Actual source code: ex22.c

petsc-master 2018-04-16
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  2: static const char help[] = "Solves PDE optimization problem using full-space method, interlaces state and adjoint variables.\n\n";


  5:  #include <petscdm.h>
  6:  #include <petscdmda.h>
  7:  #include <petscdmredundant.h>
  8:  #include <petscdmcomposite.h>
  9:  #include <petscpf.h>
 10:  #include <petscsnes.h>
 11:  #include <petsc/private/dmimpl.h>

 13: /*

 15:        w - design variables (what we change to get an optimal solution)
 16:        u - state variables (i.e. the PDE solution)
 17:        lambda - the Lagrange multipliers

 19:             U = (w [u_0 lambda_0 u_1 lambda_1 .....])

 21:        fu, fw, flambda contain the gradient of L(w,u,lambda)

 23:             FU = (fw [fu_0 flambda_0 .....])

 25:        In this example the PDE is
 26:                              Uxx = 2,
 27:                             u(0) = w(0), thus this is the free parameter
 28:                             u(1) = 0
 29:        the function we wish to minimize is
 30:                             \integral u^{2}

 32:        The exact solution for u is given by u(x) = x*x - 1.25*x + .25

 34:        Use the usual centered finite differences.

 36:        Note we treat the problem as non-linear though it happens to be linear

 38:        See ex21.c for the same code, but that does NOT interlaces the u and the lambda

 40:        The vectors u_lambda and fu_lambda contain the u and the lambda interlaced
 41: */

 43: typedef struct {
 44:   PetscViewer u_lambda_viewer;
 45:   PetscViewer fu_lambda_viewer;
 46: } UserCtx;

 48: extern PetscErrorCode ComputeFunction(SNES,Vec,Vec,void*);
 49: extern PetscErrorCode ComputeJacobian_MF(SNES,Vec,Mat,Mat,void*);
 50: extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);

 52: /*
 53:     Uses full multigrid preconditioner with GMRES (with no preconditioner inside the GMRES) as the
 54:   smoother on all levels. This is because (1) in the matrix free case no matrix entries are
 55:   available for doing Jacobi or SOR preconditioning and (2) the explicit matrix case the diagonal
 56:   entry for the control variable is zero which means default SOR will not work.

 58: */
 59: char common_options[] = "-ksp_type fgmres\
 60:                          -snes_grid_sequence 2 \
 61:                          -pc_type mg\
 62:                          -mg_levels_pc_type none \
 63:                          -mg_coarse_pc_type none \
 64:                          -pc_mg_type full \
 65:                          -mg_coarse_ksp_type gmres \
 66:                          -mg_levels_ksp_type gmres \
 67:                          -mg_coarse_ksp_max_it 6 \
 68:                          -mg_levels_ksp_max_it 3";

 70: char matrix_free_options[] = "-mat_mffd_compute_normu no \
 71:                               -mat_mffd_type wp";

 73: extern PetscErrorCode DMCreateMatrix_MF(DM,Mat*);

 75: int main(int argc,char **argv)
 76: {
 78:   UserCtx        user;
 79:   DM             red,da;
 80:   SNES           snes;
 81:   DM             packer;
 82:   PetscBool      use_monitor = PETSC_FALSE;

 84:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
 85:   PetscOptionsSetFromOptions(NULL);

 87:   /* Hardwire several options; can be changed at command line */
 88:   PetscOptionsInsertString(NULL,common_options);
 89:   PetscOptionsInsertString(NULL,matrix_free_options);
 90:   PetscOptionsInsert(NULL,&argc,&argv,NULL);
 91:   PetscOptionsGetBool(NULL,NULL,"-use_monitor",&use_monitor,PETSC_IGNORE);

 93:   /* Create a global vector that includes a single redundant array and two da arrays */
 94:   DMCompositeCreate(PETSC_COMM_WORLD,&packer);
 95:   DMRedundantCreate(PETSC_COMM_WORLD,0,1,&red);
 96:   DMSetOptionsPrefix(red,"red_");
 97:   DMCompositeAddDM(packer,red);
 98:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,2,1,NULL,&da);
 99:   DMSetOptionsPrefix(red,"da_");
100:   DMSetFromOptions(da);
101:   DMSetUp(da);
102:   DMDASetFieldName(da,0,"u");
103:   DMDASetFieldName(da,1,"lambda");
104:   DMCompositeAddDM(packer,(DM)da);
105:   DMSetApplicationContext(packer,&user);

107:   packer->ops->creatematrix = DMCreateMatrix_MF;

