Actual source code: ex13.c


  2: static char help[] = "Solves a variable Poisson problem with KSP.\n\n";

  4: /*
  5:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
  6:   automatically includes:
  7:      petscsys.h       - base PETSc routines   petscvec.h - vectors
  8:      petscmat.h - matrices
  9:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 10:      petscviewer.h - viewers               petscpc.h  - preconditioners
 11: */
 12: #include <petscksp.h>

 14: /*
 15:     User-defined context that contains all the data structures used
 16:     in the linear solution process.
 17: */
 18: typedef struct {
 19:   Vec         x,b;       /* solution vector, right-hand-side vector */
 20:   Mat         A;          /* sparse matrix */
 21:   KSP         ksp;       /* linear solver context */
 22:   PetscInt    m,n;       /* grid dimensions */
 23:   PetscScalar hx2,hy2;   /* 1/(m+1)*(m+1) and 1/(n+1)*(n+1) */
 24: } UserCtx;

 26: extern PetscErrorCode UserInitializeLinearSolver(PetscInt,PetscInt,UserCtx*);
 27: extern PetscErrorCode UserFinalizeLinearSolver(UserCtx*);
 28: extern PetscErrorCode UserDoLinearSolver(PetscScalar*,UserCtx *userctx,PetscScalar *b,PetscScalar *x);

 30: int main(int argc,char **args)
 31: {
 32:   UserCtx        userctx;
 33:   PetscInt       m = 6,n = 7,t,tmax = 2,i,Ii,j,N;
 34:   PetscScalar    *userx,*rho,*solution,*userb,hx,hy,x,y;
 35:   PetscReal      enorm;

 37:   /*
 38:      Initialize the PETSc libraries
 39:   */
 40:   PetscInitialize(&argc,&args,(char*)0,help);
 41:   /*
 42:      The next two lines are for testing only; these allow the user to
 43:      decide the grid size at runtime.
 44:   */
 45:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 46:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 48:   /*
 49:      Create the empty sparse matrix and linear solver data structures
 50:   */
 51:   UserInitializeLinearSolver(m,n,&userctx);
 52:   N    = m*n;

 54:   /*
 55:      Allocate arrays to hold the solution to the linear system.
 56:      This is not normally done in PETSc programs, but in this case,
 57:      since we are calling these routines from a non-PETSc program, we
 58:      would like to reuse the data structures from another code. So in
 59:      the context of a larger application these would be provided by
 60:      other (non-PETSc) parts of the application code.
 61:   */
 62:   PetscMalloc1(N,&userx);
 63:   PetscMalloc1(N,&userb);
 64:   PetscMalloc1(N,&solution);

 66:   /*
 67:       Allocate an array to hold the coefficients in the elliptic operator
 68:   */
 69:   PetscMalloc1(N,&rho);

 71:   /*
 72:      Fill up the array rho[] with the function rho(x,y) = x; fill the
 73:      right-hand-side b[] and the solution with a known problem for testing.
 74:   */
 75:   hx = 1.0/(m+1);
 76:   hy = 1.0/(n+1);
 77:   y  = hy;
 78:   Ii = 0;
 79:   for (j=0; j<n; j++) {
 80:     x = hx;
 81:     for (i=0; i<m; i++) {
 82:       rho[Ii]      = x;
 83:       solution[Ii] = PetscSinScalar(2.*PETSC_PI*x)*PetscSinScalar(2.*PETSC_PI*y);
 84:       userb[Ii]    = -2*PETSC_PI*PetscCosScalar(2*PETSC_PI *x)*PetscSinScalar(2*PETSC_PI*y) +
 85:                      8*PETSC_PI*PETSC_PI*x*PetscSinScalar(2*PETSC_PI *x)*PetscSinScalar(2*PETSC_PI*y);
 86:       x += hx;
 87:       Ii++;
 88:     }
 89:     y += hy;
 90:   }

 92:   /*
 93:      Loop over a bunch of timesteps, setting up and solver the linear
 94:      system for each time-step.

 96:      Note this is somewhat artificial. It is intended to demonstrate how
 97:      one may reuse the linear solver stuff in each time-step.
 98:   */
 99:   for (t=0; t<tmax; t++) {
100:     UserDoLinearSolver(rho,&userctx,userb,userx);

102:     /*
103:         Compute error: Note that this could (and usually should) all be done
104:         using the PETSc vector operations. Here we demonstrate using more
105:         standard programming practices to show how they may be mixed with
106:         PETSc.
107:     */
108:     enorm = 0.0;
109:     for (i=0; i<N; i++) enorm += PetscRealPart(PetscConj(solution[i]-userx[i])*(solution[i]-userx[i]));
110:     enorm *= PetscRealPart(hx*hy);
111:     PetscPrintf(PETSC_COMM_WORLD,"m %D n %D error norm %g\n",m,n,(double)enorm);
112:   }

114:   /*
115:      We are all finished solving linear systems, so we clean up the
116:      data structures.
117:   */
118:   PetscFree(rho);
119:   PetscFree(solution);
120:   PetscFree(userx);
121:   PetscFree(userb);
122:   UserFinalizeLinearSolver(&userctx);
123:   PetscFinalize();
124:   return 0;
125: }

127: /* ------------------------------------------------------------------------*/
128: PetscErrorCode UserInitializeLinearSolver(PetscInt m,PetscInt n,UserCtx *userctx)
129: {
130:   PetscInt       N;

