Actual source code: ex29.c

petsc-master 2017-10-19
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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: 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;

 54:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 55:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 56:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 57:   DMSetFromOptions(da);
 58:   DMSetUp(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();
 84:   return ierr;
 85: }

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

 97:   KSPGetDM(ksp,&da);
 98:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
 99:   Hx   = 1.0 / (PetscReal)(mx-1);
100:   Hy   = 1.0 / (PetscReal)(my-1);
101:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
102:   DMDAVecGetArray(da, b, &array);
103:   for (j=ys; j<ys+ym; j++) {
104:     for (i=xs; i<xs+xm; i++) {
105:       array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
106:     }
107:   }
108:   DMDAVecRestoreArray(da, b, &array);
109:   VecAssemblyBegin(b);
110:   VecAssemblyEnd(b);

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

117:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
118:     MatNullSpaceRemove(nullspace,b);
119:     MatNullSpaceDestroy(&nullspace);
120:   }
121:   return(0);
122: }


125: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
126: {
128:   if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
129:     *rho = centerRho;
130:   } else {
131:     *rho = 1.0;
132:   }
133:   return(0);
134: }

136: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
137: {
138:   UserContext    *user = (UserContext*)ctx;
139:   PetscReal      centerRho;
141:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
142:   PetscScalar    v[5];
143:   PetscReal      Hx,Hy,HydHx,HxdHy,rho;
144:   MatStencil     row, col[5];
145:   DM             da;

148:   KSPGetDM(ksp,&da);
149:   centerRho = user->rho;
150:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
151:   Hx        = 1.0 / (PetscReal)(mx-1);
152:   Hy        = 1.0 / (PetscReal)(my-1);
153:   HxdHy     = Hx/Hy;
154:   HydHx     = Hy/Hx;
155:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
156:   for (j=ys; j<ys+ym; j++) {
157:     for (i=xs; i<xs+xm; i++) {
158:       row.i = i; row.j = j;
159:       ComputeRho(i, j, mx, my, centerRho, &rho);
160:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
161:         if (user->bcType == DIRICHLET) {
162:           v[0] = 2.0*rho*(HxdHy + HydHx);
163:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
164:         } else if (user->bcType == NEUMANN) {
165:           PetscInt numx = 0, numy = 0, num = 0;
166:           if (j!=0) {
167:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j-1;
168:             numy++; num++;
169:           }
170:           if (i!=0) {
171:             v[num] = -rho*HydHx;              col[num].i = i-1; col[num].j = j;
172:             numx++; num++;
173:           }
174:           if (i!=mx-1) {
175:             v[num] = -rho*HydHx;              col[num].i = i+1; col[num].j = j;
176:             numx++; num++;
177:           }
178:           if (j!=my-1) {
179:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j+1;
180:             numy++; num++;
181:           }
182:           v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i;   col[num].j = j;
183:           num++;
184:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
185:         }
186:       } else {
187:         v[0] = -rho*HxdHy;              col[0].i = i;   col[0].j = j-1;
188:         v[1] = -rho*HydHx;              col[1].i = i-1; col[1].j = j;
189:         v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
190:         v[3] = -rho*HydHx;              col[3].i = i+1; col[3].j = j;
191:         v[4] = -rho*HxdHy;              col[4].i = i;   col[4].j = j+1;
192:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
193:       }
194:     }
195:   }
196:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
197:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
198:   if (user->bcType == NEUMANN) {
199:     MatNullSpace nullspace;

201:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
202:     MatSetNullSpace(J,nullspace);
203:     MatNullSpaceDestroy(&nullspace);
204:   }
205:   return(0);
206: }