Actual source code: ex56.c
petsc-3.12.2 2019-11-22
2: /*
3: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
5: -div \rho grad u = f, 0 < x,y < 1,
7: with forcing function
9: f = e^{-x^2/\nu} e^{-y^2/\nu}
11: with Dirichlet boundary conditions
13: u = f(x,y) for x = 0, x = 1, y = 0, y = 1
15: or pure Neumman boundary conditions
17: This uses multigrid to solve the linear system
18: */
20: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
22: #include <petscdm.h>
23: #include <petscdmda.h>
24: #include <petscksp.h>
26: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
27: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
29: typedef enum {DIRICHLET, NEUMANN} BCType;
31: typedef struct {
32: PetscReal rho;
33: PetscReal nu;
34: BCType bcType;
35: } UserContext;
37: int main(int argc,char **argv)
38: {
39: KSP ksp;
40: DM da;
41: UserContext user;
43: PetscInt bc,i, m,n,its=100;
44: Vec x,y;
45: PC pc;
46: Mat C;
47: PetscMPIInt srank;
48: PetscScalar *array;
49: #if defined(PETSC_USE_LOG)
50: PetscLogStage stages[2];
51: #endif
53: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
54: MPI_Comm_rank(PETSC_COMM_WORLD,&srank);
56: PetscLogStageRegister("Setup",&stages[0]);
57: PetscLogStageRegister("MatMult MPI",&stages[1]);
59: KSPCreate(PETSC_COMM_WORLD,&ksp);
60: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
61: DMSetFromOptions(da);
62: DMSetUp(da);
63: DMDASetUniformCoordinates(da,0,1,0,1,0,0);
64: DMDASetFieldName(da,0,"Pressure");
66: user.rho = 1.0;
67: user.nu = 0.1;
68: bc = (PetscInt)DIRICHLET;
69: user.bcType = (BCType)bc;
71: KSPSetComputeRHS(ksp,ComputeRHS,&user);
72: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
73: KSPSetDM(ksp,da);
74: KSPSetFromOptions(ksp);
75: KSPSetUp(ksp);
77: KSPGetPC(ksp,&pc);
78: PCGetOperators(pc,&C,NULL);
80: /* Create x and y with shared memory */
81: /*-----------------------------------*/
82: MatGetLocalSize(C,&m,&n);
83: VecCreate(PETSC_COMM_WORLD,&x);
84: VecSetSizes(x,n,PETSC_DECIDE);
85: VecSetType(x,VECNODE);
86: VecSetFromOptions(x);
88: VecGetArray(x,&array);
89: for (i=0; i<n; i++) {
90: array[i] = (PetscScalar)(srank+1);
91: }
92: VecRestoreArray(x,&array);
94: VecCreate(PETSC_COMM_WORLD,&y);
95: VecSetSizes(y,m,PETSC_DECIDE);
96: VecSetType(y,VECNODE);
97: VecSetFromOptions(y);
98: VecSet(y,0.0);
100: /* Compute y = C*x */
101: /*-----------------*/
102: MPI_Barrier(PETSC_COMM_WORLD);
103: PetscLogStagePush(stages[1]);
104: for (i=0; i<its; i++) {
105: MatMult(C,x,y);
106: }
107: PetscLogStagePop();
109: /* Free spaces */
110: VecDestroy(&x);
111: VecDestroy(&y);
112: DMDestroy(&da);
113: KSPDestroy(&ksp);
114: PetscFinalize();
115: return ierr;
116: }
118: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
119: {
120: UserContext *user = (UserContext*)ctx;
122: PetscInt i,j,mx,my,xm,ym,xs,ys;
123: PetscScalar Hx,Hy;
124: PetscScalar **array;
125: DM da;
128: KSPGetDM(ksp,&da);
129: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
130: Hx = 1.0 / (PetscReal)(mx-1);
131: Hy = 1.0 / (PetscReal)(my-1);
132: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
133: DMDAVecGetArray(da, b, &array);
134: for (j=ys; j<ys+ym; j++) {
135: for (i=xs; i<xs+xm; i++) {
136: array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
137: }
138: }
139: DMDAVecRestoreArray(da, b, &array);
140: VecAssemblyBegin(b);
141: VecAssemblyEnd(b);
143: /* force right hand side to be consistent for singular matrix */
144: /* note this is really a hack, normally the model would provide you with a consistent right handside */
145: if (user->bcType == NEUMANN) {
146: MatNullSpace nullspace;
148: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
149: MatNullSpaceRemove(nullspace,b);
150: MatNullSpaceDestroy(&nullspace);
151: }
152: return(0);
153: }
155: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
156: {
158: if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
159: *rho = centerRho;
160: } else {
161: *rho = 1.0;
162: }
163: return(0);
164: }
166: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
167: {
168: UserContext *user = (UserContext*)ctx;
169: PetscReal centerRho;
171: PetscInt i,j,mx,my,xm,ym,xs,ys;
172: PetscScalar v[5];
173: PetscReal Hx,Hy,HydHx,HxdHy,rho;
174: MatStencil row, col[5];
175: DM da;
178: KSPGetDM(ksp,&da);
179: centerRho = user->rho;
180: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
181: Hx = 1.0 / (PetscReal)(mx-1);
182: Hy = 1.0 / (PetscReal)(my-1);
183: HxdHy = Hx/Hy;
184: HydHx = Hy/Hx;
185: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
186: for (j=ys; j<ys+ym; j++) {
187: for (i=xs; i<xs+xm; i++) {
188: row.i = i; row.j = j;
189: ComputeRho(i, j, mx, my, centerRho, &rho);
190: if (i==0 || j==0 || i==mx-1 || j==my-1) {
191: if (user->bcType == DIRICHLET) {
192: v[0] = 2.0*rho*(HxdHy + HydHx);
193: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
194: } else if (user->bcType == NEUMANN) {
195: PetscInt numx = 0, numy = 0, num = 0;
196: if (j!=0) {
197: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
198: numy++; num++;
199: }
200: if (i!=0) {
201: v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
202: numx++; num++;
203: }
204: if (i!=mx-1) {
205: v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
206: numx++; num++;
207: }
208: if (j!=my-1) {
209: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
210: numy++; num++;
211: }
212: v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j;
213: num++;
214: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
215: }
216: } else {
217: v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
218: v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
219: v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
220: v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
221: v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
222: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
223: }
224: }
225: }
226: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
227: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
228: if (user->bcType == NEUMANN) {
229: MatNullSpace nullspace;
231: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
232: MatSetNullSpace(J,nullspace);
233: MatNullSpaceDestroy(&nullspace);
234: }
235: return(0);
236: }
238: /*TEST
240: build:
241: test:
243: TEST*/