132:   /*
133:      Here we assume use of a grid of size m x n, with all points on the
134:      interior of the domain, i.e., we do not include the points corresponding
135:      to homogeneous Dirichlet boundary conditions.  We assume that the domain
136:      is [0,1]x[0,1].
137:   */
138:   userctx->m   = m;
139:   userctx->n   = n;
140:   userctx->hx2 = (m+1)*(m+1);
141:   userctx->hy2 = (n+1)*(n+1);
142:   N            = m*n;

144:   /*
145:      Create the sparse matrix. Preallocate 5 nonzeros per row.
146:   */
147:   MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,5,0,&userctx->A);

149:   /*
150:      Create vectors. Here we create vectors with no memory allocated.
151:      This way, we can use the data structures already in the program
152:      by using VecPlaceArray() subroutine at a later stage.
153:   */
154:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,N,NULL,&userctx->b);
155:   VecDuplicate(userctx->b,&userctx->x);

157:   /*
158:      Create linear solver context. This will be used repeatedly for all
159:      the linear solves needed.
160:   */
161:   KSPCreate(PETSC_COMM_SELF,&userctx->ksp);

163:   return 0;
164: }

166: /*
167:    Solves -div (rho grad psi) = F using finite differences.
168:    rho is a 2-dimensional array of size m by n, stored in Fortran
169:    style by columns. userb is a standard one-dimensional array.
170: */
171: /* ------------------------------------------------------------------------*/
172: PetscErrorCode UserDoLinearSolver(PetscScalar *rho,UserCtx *userctx,PetscScalar *userb,PetscScalar *userx)
173: {
174:   PetscInt       i,j,Ii,J,m = userctx->m,n = userctx->n;
175:   Mat            A = userctx->A;
176:   PC             pc;
177:   PetscScalar    v,hx2 = userctx->hx2,hy2 = userctx->hy2;

179:   /*
180:      This is not the most efficient way of generating the matrix
181:      but let's not worry about it. We should have separate code for
182:      the four corners, each edge and then the interior. Then we won't
183:      have the slow if-tests inside the loop.

185:      Computes the operator
186:              -div rho grad
187:      on an m by n grid with zero Dirichlet boundary conditions. The rho
188:      is assumed to be given on the same grid as the finite difference
189:      stencil is applied.  For a staggered grid, one would have to change
190:      things slightly.
191:   */
192:   Ii = 0;
193:   for (j=0; j<n; j++) {
194:     for (i=0; i<m; i++) {
195:       if (j>0) {
196:         J    = Ii - m;
197:         v    = -.5*(rho[Ii] + rho[J])*hy2;
198:         MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
199:       }
200:       if (j<n-1) {
201:         J    = Ii + m;
202:         v    = -.5*(rho[Ii] + rho[J])*hy2;
203:         MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
204:       }
205:       if (i>0) {
206:         J    = Ii - 1;
207:         v    = -.5*(rho[Ii] + rho[J])*hx2;
208:         MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
209:       }
210:       if (i<m-1) {
211:         J    = Ii + 1;
212:         v    = -.5*(rho[Ii] + rho[J])*hx2;
213:         MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
214:       }
215:       v    = 2.0*rho[Ii]*(hx2+hy2);
216:       MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
217:       Ii++;
218:     }
219:   }

221:   /*
222:      Assemble matrix
223:   */
224:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
225:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

227:   /*
228:      Set operators. Here the matrix that defines the linear system
229:      also serves as the preconditioning matrix. Since all the matrices
230:      will have the same nonzero pattern here, we indicate this so the
231:      linear solvers can take advantage of this.
232:   */
233:   KSPSetOperators(userctx->ksp,A,A);

235:   /*
236:      Set linear solver defaults for this problem (optional).
237:      - Here we set it to use direct LU factorization for the solution
238:   */
239:   KSPGetPC(userctx->ksp,&pc);
240:   PCSetType(pc,PCLU);

242:   /*
243:      Set runtime options, e.g.,
244:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
245:      These options will override those specified above as long as
246:      KSPSetFromOptions() is called _after_ any other customization
247:      routines.

249:      Run the program with the option -help to see all the possible
250:      linear solver options.
251:   */
252:   KSPSetFromOptions(userctx->ksp);

254:   /*
255:      This allows the PETSc linear solvers to compute the solution
256:      directly in the user's array rather than in the PETSc vector.

258:      This is essentially a hack and not highly recommend unless you
259:      are quite comfortable with using PETSc. In general, users should
260:      write their entire application using PETSc vectors rather than
261:      arrays.
262:   */
263:   VecPlaceArray(userctx->x,userx);
264:   VecPlaceArray(userctx->b,userb);

266:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
267:                       Solve the linear system
268:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

270:   KSPSolve(userctx->ksp,userctx->b,userctx->x);

272:   /*
273:     Put back the PETSc array that belongs in the vector xuserctx->x
274:   */
275:   VecResetArray(userctx->x);
276:   VecResetArray(userctx->b);

278:   return 0;
279: }

281: /* ------------------------------------------------------------------------*/
282: PetscErrorCode UserFinalizeLinearSolver(UserCtx *userctx)
283: {
284:   /*
285:      We are all done and don't need to solve any more linear systems, so
286:      we free the work space.  All PETSc objects should be destroyed when
287:      they are no longer needed.
288:   */
289:   KSPDestroy(&userctx->ksp);
290:   VecDestroy(&userctx->x);
291:   VecDestroy(&userctx->b);
292:   MatDestroy(&userctx->A);
293:   return 0;
294: }

296: /*TEST

298:    test:
299:       args: -m 19 -n 20 -ksp_gmres_cgs_refinement_type refine_always

301: TEST*/