Actual source code: ex34.c
petsc-3.7.5 2017-01-01
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*);
34: int main(int argc,char **argv)
35: {
36: KSP ksp;
37: DM da;
38: PetscReal norm;
41: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
42: PetscScalar Hx,Hy,Hz;
43: PetscScalar ***array;
44: Vec x,b,r;
45: Mat J;
47: PetscInitialize(&argc,&argv,(char*)0,help);
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,1,1,0,0,0,&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: DMDAVecGetArray(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: array[k][j][i] -=
80: PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
81: PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
82: PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
83: }
84: }
85: }
86: DMDAVecRestoreArray(da, x, &array);
87: VecAssemblyBegin(x);
88: VecAssemblyEnd(x);
90: VecNorm(x,NORM_INFINITY,&norm);
91: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)norm);
92: VecNorm(x,NORM_1,&norm);
93: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
94: VecNorm(x,NORM_2,&norm);
95: PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
97: VecDestroy(&r);
98: KSPDestroy(&ksp);
99: DMDestroy(&da);
100: PetscFinalize();
101: return 0;
102: }
106: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
107: {
109: PetscInt 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, 0,0,0,0,0,0,0,0,0);
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: DMDAVecGetArray(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: array[k][j][i] = 12 * PETSC_PI * PETSC_PI
127: * PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))
128: * PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))
129: * PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz))
130: * Hx * Hy * Hz;
131: }
132: }
133: }
134: DMDAVecRestoreArray(da, b, &array);
135: VecAssemblyBegin(b);
136: VecAssemblyEnd(b);
138: /* force right hand side to be consistent for singular matrix */
139: /* note this is really a hack, normally the model would provide you with a consistent right handside */
141: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
142: MatNullSpaceRemove(nullspace,b);
143: MatNullSpaceDestroy(&nullspace);
144: return(0);
145: }
150: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
151: {
153: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
154: PetscScalar v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
155: MatStencil row, col[7];
156: DM da;
157: MatNullSpace nullspace;
160: KSPGetDM(ksp,&da);
161: DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
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: row.i = i; row.j = j; row.k = k;
173: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
174: num = 0; numi=0; numj=0; numk=0;
175: if (k!=0) {
176: v[num] = -HxHydHz;
177: col[num].i = i;
178: col[num].j = j;
179: col[num].k = k-1;
180: num++; numk++;
181: }
182: if (j!=0) {
183: v[num] = -HxHzdHy;
184: col[num].i = i;
185: col[num].j = j-1;
186: col[num].k = k;
187: num++; numj++;
188: }
189: if (i!=0) {
190: v[num] = -HyHzdHx;
191: col[num].i = i-1;
192: col[num].j = j;
193: col[num].k = k;
194: num++; numi++;
195: }
196: if (i!=mx-1) {
197: v[num] = -HyHzdHx;
198: col[num].i = i+1;
199: col[num].j = j;
200: col[num].k = k;
201: num++; numi++;
202: }
203: if (j!=my-1) {
204: v[num] = -HxHzdHy;
205: col[num].i = i;
206: col[num].j = j+1;
207: col[num].k = k;
208: num++; numj++;
209: }
210: if (k!=mz-1) {
211: v[num] = -HxHydHz;
212: col[num].i = i;
213: col[num].j = j;
214: col[num].k = k+1;
215: num++; numk++;
216: }
217: v[num] = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
218: col[num].i = i; col[num].j = j; col[num].k = k;
219: num++;
220: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
221: } else {
222: v[0] = -HxHydHz; col[0].i = i; col[0].j = j; col[0].k = k-1;
223: v[1] = -HxHzdHy; col[1].i = i; col[1].j = j-1; col[1].k = k;
224: v[2] = -HyHzdHx; col[2].i = i-1; col[2].j = j; col[2].k = k;
225: v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i; col[3].j = j; col[3].k = k;
226: v[4] = -HyHzdHx; col[4].i = i+1; col[4].j = j; col[4].k = k;
227: v[5] = -HxHzdHy; col[5].i = i; col[5].j = j+1; col[5].k = k;
228: v[6] = -HxHydHz; col[6].i = i; col[6].j = j; col[6].k = k+1;
229: MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
230: }
231: }
232: }
233: }
234: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
235: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
236: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
237: MatSetNullSpace(J,nullspace);
238: MatNullSpaceDestroy(&nullspace);
239: return(0);
240: }