Actual source code: ex29.c
petsc-3.4.5 2014-06-29
1: /*T
2: Concepts: KSP^solving a system of linear equations
3: Concepts: KSP^Laplacian, 2d
4: Processors: n
5: T*/
7: /*
8: Added at the request of Marc Garbey.
10: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
12: -div \rho grad u = f, 0 < x,y < 1,
14: with forcing function
16: f = e^{-x^2/\nu} e^{-y^2/\nu}
18: with Dirichlet boundary conditions
20: u = f(x,y) for x = 0, x = 1, y = 0, y = 1
22: or pure Neumman boundary conditions
24: This uses multigrid to solve the linear system
25: */
27: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
29: #include <petscdmda.h>
30: #include <petscksp.h>
32: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,MatStructure*,void*);
33: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
35: typedef enum {DIRICHLET, NEUMANN} BCType;
37: typedef struct {
38: PetscReal rho;
39: PetscReal nu;
40: BCType bcType;
41: } UserContext;
45: int main(int argc,char **argv)
46: {
47: KSP ksp;
48: DM da;
49: UserContext user;
50: const char *bcTypes[2] = {"dirichlet","neumann"};
52: PetscInt bc;
53: Vec b,x;
55: PetscInitialize(&argc,&argv,(char*)0,help);
57: KSPCreate(PETSC_COMM_WORLD,&ksp);
58: DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-3,-3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
59: DMDASetUniformCoordinates(da,0,1,0,1,0,0);
60: DMDASetFieldName(da,0,"Pressure");
62: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
63: user.rho = 1.0;
64: PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);
65: user.nu = 0.1;
66: PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);
67: bc = (PetscInt)DIRICHLET;
68: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
69: user.bcType = (BCType)bc;
70: PetscOptionsEnd();
72: KSPSetComputeRHS(ksp,ComputeRHS,&user);
73: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
74: KSPSetDM(ksp,da);
75: KSPSetFromOptions(ksp);
76: KSPSetUp(ksp);
77: KSPSolve(ksp,NULL,NULL);
78: KSPGetSolution(ksp,&x);
79: KSPGetRhs(ksp,&b);
81: DMDestroy(&da);
82: KSPDestroy(&ksp);
83: PetscFinalize();
85: return 0;
86: }
90: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
91: {
92: UserContext *user = (UserContext*)ctx;
94: PetscInt i,j,mx,my,xm,ym,xs,ys;
95: PetscScalar Hx,Hy;
96: PetscScalar **array;
97: DM da;
100: KSPGetDM(ksp,&da);
101: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
102: Hx = 1.0 / (PetscReal)(mx-1);
103: Hy = 1.0 / (PetscReal)(my-1);
104: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
105: DMDAVecGetArray(da, b, &array);
106: for (j=ys; j<ys+ym; j++) {
107: for (i=xs; i<xs+xm; i++) {
108: array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
109: }
110: }
111: DMDAVecRestoreArray(da, b, &array);
112: VecAssemblyBegin(b);
113: VecAssemblyEnd(b);
115: /* force right hand side to be consistent for singular matrix */
116: /* note this is really a hack, normally the model would provide you with a consistent right handside */
117: if (user->bcType == NEUMANN) {
118: MatNullSpace nullspace;
120: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
121: MatNullSpaceRemove(nullspace,b,NULL);
122: MatNullSpaceDestroy(&nullspace);
123: }
124: return(0);
125: }
130: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
131: {
133: if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
134: *rho = centerRho;
135: } else {
136: *rho = 1.0;
137: }
138: return(0);
139: }
143: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,MatStructure *str,void *ctx)
144: {
145: UserContext *user = (UserContext*)ctx;
146: PetscReal centerRho;
148: PetscInt i,j,mx,my,xm,ym,xs,ys;
149: PetscScalar v[5];
150: PetscReal Hx,Hy,HydHx,HxdHy,rho;
151: MatStencil row, col[5];
152: DM da;
155: KSPGetDM(ksp,&da);
156: centerRho = user->rho;
157: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
158: Hx = 1.0 / (PetscReal)(mx-1);
159: Hy = 1.0 / (PetscReal)(my-1);
160: HxdHy = Hx/Hy;
161: HydHx = Hy/Hx;
162: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
163: for (j=ys; j<ys+ym; j++) {
164: for (i=xs; i<xs+xm; i++) {
165: row.i = i; row.j = j;
166: ComputeRho(i, j, mx, my, centerRho, &rho);
167: if (i==0 || j==0 || i==mx-1 || j==my-1) {
168: if (user->bcType == DIRICHLET) {
169: v[0] = 2.0*rho*(HxdHy + HydHx);
170: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
171: } else if (user->bcType == NEUMANN) {
172: PetscInt numx = 0, numy = 0, num = 0;
173: if (j!=0) {
174: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
175: numy++; num++;
176: }
177: if (i!=0) {
178: v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
179: numx++; num++;
180: }
181: if (i!=mx-1) {
182: v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
183: numx++; num++;
184: }
185: if (j!=my-1) {
186: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
187: numy++; num++;
188: }
189: v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j;
190: num++;
191: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
192: }
193: } else {
194: v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
195: v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
196: v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
197: v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
198: v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
199: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
200: }
201: }
202: }
203: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
204: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
205: if (user->bcType == NEUMANN) {
206: MatNullSpace nullspace;
208: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
209: MatSetNullSpace(jac,nullspace);
210: MatNullSpaceDestroy(&nullspace);
211: }
212: return(0);
213: }