfmg -dm_mat_type hyprestruct -ksp_monitor -da_refine 3
305: TEST*/