109:   /* create nonlinear multi-level solver */
110:   SNESCreate(PETSC_COMM_WORLD,&snes);
111:   SNESSetDM(snes,packer);
112:   SNESSetFunction(snes,NULL,ComputeFunction,NULL);
113:   SNESSetJacobian(snes,NULL, NULL,ComputeJacobian_MF,NULL);

115:   SNESSetFromOptions(snes);

117:   if (use_monitor) {
118:     /* create graphics windows */
119:     PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u_lambda - state variables and Lagrange multipliers",-1,-1,-1,-1,&user.u_lambda_viewer);
120:     PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu_lambda - derivate w.r.t. state variables and Lagrange multipliers",-1,-1,-1,-1,&user.fu_lambda_viewer);
121:     SNESMonitorSet(snes,Monitor,0,0);
122:   }

124:   SNESSolve(snes,NULL,NULL);
125:   SNESDestroy(&snes);

127:   DMDestroy(&red);
128:   DMDestroy(&da);
129:   DMDestroy(&packer);
130:   if (use_monitor) {
131:     PetscViewerDestroy(&user.u_lambda_viewer);
132:     PetscViewerDestroy(&user.fu_lambda_viewer);
133:   }
134:   PetscFinalize();
135:   return ierr;
136: }

138: typedef struct {
139:   PetscScalar u;
140:   PetscScalar lambda;
141: } ULambda;

143: /*
144:       Evaluates FU = Gradiant(L(w,u,lambda))

146:      This local function acts on the ghosted version of U (accessed via DMCompositeGetLocalVectors() and
147:    DMCompositeScatter()) BUT the global, nonghosted version of FU (via DMCompositeGetAccess()).

149: */
150: PetscErrorCode ComputeFunction(SNES snes,Vec U,Vec FU,void *ctx)
151: {
153:   PetscInt       xs,xm,i,N;
154:   ULambda        *u_lambda,*fu_lambda;
155:   PetscScalar    d,h,*w,*fw;
156:   Vec            vw,vfw,vu_lambda,vfu_lambda;
157:   DM             packer,red,da;

160:   VecGetDM(U, &packer);
161:   DMCompositeGetEntries(packer,&red,&da);
162:   DMCompositeGetLocalVectors(packer,&vw,&vu_lambda);
163:   DMCompositeScatter(packer,U,vw,vu_lambda);
164:   DMCompositeGetAccess(packer,FU,&vfw,&vfu_lambda);

166:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
167:   DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);
168:   VecGetArray(vw,&w);
169:   VecGetArray(vfw,&fw);
170:   DMDAVecGetArray(da,vu_lambda,&u_lambda);
171:   DMDAVecGetArray(da,vfu_lambda,&fu_lambda);
172:   d    = N-1.0;
173:   h    = 1.0/d;

175:   /* derivative of L() w.r.t. w */
176:   if (xs == 0) { /* only first processor computes this */
177:     fw[0] = -2.0*d*u_lambda[0].lambda;
178:   }

180:   /* derivative of L() w.r.t. u */
181:   for (i=xs; i<xs+xm; i++) {
182:     if      (i == 0)   fu_lambda[0].lambda   =    h*u_lambda[0].u   + 2.*d*u_lambda[0].lambda   - d*u_lambda[1].lambda;
183:     else if (i == 1)   fu_lambda[1].lambda   = 2.*h*u_lambda[1].u   + 2.*d*u_lambda[1].lambda   - d*u_lambda[2].lambda;
184:     else if (i == N-1) fu_lambda[N-1].lambda =    h*u_lambda[N-1].u + 2.*d*u_lambda[N-1].lambda - d*u_lambda[N-2].lambda;
185:     else if (i == N-2) fu_lambda[N-2].lambda = 2.*h*u_lambda[N-2].u + 2.*d*u_lambda[N-2].lambda - d*u_lambda[N-3].lambda;
186:     else               fu_lambda[i].lambda   = 2.*h*u_lambda[i].u   - d*(u_lambda[i+1].lambda - 2.0*u_lambda[i].lambda + u_lambda[i-1].lambda);
187:   }

189:   /* derivative of L() w.r.t. lambda */
190:   for (i=xs; i<xs+xm; i++) {
191:     if      (i == 0)   fu_lambda[0].u   = 2.0*d*(u_lambda[0].u - w[0]);
192:     else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
193:     else               fu_lambda[i].u   = -(d*(u_lambda[i+1].u - 2.0*u_lambda[i].u + u_lambda[i-1].u) - 2.0*h);
194:   }

