Actual source code: ex32.c
petsc-3.7.5 2017-01-01
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;
51: int main(int argc,char **argv)
52: {
53: KSP ksp;
54: DM da;
55: UserContext user;
56: const char *bcTypes[2] = {"dirichlet","neumann"};
58: PetscInt bc;
60: PetscInitialize(&argc,&argv,(char*)0,help);
62: KSPCreate(PETSC_COMM_WORLD,&ksp);
63: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
64: DMDASetInterpolationType(da, DMDA_Q0);
66: KSPSetDM(ksp,da);
69: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
70: user.nu = 0.1;
71: PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
72: bc = (PetscInt)NEUMANN;
73: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
74: user.bcType = (BCType)bc;
75: PetscOptionsEnd();
77: KSPSetComputeRHS(ksp,ComputeRHS,&user);
78: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
79: KSPSetFromOptions(ksp);
81: KSPSolve(ksp,NULL,NULL);
83: KSPDestroy(&ksp);
84: DMDestroy(&da);
85: PetscFinalize();
86: return 0;
87: }
91: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
92: {
93: UserContext *user = (UserContext*)ctx;
95: PetscInt i,j,mx,my,xm,ym,xs,ys;
96: PetscScalar Hx,Hy;
97: PetscScalar **array;
98: DM da;
101: KSPGetDM(ksp,&da);
102: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
103: Hx = 1.0 / (PetscReal)(mx);
104: Hy = 1.0 / (PetscReal)(my);
105: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
106: DMDAVecGetArray(da, b, &array);
107: for (j=ys; j<ys+ym; j++) {
108: for (i=xs; i<xs+xm; i++) {
109: 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;
110: }
111: }
112: DMDAVecRestoreArray(da, b, &array);
113: VecAssemblyBegin(b);
114: VecAssemblyEnd(b);
116: /* force right hand side to be consistent for singular matrix */
117: /* note this is really a hack, normally the model would provide you with a consistent right handside */
118: if (user->bcType == NEUMANN) {
119: MatNullSpace nullspace;
121: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
122: MatNullSpaceRemove(nullspace,b);
123: MatNullSpaceDestroy(&nullspace);
124: }
125: return(0);
126: }
131: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
132: {
133: UserContext *user = (UserContext*)ctx;
135: PetscInt i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
136: PetscScalar v[5],Hx,Hy,HydHx,HxdHy;
137: MatStencil row, col[5];
138: DM da;
141: KSPGetDM(ksp,&da);
142: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
143: Hx = 1.0 / (PetscReal)(mx);
144: Hy = 1.0 / (PetscReal)(my);
145: HxdHy = Hx/Hy;
146: HydHx = Hy/Hx;
147: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
148: for (j=ys; j<ys+ym; j++) {
149: for (i=xs; i<xs+xm; i++) {
150: row.i = i; row.j = j;
151: if (i==0 || j==0 || i==mx-1 || j==my-1) {
152: if (user->bcType == DIRICHLET) {
153: v[0] = 2.0*(HxdHy + HydHx);
154: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
155: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n");
156: } else if (user->bcType == NEUMANN) {
157: num = 0; numi=0; numj=0;
158: if (j!=0) {
159: v[num] = -HxdHy;
160: col[num].i = i;
161: col[num].j = j-1;
162: num++; numj++;
163: }
164: if (i!=0) {
165: v[num] = -HydHx;
166: col[num].i = i-1;
167: col[num].j = j;
168: num++; numi++;
169: }
170: if (i!=mx-1) {
171: v[num] = -HydHx;
172: col[num].i = i+1;
173: col[num].j = j;
174: num++; numi++;
175: }
176: if (j!=my-1) {
177: v[num] = -HxdHy;
178: col[num].i = i;
179: col[num].j = j+1;
180: num++; numj++;
181: }
182: v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i; col[num].j = j;
183: num++;
184: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
185: }
186: } else {
187: v[0] = -HxdHy; col[0].i = i; col[0].j = j-1;
188: v[1] = -HydHx; col[1].i = i-1; col[1].j = j;
189: v[2] = 2.0*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
190: v[3] = -HydHx; col[3].i = i+1; col[3].j = j;
191: v[4] = -HxdHy; col[4].i = i; col[4].j = j+1;
192: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
193: }
194: }
195: }
196: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
197: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
198: if (user->bcType == NEUMANN) {
199: MatNullSpace nullspace;
201: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
202: MatSetNullSpace(J,nullspace);
203: MatNullSpaceDestroy(&nullspace);
204: }
205: return(0);
206: }