Actual source code: ex29.c
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^{-(1 - x)^2/\nu} e^{-(1 - 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 petscda.h
30: #include petscksp.h
31: #include petscmg.h
32: #include petscdmmg.h
38: typedef enum {DIRICHLET, NEUMANN} BCType;
40: typedef struct {
41: PetscScalar nu;
42: BCType bcType;
43: } UserContext;
47: int main(int argc,char **argv)
48: {
49: DMMG *dmmg;
50: DA da;
51: UserContext user;
52: PetscReal norm;
53: const char *bcTypes[2] = {"dirichlet","neumann"};
55: PetscInt l,bc;
57: PetscInitialize(&argc,&argv,(char *)0,help);
59: DMMGCreate(PETSC_COMM_WORLD,3,PETSC_NULL,&dmmg);
60: DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-3,-3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
61: DMMGSetDM(dmmg,(DM)da);
62: DADestroy(da);
63: for (l = 0; l < DMMGGetLevels(dmmg); l++) {
64: DMMGSetUser(dmmg,l,&user);
65: }
67: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMMG");
68: user.nu = 0.1;
69: PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, PETSC_NULL);
70: bc = (PetscInt)DIRICHLET;
71: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,PETSC_NULL);
72: user.bcType = (BCType)bc;
73: PetscOptionsEnd();
75: DMMGSetKSP(dmmg,ComputeRHS,ComputeJacobian);
76: if (user.bcType == NEUMANN) {
77: DMMGSetNullSpace(dmmg,PETSC_TRUE,0,PETSC_NULL);
78: }
80: DMMGSolve(dmmg);
82: MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
83: VecAXPY(DMMGGetr(dmmg),-1.0,DMMGGetRHS(dmmg));
84: VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
85: /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm); */
86: VecAssemblyBegin(DMMGGetx(dmmg));
87: VecAssemblyEnd(DMMGGetx(dmmg));
88: VecView_VTK(DMMGGetRHS(dmmg), "rhs.vtk", bcTypes[user.bcType]);
89: VecView_VTK(DMMGGetx(dmmg), "solution.vtk", bcTypes[user.bcType]);
91: DMMGDestroy(dmmg);
92: PetscFinalize();
94: return 0;
95: }
99: PetscErrorCode ComputeRHS(DMMG dmmg, Vec b)
100: {
101: DA da = (DA)dmmg->dm;
102: UserContext *user = (UserContext *) dmmg->user;
104: PetscInt i,j,mx,my,xm,ym,xs,ys;
105: PetscScalar Hx,Hy;
106: PetscScalar **array;
109: DAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0);
110: Hx = 1.0 / (PetscReal)(mx-1);
111: Hy = 1.0 / (PetscReal)(my-1);
112: DAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
113: DAVecGetArray(da, b, &array);
114: for (j=ys; j<ys+ym; j++){
115: for(i=xs; i<xs+xm; i++){
116: array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
117: }
118: }
119: DAVecRestoreArray(da, b, &array);
120: VecAssemblyBegin(b);
121: VecAssemblyEnd(b);
123: /* force right hand side to be consistent for singular matrix */
124: /* note this is really a hack, normally the model would provide you with a consistent right handside */
125: if (user->bcType == NEUMANN) {
126: MatNullSpace nullspace;
128: KSPGetNullSpace(dmmg->ksp,&nullspace);
129: MatNullSpaceRemove(nullspace,b,PETSC_NULL);
130: }
131: return(0);
132: }
134:
137: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscScalar *rho)
138: {
140: if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
141: *rho = 100.0;
142: } else {
143: *rho = 1.0;
144: }
145: return(0);
146: }
150: PetscErrorCode ComputeJacobian(DMMG dmmg, Mat J,Mat jac)
151: {
152: DA da = (DA) dmmg->dm;
153: UserContext *user = (UserContext *) dmmg->user;
155: PetscInt i,j,mx,my,xm,ym,xs,ys,num;
156: PetscScalar v[5],Hx,Hy,HydHx,HxdHy,rho;
157: MatStencil row, col[5];
160: DAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0);
161: Hx = 1.0 / (PetscReal)(mx-1);
162: Hy = 1.0 / (PetscReal)(my-1);
163: HxdHy = Hx/Hy;
164: HydHx = Hy/Hx;
165: DAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
166: for (j=ys; j<ys+ym; j++){
167: for(i=xs; i<xs+xm; i++){
168: row.i = i; row.j = j;
169: ComputeRho(i, j, mx, my, &rho);
170: if (i==0 || j==0 || i==mx-1 || j==my-1) {
171: if (user->bcType == DIRICHLET) {
172: v[0] = 2.0*rho*(HxdHy + HydHx);
173: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
174: } else if (user->bcType == NEUMANN) {
175: num = 0;
176: if (j!=0) {
