Actual source code: ex56.c

petsc-3.13.4 2020-08-01
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  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*/