Actual source code: ex32.c
1: /*T
2: Concepts: KSP^solving a system of linear equations
3: Concepts: KSP^Laplacian, 2d
4: Processors: n
5: T*/
7: /*
8: Laplacian in 2D. Modeled by the partial differential equation
10: div grad u = f, 0 < x,y < 1,
12: with forcing function
14: f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}
16: with pure Neumann boundary conditions
18: The functions are cell-centered
20: This uses multigrid to solve the linear system
22: Contributed by Andrei Draganescu <aidraga@sandia.gov>
24: Note the nice multigrid convergence despite the fact it is only using
25: peicewise constant interpolation/restriction. This is because cell-centered multigrid
26: does not need the same rule:
28: polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE
30: that vertex based multigrid needs.
31: */
33: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
35: #include <petscdm.h>
36: #include <petscdmda.h>
37: #include <petscksp.h>
39: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
40: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
42: typedef enum {DIRICHLET, NEUMANN} BCType;
44: typedef struct {
45: PetscScalar nu;
46: BCType bcType;
47: } UserContext;
49: int main(int argc,char **argv)
50: {
51: KSP ksp;
52: DM da;
53: UserContext user;
54: const char *bcTypes[2] = {"dirichlet","neumann"};
56: PetscInt bc;
58: PetscInitialize(&argc,&argv,(char*)0,help);
59: KSPCreate(PETSC_COMM_WORLD,&ksp);
60: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
61: DMSetFromOptions(da);
62: DMSetUp(da);
63: DMDASetInterpolationType(da, DMDA_Q0);
65: KSPSetDM(ksp,da);
67: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
68: user.nu = 0.1;
69: PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
70: bc = (PetscInt)NEUMANN;
71: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
72: user.bcType = (BCType)bc;
73: PetscOptionsEnd();
75: KSPSetComputeRHS(ksp,ComputeRHS,&user);
76: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
77: KSPSetFromOptions(ksp);
78: KSPSolve(ksp,NULL,NULL);
79: KSPDestroy(&ksp);
80: DMDestroy(&da);
81: PetscFinalize();
82: return 0;
83: }
85: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
86: {
87: UserContext *user = (UserContext*)ctx;
88: PetscInt i,j,mx,my,xm,ym,xs,ys;
89: PetscScalar Hx,Hy;
90: PetscScalar **array;
91: DM da;
94: KSPGetDM(ksp,&da);
95: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
96: Hx = 1.0 / (PetscReal)(mx);
97: Hy = 1.0 / (PetscReal)(my);
98: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
99: DMDAVecGetArray(da, b, &array);
100: for (j=ys; j<ys+ym; j++) {
101: for (i=xs; i<xs+xm; i++) {
102: 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;
103: }
104: }
105: DMDAVecRestoreArray(da, b, &array);
106: VecAssemblyBegin(b);
107: VecAssemblyEnd(b);
109: /* force right hand side to be consistent for singular matrix */
110: /* note this is really a hack, normally the model would provide you with a consistent right handside */
111: if (user->bcType == NEUMANN) {
112: MatNullSpace nullspace;
114: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
115: MatNullSpaceRemove(nullspace,b);
116: MatNullSpaceDestroy(&nullspace);
117: }
118: return 0;
119: }
121: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
122: {
123: UserContext *user = (UserContext*)ctx;
124: PetscInt i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
125: PetscScalar v[5],Hx,Hy,HydHx,HxdHy;
126: MatStencil row, col[5];
127: DM da;
130: KSPGetDM(ksp,&da);
131: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
132: Hx = 1.0 / (PetscReal)(mx);
133: Hy = 1.0 / (PetscReal)(my);
134: HxdHy = Hx/Hy;
135: HydHx = Hy/Hx;
136: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
137: for (j=ys; j<ys+ym; j++) {
138: for (i=xs; i<xs+xm; i++) {
139: row.i = i; row.j = j;
140: if (i==0 || j==0 || i==mx-1 || j==my-1) {
141: if (user->bcType == DIRICHLET) {
142: v[0] = 2.0*(HxdHy + HydHx);
143: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
144: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !");
145: } else if (user->bcType == NEUMANN) {
146: num = 0; numi=0; numj=0;
147: if (j!=0) {
148: v[num] = -HxdHy;
149: col[num].i = i;
150: col[num].j = j-1;
151: num++; numj++;
152: }
153: if (i!=0) {
154: v[num] = -HydHx;
155: col[num].i = i-1;
156: col[num].j = j;
157: num++; numi++;
158: }
159: if (i!=mx-1) {
160: v[num] = -HydHx;
161: col[num].i = i+1;
162: col[num].j = j;
163: num++; numi++;
164: }
165: if (j!=my-1) {
166: v[num] = -HxdHy;
167: col[num].i = i;
168: col[num].j = j+1;
169: num++; numj++;
170: }
171: v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i; col[num].j = j;
172: num++;
173: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
174: }
175: } else {
176: v[0] = -HxdHy; col[0].i = i; col[0].j = j-1;
177: v[1] = -HydHx; col[1].i = i-1; col[1].j = j;
178: v[2] = 2.0*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
179: v[3] = -HydHx; col[3].i = i+1; col[3].j = j;
180: v[4] = -HxdHy; col[4].i = i; col[4].j = j+1;
181: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
182: }
183: }
184: }
185: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
186: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
187: if (user->bcType == NEUMANN) {
188: MatNullSpace nullspace;
190: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
191: MatSetNullSpace(J,nullspace);
192: MatNullSpaceDestroy(&nullspace);
193: }
194: return 0;
195: }
197: /*TEST
199: test:
200: 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
202: TEST*/