Actual source code: ex34.c
petsc-dev 2014-02-02
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 <petscdmda.h>
26: #include <petscksp.h>
28: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,MatStructure*,void*);
29: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
33: int main(int argc,char **argv)
34: {
35: KSP ksp;
36: DM da;
37: PetscReal norm;
40: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
41: PetscScalar Hx,Hy,Hz;
42: PetscScalar ***array;
43: Vec x,b,r;
44: Mat J;
46: PetscInitialize(&argc,&argv,(char*)0,help);
48: KSPCreate(PETSC_COMM_WORLD,&ksp);
49: DMDACreate3d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,12,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
50: DMDASetInterpolationType(da, DMDA_Q0);
52: KSPSetDM(ksp,da);
54: KSPSetComputeRHS(ksp,ComputeRHS,NULL);
55: KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
56: KSPSetFromOptions(ksp);
57: KSPSolve(ksp,NULL,NULL);
58: KSPGetSolution(ksp,&x);
59: KSPGetRhs(ksp,&b);
60: KSPGetOperators(ksp,NULL,&J,NULL);
61: VecDuplicate(b,&r);
63: MatMult(J,x,r);
64: VecAXPY(r,-1.0,b);
65: VecNorm(r,NORM_2,&norm);
66: PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);
68: DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);
69: Hx = 1.0 / (PetscReal)(mx);
70: Hy = 1.0 / (PetscReal)(my);
71: Hz = 1.0 / (PetscReal)(mz);
72: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
73: DMDAVecGetArray(da, x, &array);
75: for (k=zs; k<zs+zm; k++) {
76: for (j=ys; j<ys+ym; j++) {
77: for (i=xs; i<xs+xm; i++) {
78: array[k][j][i] -=
79: PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
80: PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
81: PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
82: }
83: }
84: }
85: DMDAVecRestoreArray(da, x, &array);
86: VecAssemblyBegin(x);
87: VecAssemblyEnd(x);
89: VecNorm(x,NORM_INFINITY,&norm);
90: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)norm);
91: VecNorm(x,NORM_1,&norm);
92: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
93: VecNorm(x,NORM_2,&norm);
94: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
96: VecDestroy(&r);
97: KSPDestroy(&ksp);
98: DMDestroy(&da);
99: PetscFinalize();
100: return 0;
101: }
105: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
106: {
108: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
109: PetscScalar Hx,Hy,Hz;
110: PetscScalar ***array;
111: DM da;
112: MatNullSpace nullspace;
115: KSPGetDM(ksp,&da);
116: DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);
117: Hx = 1.0 / (PetscReal)(mx);
118: Hy = 1.0 / (PetscReal)(my);
119: Hz = 1.0 / (PetscReal)(mz);
120: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
121: DMDAVecGetArray(da, b, &array);
122: for (k=zs; k<zs+zm; k++) {
123: for (j=ys; j<ys+ym; j++) {
124: for (i=xs; i<xs+xm; i++) {
125: array[k][j][i] = 12 * PETSC_PI * PETSC_PI
126: * PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))
127: * PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))
128: * PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz))
129: * Hx * Hy * Hz;
130: }
131: }
132: }
133: DMDAVecRestoreArray(da, b, &array);
134: VecAssemblyBegin(b);
135: VecAssemblyEnd(b);
137: /* force right hand side to be consistent for singular matrix */
138: /* note this is really a hack, normally the model would provide you with a consistent right handside */
140: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
141: MatNullSpaceRemove(nullspace,b);
142: MatNullSpaceDestroy(&nullspace);
143: return(0);
144: }
149: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac,MatStructure *str, void *ctx)
150: {
152: PetscInt i,j,k,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;
159: KSPGetDM(ksp,&da);
160: DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
161: Hx = 1.0 / (PetscReal)(mx);
162: Hy = 1.0 / (PetscReal)(my);
163: Hz = 1.0 / (PetscReal)(mz);
164: HyHzdHx = Hy*Hz/Hx;
165: HxHzdHy = Hx*Hz/Hy;
166: HxHydHz = Hx*Hy/Hz;
167: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
168: for (k=zs; k<zs+zm; k++) {
169: for (j=ys; j<ys+ym; j++) {
170: for (i=xs; i<xs+xm; i++) {
171: row.i = i; row.j = j; row.k = k;
172: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
173: num = 0; numi=0; numj=0; numk=0;
174: if (k!=0) {
175: v[num] = -HxHydHz;
176: col[num].i = i;
177: col[num].j = j;
178: col[num].k = k-1;
179: num++; numk++;
180: }
181: if (j!=0) {
182: v[num] = -HxHzdHy;
183: col[num].i = i;
184: col[num].j = j-1;
185: col[num].k = k;
186: num++; numj++;
187: }
188: if (i!=0) {
189: v[num] = -HyHzdHx;
190: col[num].i = i-1;
191: col[num].j = j;
192: col[num].k = k;
193: num++; numi++;
194: }
195: if (i!=mx-1) {
196: v[num] = -HyHzdHx;
197: col[num].i = i+1;
198: col[num].j = j;
199: col[num].k = k;
200: num++; numi++;
201: }
202: if (j!=my-1) {
203: v[num] = -HxHzdHy;
204: col[num].i = i;
205: col[num].j = j+1;
206: col[num].k = k;
207: num++; numj++;
208: }
209: if (k!=mz-1) {
210: v[num] = -HxHydHz;
211: col[num].i = i;
212: col[num].j = j;
213: col[num].k = k+1;
214: num++; numk++;
215: }
216: v[num] = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
217: col[num].i = i; col[num].j = j; col[num].k = k;
218: num++;
219: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
220: } else {
221: v[0] = -HxHydHz; col[0].i = i; col[0].j = j; col[0].k = k-1;
222: v[1] = -HxHzdHy; col[1].i = i; col[1].j = j-1; col[1].k = k;
223: v[2] = -HyHzdHx; col[2].i = i-1; col[2].j = j; col[2].k = k;
224: v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i; col[3].j = j; col[3].k = k;
225: v[4] = -HyHzdHx; col[4].i = i+1; col[4].j = j; col[4].k = k;
226: v[5] = -HxHzdHy; col[5].i = i; col[5].j = j+1; col[5].k = k;
227: v[6] = -HxHydHz; col[6].i = i; col[6].j = j; col[6].k = k+1;
228: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
229: }
230: }
231: }
232: }
233: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
234: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
235: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
236: MatSetNullSpace(jac,nullspace);
237: MatNullSpaceDestroy(&nullspace);
238: return(0);
239: }