196:   VecRestoreArray(vw,&w);
197:   VecRestoreArray(vfw,&fw);
198:   DMDAVecRestoreArray(da,vu_lambda,&u_lambda);
199:   DMDAVecRestoreArray(da,vfu_lambda,&fu_lambda);
200:   DMCompositeRestoreLocalVectors(packer,&vw,&vu_lambda);
201:   DMCompositeRestoreAccess(packer,FU,&vfw,&vfu_lambda);
202:   PetscLogFlops(13.0*N);
203:   return(0);
204: }

206: /*
207:     Computes the exact solution
208: */
209: PetscErrorCode u_solution(void *dummy,PetscInt n,const PetscScalar *x,PetscScalar *u)
210: {
211:   PetscInt i;

214:   for (i=0; i<n; i++) u[2*i] = x[i]*x[i] - 1.25*x[i] + .25;
215:   return(0);
216: }

218: PetscErrorCode ExactSolution(DM packer,Vec U)
219: {
220:   PF             pf;
221:   Vec            x,u_global;
222:   PetscScalar    *w;
223:   DM             da;
225:   PetscInt       m;

228:   DMCompositeGetEntries(packer,&m,&da);

230:   PFCreate(PETSC_COMM_WORLD,1,2,&pf);
231:   /* The cast through PETSC_UINTPTR_T is so that compilers will warn about casting to void * from void(*)(void) */
232:   PFSetType(pf,PFQUICK,(void*)(PETSC_UINTPTR_T)u_solution);
233:   DMGetCoordinates(da,&x);
234:   if (!x) {
235:     DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
236:     DMGetCoordinates(da,&x);
237:   }
238:   DMCompositeGetAccess(packer,U,&w,&u_global,0);
239:   if (w) w[0] = .25;
240:   PFApplyVec(pf,x,u_global);
241:   PFDestroy(&pf);
242:   DMCompositeRestoreAccess(packer,U,&w,&u_global,0);
243:   return(0);
244: }

246: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
247: {
248:   UserCtx        *user;
250:   PetscInt       m,N;
251:   PetscScalar    *w,*dw;
252:   Vec            u_lambda,U,F,Uexact;
253:   DM             packer;
254:   PetscReal      norm;
255:   DM             da;

258:   SNESGetDM(snes,&packer);
259:   DMGetApplicationContext(packer,&user);
260:   SNESGetSolution(snes,&U);
261:   DMCompositeGetAccess(packer,U,&w,&u_lambda);
262:   VecView(u_lambda,user->u_lambda_viewer);
263:   DMCompositeRestoreAccess(packer,U,&w,&u_lambda);

265:   SNESGetFunction(snes,&F,0,0);
266:   DMCompositeGetAccess(packer,F,&w,&u_lambda);
267:   /* VecView(u_lambda,user->fu_lambda_viewer); */
268:   DMCompositeRestoreAccess(packer,U,&w,&u_lambda);

270:   DMCompositeGetEntries(packer,&m,&da);
271:   DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);
272:   VecDuplicate(U,&Uexact);
273:   ExactSolution(packer,Uexact);
274:   VecAXPY(Uexact,-1.0,U);
275:   DMCompositeGetAccess(packer,Uexact,&dw,&u_lambda);
276:   VecStrideNorm(u_lambda,0,NORM_2,&norm);
277:   norm = norm/PetscSqrtReal((PetscReal)N-1.);
278:   if (dw) PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Error at x = 0 %g\n",(double)norm,(double)PetscRealPart(dw[0]));
279:   VecView(u_lambda,user->fu_lambda_viewer);
280:   DMCompositeRestoreAccess(packer,Uexact,&dw,&u_lambda);
281:   VecDestroy(&Uexact);
282:   return(0);
283: }

285: PetscErrorCode DMCreateMatrix_MF(DM packer,Mat *A)
286: {
288:   Vec            t;
289:   PetscInt       m;

292:   DMGetGlobalVector(packer,&t);
293:   VecGetLocalSize(t,&m);
294:   DMRestoreGlobalVector(packer,&t);
295:   MatCreateMFFD(PETSC_COMM_WORLD,m,m,PETSC_DETERMINE,PETSC_DETERMINE,A);
296:   MatSetUp(*A);
297:   return(0);
298: }

300: PetscErrorCode ComputeJacobian_MF(SNES snes,Vec x,Mat A,Mat B,void *ctx)
301: {

305:   MatMFFDSetFunction(A,(PetscErrorCode (*)(void*,Vec,Vec))SNESComputeFunction,snes);
306:   MatMFFDSetBase(A,x,NULL);
307:   return(0);
308: }


311: /*TEST

313:    test:
314:       nsize: 2
315:       args: -da_grid_x 10 -snes_converged_reason -ksp_converged_reason -snes_view
316:       requires: !single

318: TEST*/