Date: 2022-03-31T04:48:33+00:00

Actual source code: ex21.c

      2: static const char help[] = "Solves PDE optimization problem using full-space method, treats state and adjoint variables separately.\n\n";

      4: #include <petscdm.h>
      5: #include <petscdmda.h>
      6: #include <petscdmredundant.h>
      7: #include <petscdmcomposite.h>
      8: #include <petscpf.h>
      9: #include <petscsnes.h>

     11: /*

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

     17:             U = (w u lambda)

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

     21:             FU = (fw fu flambda)

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

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

     32:        Use the usual centered finite differences.

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

     36:        See ex22.c for the same code, but that interlaces the u and the lambda

     38: */

     40: typedef struct {
     41:   DM          red1,da1,da2;
     42:   DM          packer;
     43:   PetscViewer u_viewer,lambda_viewer;
     44:   PetscViewer fu_viewer,flambda_viewer;
     45: } UserCtx;

     47: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
     48: extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);

     50: int main(int argc,char **argv)
     51: {
     52:   PetscInt       its;
     53:   Vec            U,FU;
     54:   SNES           snes;
     55:   UserCtx        user;

     57:   PetscInitialize(&argc,&argv,(char*)0,help);

     59:   /* Create a global vector that includes a single redundant array and two da arrays */
     60:   DMCompositeCreate(PETSC_COMM_WORLD,&user.packer);
     61:   DMRedundantCreate(PETSC_COMM_WORLD,0,1,&user.red1);
     62:   DMCompositeAddDM(user.packer,user.red1);
     63:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da1);
     64:   DMSetFromOptions(user.da1);
     65:   DMSetUp(user.da1);
     66:   DMCompositeAddDM(user.packer,user.da1);
     67:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da2);
     68:   DMSetFromOptions(user.da2);
     69:   DMSetUp(user.da2);
     70:   DMDASetFieldName(user.da1,0,"u");
     71:   DMDASetFieldName(user.da2,0,"lambda");
     72:   DMCompositeAddDM(user.packer,user.da2);
     73:   DMCreateGlobalVector(user.packer,&U);
     74:   VecDuplicate(U,&FU);

     76:   /* create graphics windows */
     77:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u - state variables",-1,-1,-1,-1,&user.u_viewer);
     78:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"lambda - Lagrange multipliers",-1,-1,-1,-1,&user.lambda_viewer);
     79:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu - derivate w.r.t. state variables",-1,-1,-1,-1,&user.fu_viewer);
     80:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"flambda - derivate w.r.t. Lagrange multipliers",-1,-1,-1,-1,&user.flambda_viewer);

     82:   /* create nonlinear solver */
     83:   SNESCreate(PETSC_COMM_WORLD,&snes);
     84:   SNESSetFunction(snes,FU,FormFunction,&user);
     85:   SNESSetFromOptions(snes);
     86:   SNESMonitorSet(snes,Monitor,&user,0);
     87:   SNESSolve(snes,NULL,U);
     88:   SNESGetIterationNumber(snes,&its);
     89:   SNESDestroy(&snes);

     91:   DMDestroy(&user.red1);
     92:   DMDestroy(&user.da1);
     93:   DMDestroy(&user.da2);
     94:   DMDestroy(&user.packer);
     95:   VecDestroy(&U);
     96:   VecDestroy(&FU);
     97:   PetscViewerDestroy(&user.u_viewer);
     98:   PetscViewerDestroy(&user.lambda_viewer);
     99:   PetscViewerDestroy(&user.fu_viewer);
    100:   PetscViewerDestroy(&user.flambda_viewer);
    101:   PetscFinalize();
    102:   return 0;
    103: }

    105: /*
    106:       Evaluates FU = Gradiant(L(w,u,lambda))

    108: */
    109: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void *dummy)
    110: {
    111:   UserCtx        *user = (UserCtx*)dummy;
    112:   PetscInt       xs,xm,i,N;
    113:   PetscScalar    *u,*lambda,*w,*fu,*fw,*flambda,d,h;
    114:   Vec            vw,vu,vlambda,vfw,vfu,vflambda;

