Actual source code: ex29.c
petsc-3.14.0 2020-09-29
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 <petscdm.h>
30: #include <petscdmda.h>
31: #include <petscksp.h>
33: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
34: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
36: typedef enum {DIRICHLET, NEUMANN} BCType;
38: typedef struct {
39: PetscReal rho;
40: PetscReal nu;
41: BCType bcType;
42: } UserContext;
44: int main(int argc,char **argv)
45: {
46: KSP ksp;
47: DM da;
48: UserContext user;
49: const char *bcTypes[2] = {"dirichlet","neumann"};
51: PetscInt bc;
52: Vec b,x;
53: PetscBool testsolver = PETSC_FALSE;
55: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
56: KSPCreate(PETSC_COMM_WORLD,&ksp);
57: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
58: DMSetFromOptions(da);
59: DMSetUp(da);
60: DMDASetUniformCoordinates(da,0,1,0,1,0,0);
61: DMDASetFieldName(da,0,"Pressure");
63: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
64: user.rho = 1.0;
65: PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);
66: user.nu = 0.1;
67: PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);
68: bc = (PetscInt)DIRICHLET;
69: PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
70: user.bcType = (BCType)bc;
71: PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL);
72: PetscOptionsEnd();
74: KSPSetComputeRHS(ksp,ComputeRHS,&user);
75: KSPSetComputeOperators(ksp,ComputeMatrix,&user);
76: KSPSetDM(ksp,da);
77: KSPSetFromOptions(ksp);
78: KSPSetUp(ksp);
79: KSPSolve(ksp,NULL,NULL);
81: if (testsolver) {
82: KSPGetSolution(ksp,&x);
83: KSPGetRhs(ksp,&b);
84: KSPSetDMActive(ksp,PETSC_FALSE);
85: KSPSolve(ksp,b,x);
86: {
87: #if defined(PETSC_USE_LOG)
88: PetscLogStage stage;
89: #endif
90: PetscInt i,n = 20;
92: PetscLogStageRegister("Solve only",&stage);
93: PetscLogStagePush(stage);
94: for (i=0; i<n; i++) {
95: KSPSolve(ksp,b,x);
96: }
97: PetscLogStagePop();
98: }
99: }
101: DMDestroy(&da);
102: KSPDestroy(&ksp);
103: PetscFinalize();
104: return ierr;
105: }
107: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
108: {
109: UserContext *user = (UserContext*)ctx;
111: PetscInt i,j,mx,my,xm,ym,xs,ys;
112: PetscScalar Hx,Hy;
113: PetscScalar **array;
114: DM da;
117: KSPGetDM(ksp,&da);
118: DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
119: Hx = 1.0 / (PetscReal)(mx-1);
120: Hy = 1.0 / (PetscReal)(my-1);
121: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
122: DMDAVecGetArray(da, b, &array);
123: for (j=ys; j<ys+ym; j++) {
124: for (i=xs; i<xs+xm; i++) {
125: array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
126: }
127: }
128: DMDAVecRestoreArray(da, b, &array);
129: VecAssemblyBegin(b);
130: VecAssemblyEnd(b);
132: /* force right hand side to be consistent for singular matrix */
133: /* note this is really a hack, normally the model would provide you with a consistent right handside */
134: if (user->bcType == NEUMANN) {
135: MatNullSpace nullspace;
137: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
138: MatNullSpaceRemove(nullspace,b);
139: MatNullSpaceDestroy(&nullspace);
140: }
141: return(0);
142: }
145: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
146: {
148: if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
149: *rho = centerRho;
150: } else {
151: *rho = 1.0;
152: }
153: return(0);
154: }
156: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
157: {
158: UserContext *user = (UserContext*)ctx;
159: PetscReal centerRho;
161: PetscInt i,j,mx,my,xm,ym,xs,ys;
162: PetscScalar v[5];
163: PetscReal Hx,Hy,HydHx,HxdHy,rho;
164: MatStencil row, col[5];
165: DM da;
166: PetscBool check_matis = PETSC_FALSE;
169: KSPGetDM(ksp,&da);
170: centerRho = user->rho;
171: DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
172: Hx = 1.0 / (PetscReal)(mx-1);
173: Hy = 1.0 / (PetscReal)(my-1);
174: HxdHy = Hx/Hy;
175: HydHx = Hy/Hx;
176: DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
177: for (j=ys; j<ys+ym; j++) {
178: for (i=xs; i<xs+xm; i++) {
179: row.i = i; row.j = j;
180: ComputeRho(i, j, mx, my, centerRho, &rho);
181: if (i==0 || j==0 || i==mx-1 || j==my-1) {
182: if (user->bcType == DIRICHLET) {
183: v[0] = 2.0*rho*(HxdHy + HydHx);
184: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
185: } else if (user->bcType == NEUMANN) {
186: PetscInt numx = 0, numy = 0, num = 0;
187: if (j!=0) {
188: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
189: numy++; num++;
190: }
191: if (i!=0) {
192: v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
193: numx++; num++;
194: }
195: if (i!=mx-1) {
196: v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
197: numx++; num++;
198: }
199: if (j!=my-1) {
200: v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
201: numy++; num++;
202: }
203: v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j;
204: num++;
205: MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
206: }
207: } else {
208: v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
209: v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
210: v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
211: v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
212: v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
213: MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
214: }
215: }
216: }
217: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
218: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
219: MatViewFromOptions(jac,NULL,"-view_mat");
220: PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
221: if (check_matis) {
222: void (*f)(void);
223: Mat J2;
224: MatType jtype;
225: PetscReal nrm;
227: MatGetType(jac,&jtype);
228: MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
229: MatViewFromOptions(J2,NULL,"-view_conv");
230: MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
231: MatGetOperation(jac,MATOP_VIEW,&f);
232: MatSetOperation(J2,MATOP_VIEW,f);
233: MatSetDM(J2,da);
234: MatViewFromOptions(J2,NULL,"-view_conv_assembled");
235: MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
236: MatNorm(J2,NORM_FROBENIUS,&nrm);
237: PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
238: MatViewFromOptions(J2,NULL,"-view_conv_err");
239: MatDestroy(&J2);
240: }
241: if (user->bcType == NEUMANN) {
242: MatNullSpace nullspace;
244: MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
245: MatSetNullSpace(J,nullspace);
246: MatNullSpaceDestroy(&nullspace);
247: }
248: return(0);
249: }
252: /*TEST
254: test:
255: args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3
257: test:
258: suffix: 2
259: args: -bc_type neumann -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -mg_coarse_pc_factor_shift_type nonzero
260: requires: !single
262: test:
263: suffix: telescope
264: nsize: 4
265: args: -ksp_monitor_short -da_grid_x 257 -da_grid_y 257 -pc_type mg -pc_mg_galerkin pmat -pc_mg_levels 4 -ksp_type richardson -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type chebyshev -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_coarse_pc_telescope_reduction_factor 4
267: test:
268: suffix: 3
269: args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi
271: test:
272: suffix: 4
273: args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_ksp_max_it 3 -mg_levels_ksp_max_it 4
275: test:
276: suffix: 5
277: nsize: 2
278: requires: hypre !complex
279: args: -pc_type mg -da_refine 2 -ksp_monitor -matptap_via hypre -pc_mg_galerkin both
281: TEST*/