Actual source code: ex32.c
2: /*
3: Laplacian in 2D. Modeled by the partial differential equation
5: div grad u = f, 0 < x,y < 1,
7: with forcing function
9: f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}
11: with pure Neumann boundary conditions
13: The functions are cell-centered
15: This uses multigrid to solve the linear system
17: Contributed by Andrei Draganescu <aidraga@sandia.gov>
19: Note the nice multigrid convergence despite the fact it is only using
20: peicewise constant interpolation/restriction. This is because cell-centered multigrid
21: does not need the same rule:
23: polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE
25: that vertex based multigrid needs.
26: */
28: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
30: #include <petscdm.h>
31: #include <petscdmda.h>
32: #include <petscksp.h>
34: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
35: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
37: typedef enum {DIRICHLET, NEUMANN} BCType;
39: typedef struct {
40: PetscScalar nu;
41: BCType bcType;
42: } UserContext;
44: int main(int argc,char **argv)
45: {
46: KSP ksp;
47: DM da;
48: UserContext user;
49: const char *bcTypes[2] = {"dirichlet","neumann"};
51: PetscInt bc;
53: PetscInitialize(&argc,&argv,(char*)0,help);
54: KSPCreate(PETSC_COMM_WORLD,&ksp);
55: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
56: DMSetFromOptions(da);
57: DMSetUp(da);
58: DMDASetInterpolationType(da, DMDA_Q0);
60: KSPSetDM(ksp,da);
62: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
63: user.nu = 0.1;
64: PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
65: bc = (PetscInt)NEUMANN;
66: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
67: user.bcType = (BCType)bc;
68: PetscOptionsEnd();
70: KSPSetComputeRHS(ksp,ComputeRHS,&user);
71: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
72: KSPSetFromOptions(ksp);
73: KSPSolve(ksp,NULL,NULL);
74: KSPDestroy(&ksp);
75: DMDestroy(&da);
76: PetscFinalize();
77: return 0;
78: }
80: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
81: {
82: UserContext *user = (UserContext*)ctx;
83: PetscInt i,j,mx,my,xm,ym,xs,ys;
84: PetscScalar Hx,Hy;
85: PetscScalar **array;
86: DM da;
89: KSPGetDM(ksp,&da);
90: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
91: Hx = 1.0 / (PetscReal)(mx);
92: Hy = 1.0 / (PetscReal)(my);
93: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
94: DMDAVecGetArray(da, b, &array);
95: for (j=ys; j<ys+ym; j++) {
96: for (i=xs; i<xs+xm; i++) {
97: array[j][i] = PetscExpScalar(-(((PetscReal)i+0.5)*Hx)*(((PetscReal)i+0.5)*Hx)/user->nu)*PetscExpScalar(-(((PetscReal)j+0.5)*Hy)*(((PetscReal)j+0.5)*Hy)/user->nu)*Hx*Hy;
98: }
99: }
100: DMDAVecRestoreArray(da, b, &array);
101: VecAssemblyBegin(b);
102: VecAssemblyEnd(b);
104: /* force right hand side to be consistent for singular matrix */
105: /* note this is really a hack, normally the model would provide you with a consistent right handside */
106: if (user->bcType == NEUMANN) {
107: MatNullSpace nullspace;
109: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
110: MatNullSpaceRemove(nullspace,b);
111: MatNullSpaceDestroy(&nullspace);
112: }
113: return 0;
114: }
116: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
117: {
118: UserContext *user = (UserContext*)ctx;
119: PetscInt i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
120: PetscScalar v[5],Hx,Hy,HydHx,HxdHy;
121: MatStencil row, col[5];
122: DM da;
125: KSPGetDM(ksp,&da);
126: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
127: Hx = 1.0 / (PetscReal)(mx);
128: Hy = 1.0 / (PetscReal)(my);
129: HxdHy = Hx/Hy;
130: HydHx = Hy/Hx;
131: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
132: for (j=ys; j<ys+ym; j++) {
133: for (i=xs; i<xs+xm; i++) {
134: row.i = i; row.j = j;
135: if (i==0 || j==0 || i==mx-1 || j==my-1) {
136: if (user->bcType == DIRICHLET) {
137: v[0] = 2.0*(HxdHy + HydHx);
138: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
139: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !");
140: } else if (user->bcType == NEUMANN) {
141: num = 0; numi=0; numj=0;
142: if (j!=0) {
143: v[num] = -HxdHy;
144: col[num].i = i;
145: col[num].j = j-1;
146: num++; numj++;
147: }
148: if (i!=0) {
149: v[num] = -HydHx;
150: col[num].i = i-1;
151: col[num].j = j;
152: num++; numi++;
153: }
154: if (i!=mx-1) {
155: v[num] = -HydHx;
156: col[num].i = i+1;
157: col[num].j = j;
158: num++; numi++;
159: }
160: if (j!=my-1) {
161: v[num] = -HxdHy;
162: col[num].i = i;
163: col[num].j = j+1;
164: num++; numj++;
165: }
166: v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i; col[num].j = j;
167: num++;
168: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
169: }
170: } else {
171: v[0] = -HxdHy; col[0].i = i; col[0].j = j-1;
172: v[1] = -HydHx; col[1].i = i-1; col[1].j = j;
173: v[2] = 2.0*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
174: v[3] = -HydHx; col[3].i = i+1; col[3].j = j;
175: v[4] = -HxdHy; col[4].i = i; col[4].j = j+1;
176: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
177: }
178: }
179: }
180: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
181: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
182: if (user->bcType == NEUMANN) {
183: MatNullSpace nullspace;
185: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
186: MatSetNullSpace(J,nullspace);
187: MatNullSpaceDestroy(&nullspace);
188: }
189: return 0;
190: }
192: /*TEST
194: test:
195: 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
197: TEST*/