    117:   DMCompositeGetLocalVectors(user->packer,&vw,&vu,&vlambda);
    118:   DMCompositeGetLocalVectors(user->packer,&vfw,&vfu,&vflambda);
    119:   DMCompositeScatter(user->packer,U,vw,vu,vlambda);

    121:   DMDAGetCorners(user->da1,&xs,NULL,NULL,&xm,NULL,NULL);
    122:   DMDAGetInfo(user->da1,0,&N,0,0,0,0,0,0,0,0,0,0,0);
    123:   VecGetArray(vw,&w);
    124:   VecGetArray(vfw,&fw);
    125:   DMDAVecGetArray(user->da1,vu,&u);
    126:   DMDAVecGetArray(user->da1,vfu,&fu);
    127:   DMDAVecGetArray(user->da1,vlambda,&lambda);
    128:   DMDAVecGetArray(user->da1,vflambda,&flambda);
    129:   d    = (N-1.0);
    130:   h    = 1.0/d;

    132:   /* derivative of L() w.r.t. w */
    133:   if (xs == 0) { /* only first processor computes this */
    134:     fw[0] = -2.*d*lambda[0];
    135:   }

    137:   /* derivative of L() w.r.t. u */
    138:   for (i=xs; i<xs+xm; i++) {
    139:     if      (i == 0)   flambda[0]   =    h*u[0]   + 2.*d*lambda[0]   - d*lambda[1];
    140:     else if (i == 1)   flambda[1]   = 2.*h*u[1]   + 2.*d*lambda[1]   - d*lambda[2];
    141:     else if (i == N-1) flambda[N-1] =    h*u[N-1] + 2.*d*lambda[N-1] - d*lambda[N-2];
    142:     else if (i == N-2) flambda[N-2] = 2.*h*u[N-2] + 2.*d*lambda[N-2] - d*lambda[N-3];
    143:     else               flambda[i]   = 2.*h*u[i]   - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]);
    144:   }

    146:   /* derivative of L() w.r.t. lambda */
    147:   for (i=xs; i<xs+xm; i++) {
    148:     if      (i == 0)   fu[0]   = 2.0*d*(u[0] - w[0]);
    149:     else if (i == N-1) fu[N-1] = 2.0*d*u[N-1];
    150:     else               fu[i]   = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h);
    151:   }

    153:   VecRestoreArray(vw,&w);
    154:   VecRestoreArray(vfw,&fw);
    155:   DMDAVecRestoreArray(user->da1,vu,&u);
    156:   DMDAVecRestoreArray(user->da1,vfu,&fu);
    157:   DMDAVecRestoreArray(user->da1,vlambda,&lambda);
    158:   DMDAVecRestoreArray(user->da1,vflambda,&flambda);

    160:   DMCompositeGather(user->packer,INSERT_VALUES,FU,vfw,vfu,vflambda);
    161:   DMCompositeRestoreLocalVectors(user->packer,&vw,&vu,&vlambda);
    162:   DMCompositeRestoreLocalVectors(user->packer,&vfw,&vfu,&vflambda);
    163:   return 0;
    164: }

    166: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
    167: {
    168:   UserCtx        *user = (UserCtx*)dummy;
    169:   Vec            w,u,lambda,U,F;

    172:   SNESGetSolution(snes,&U);
    173:   DMCompositeGetAccess(user->packer,U,&w,&u,&lambda);
    174:   VecView(u,user->u_viewer);
    175:   VecView(lambda,user->lambda_viewer);
    176:   DMCompositeRestoreAccess(user->packer,U,&w,&u,&lambda);

    178:   SNESGetFunction(snes,&F,0,0);
    179:   DMCompositeGetAccess(user->packer,F,&w,&u,&lambda);
    180:   VecView(u,user->fu_viewer);
    181:   VecView(lambda,user->flambda_viewer);
    182:   DMCompositeRestoreAccess(user->packer,F,&w,&u,&lambda);
    183:   return 0;
    184: }

    186: /*TEST

    188:    test:
    189:       nsize: 4
    190:       args: -snes_linesearch_monitor -snes_mf -pc_type none -snes_monitor_short -nox -ksp_monitor_short -snes_converged_reason
    191:       requires: !single

    193: TEST*/