Actual source code: ex32.c

petsc-master 2017-06-21
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  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;

 49: int main(int argc,char **argv)
 50: {
 51:   KSP            ksp;
 52:   DM             da;
 53:   UserContext    user;
 54:   const char     *bcTypes[2] = {"dirichlet","neumann"};
 56:   PetscInt       bc;

 58:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 59:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 60:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 61:   DMSetFromOptions(da);
 62:   DMSetUp(da);
 63:   DMDASetInterpolationType(da, DMDA_Q0);

 65:   KSPSetDM(ksp,da);


 68:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
 69:   user.nu     = 0.1;
 70:   PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
 71:   bc          = (PetscInt)NEUMANN;
 72:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
 73:   user.bcType = (BCType)bc;
 74:   PetscOptionsEnd();

 76:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
 77:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
 78:   KSPSetFromOptions(ksp);
 79:   KSPSolve(ksp,NULL,NULL);
 80:   KSPDestroy(&ksp);
 81:   DMDestroy(&da);
 82:   PetscFinalize();
 83:   return ierr;
 84: }

 86: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
 87: {
 88:   UserContext    *user = (UserContext*)ctx;
 90:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
 91:   PetscScalar    Hx,Hy;
 92:   PetscScalar    **array;
 93:   DM             da;

 96:   KSPGetDM(ksp,&da);
 97:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
 98:   Hx   = 1.0 / (PetscReal)(mx);
 99:   Hy   = 1.0 / (PetscReal)(my);
100:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
101:   DMDAVecGetArray(da, b, &array);
102:   for (j=ys; j<ys+ym; j++) {
103:     for (i=xs; i<xs+xm; i++) {
104:       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;
105:     }
106:   }
107:   DMDAVecRestoreArray(da, b, &array);
108:   VecAssemblyBegin(b);
109:   VecAssemblyEnd(b);

111:   /* force right hand side to be consistent for singular matrix */
112:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
113:   if (user->bcType == NEUMANN) {
114:     MatNullSpace nullspace;

116:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
117:     MatNullSpaceRemove(nullspace,b);
118:     MatNullSpaceDestroy(&nullspace);
119:   }
120:   return(0);
121: }


124: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
125: {
126:   UserContext    *user = (UserContext*)ctx;
128:   PetscInt       i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
129:   PetscScalar    v[5],Hx,Hy,HydHx,HxdHy;
130:   MatStencil     row, col[5];
131:   DM             da;

134:   KSPGetDM(ksp,&da);
135:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
136:   Hx    = 1.0 / (PetscReal)(mx);
137:   Hy    = 1.0 / (PetscReal)(my);
138:   HxdHy = Hx/Hy;
139:   HydHx = Hy/Hx;
140:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
141:   for (j=ys; j<ys+ym; j++) {
142:     for (i=xs; i<xs+xm; i++) {
143:       row.i = i; row.j = j;
144:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
145:         if (user->bcType == DIRICHLET) {
146:           v[0] = 2.0*(HxdHy + HydHx);
147:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
148:           SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n");
149:         } else if (user->bcType == NEUMANN) {
150:           num = 0; numi=0; numj=0;
151:           if (j!=0) {
152:             v[num] = -HxdHy;
153:             col[num].i = i;
154:             col[num].j = j-1;
155:             num++; numj++;
156:           }
157:           if (i!=0) {
158:             v[num]     = -HydHx;
159:             col[num].i = i-1;
160:             col[num].j = j;
161:             num++; numi++;
162:           }
163:           if (i!=mx-1) {
164:             v[num]     = -HydHx;
165:             col[num].i = i+1;
166:             col[num].j = j;
167:             num++; numi++;
168:           }
169:           if (j!=my-1) {
170:             v[num]     = -HxdHy;
171:             col[num].i = i;
172:             col[num].j = j+1;
173:             num++; numj++;
174:           }
175:           v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i;   col[num].j = j;
176:           num++;
177:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
178:         }
179:       } else {
180:         v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
181:         v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
182:         v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
183:         v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
184:         v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
185:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
186:       }
187:     }
188:   }
189:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
190:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
191:   if (user->bcType == NEUMANN) {
192:     MatNullSpace nullspace;

194:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
195:     MatSetNullSpace(J,nullspace);
196:     MatNullSpaceDestroy(&nullspace);
197:   }
198:   return(0);
199: }