177: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
178: num++;
179: }
180: if (i!=0) {
181: v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
182: num++;
183: }
184: if (i!=mx-1) {
185: v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
186: num++;
187: }
188: if (j!=my-1) {
189: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
190: num++;
191: }
192: v[num] = (num/2.0)*rho*(HxdHy + HydHx); col[num].i = i; col[num].j = j;
193: num++;
194: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
195: }
196: } else {
197: v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
198: v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
199: v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
200: v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
201: v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
202: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
203: }
204: }
205: }
206: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
207: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
208: return(0);
209: }
213: PetscErrorCode VecView_VTK(Vec x, const char filename[], const char bcName[])
214: {
215: MPI_Comm comm;
216: DA da;
217: Vec coords;
218: PetscViewer viewer;
219: PetscScalar *array, *values;
220: PetscInt n, N, maxn, mx, my, dof;
221: PetscInt i, p;
222: MPI_Status status;
223: PetscMPIInt rank, size, tag;
224: PetscErrorCode ierr;
227: PetscObjectGetComm((PetscObject) x, &comm);
228: PetscViewerASCIIOpen(comm, filename, &viewer);
230: VecGetSize(x, &N);
231: VecGetLocalSize(x, &n);
232: PetscObjectQuery((PetscObject) x, "DA", (PetscObject *) &da);
233: if (!da) SETERRQ(PETSC_ERR_ARG_WRONG,"Vector not generated from a DA");
235: DAGetInfo(da, 0, &mx, &my, 0,0,0,0, &dof,0,0,0);
237: PetscViewerASCIIPrintf(viewer, "# vtk DataFile Version 2.0\n");
238: PetscViewerASCIIPrintf(viewer, "Inhomogeneous Poisson Equation with %s boundary conditions\n", bcName);
239: PetscViewerASCIIPrintf(viewer, "ASCII\n");
240: /* get coordinates of nodes */
241: DAGetCoordinates(da, &coords);
242: if (!coords) {
243: DASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0);
244: DAGetCoordinates(da, &coords);
245: }
246: PetscViewerASCIIPrintf(viewer, "DATASET RECTILINEAR_GRID\n");
247: PetscViewerASCIIPrintf(viewer, "DIMENSIONS %d %d %d\n", mx, my, 1);
248: VecGetArray(coords, &array);
249: PetscViewerASCIIPrintf(viewer, "X_COORDINATES %d double\n", mx);
250: for(i = 0; i < mx; i++) {
251: PetscViewerASCIIPrintf(viewer, "%G ", PetscRealPart(array[i*2]));
252: }
253: PetscViewerASCIIPrintf(viewer, "\n");
254: PetscViewerASCIIPrintf(viewer, "Y_COORDINATES %d double\n", my);
255: for(i = 0; i < my; i++) {
256: PetscViewerASCIIPrintf(viewer, "%G ", PetscRealPart(array[i*mx*2+1]));
257: }
258: PetscViewerASCIIPrintf(viewer, "\n");
259: PetscViewerASCIIPrintf(viewer, "Z_COORDINATES %d double\n", 1);
260: PetscViewerASCIIPrintf(viewer, "%G\n", 0.0);
261: VecRestoreArray(coords, &array);
262: PetscViewerASCIIPrintf(viewer, "POINT_DATA %d\n", N);
263: PetscViewerASCIIPrintf(viewer, "SCALARS scalars double %d\n", dof);
264: PetscViewerASCIIPrintf(viewer, "LOOKUP_TABLE default\n");
265: VecGetArray(x, &array);
266: /* Determine maximum message to arrive */
267: MPI_Comm_rank(comm, &rank);
268: MPI_Comm_size(comm, &size);
269: MPI_Reduce(&n, &maxn, 1, MPIU_INT, MPI_MAX, 0, comm);
270: tag = ((PetscObject) viewer)->tag;
271: if (!rank) {
272: PetscMalloc((maxn+1) * sizeof(PetscScalar), &values);
273: for(i = 0; i < n; i++) {
274: PetscViewerASCIIPrintf(viewer, "%G\n", PetscRealPart(array[i]));
275: }
276: for(p = 1; p < size; p++) {
277: MPI_Recv(values, (PetscMPIInt) n, MPIU_SCALAR, p, tag, comm, &status);
278: MPI_Get_count(&status, MPIU_SCALAR, &n);
279: for(i = 0; i < n; i++) {
280: PetscViewerASCIIPrintf(viewer, "%G\n", PetscRealPart(array[i]));
281: }
282: }
283: PetscFree(values);
284: } else {
285: MPI_Send(array, n, MPIU_SCALAR, 0, tag, comm);
286: }
287: VecRestoreArray(x, &array);
288: PetscViewerFlush(viewer);
289: PetscViewerDestroy(viewer);
290: return(0);
291: }