Date: 2021-03-03T22:27:45+00:00

Actual source code: ex21.c
petsc-3.14.5 2021-03-03
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      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*);

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

     59:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

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

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

     94:   DMDestroy(&user.red1);
     95:   DMDestroy(&user.da1);
     96:   DMDestroy(&user.da2);
     97:   DMDestroy(&user.packer);
     98:   VecDestroy(&U);
     99:   VecDestroy(&FU);
    100:   PetscViewerDestroy(&user.u_viewer);
    101:   PetscViewerDestroy(&user.lambda_viewer);
    102:   PetscViewerDestroy(&user.fu_viewer);
    103:   PetscViewerDestroy(&user.flambda_viewer);
    104:   PetscFinalize();
    105:   return ierr;
    106: }

    108: /*
    109:       Evaluates FU = Gradiant(L(w,u,lambda))

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

    121:   DMCompositeGetLocalVectors(user->packer,&vw,&vu,&vlambda);
    122:   DMCompositeGetLocalVectors(user->packer,&vfw,&vfu,&vflambda);
    123:   DMCompositeScatter(user->packer,U,vw,vu,vlambda);

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

    136:   /* derivative of L() w.r.t. w */
    137:   if (xs == 0) { /* only first processor computes this */
    138:     fw[0] = -2.*d*lambda[0];
    139:   }

    141:   /* derivative of L() w.r.t. u */
    142:   for (i=xs; i<xs+xm; i++) {
    143:     if      (i == 0)   flambda[0]   =    h*u[0]   + 2.*d*lambda[0]   - d*lambda[1];
    144:     else if (i == 1)   flambda[1]   = 2.*h*u[1]   + 2.*d*lambda[1]   - d*lambda[2];
    145:     else if (i == N-1) flambda[N-1] =    h*u[N-1] + 2.*d*lambda[N-1] - d*lambda[N-2];
    146:     else if (i == N-2) flambda[N-2] = 2.*h*u[N-2] + 2.*d*lambda[N-2] - d*lambda[N-3];
    147:     else               flambda[i]   = 2.*h*u[i]   - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]);
    148:   }

    150:   /* derivative of L() w.r.t. lambda */
    151:   for (i=xs; i<xs+xm; i++) {
    152:     if      (i == 0)   fu[0]   = 2.0*d*(u[0] - w[0]);
    153:     else if (i == N-1) fu[N-1] = 2.0*d*u[N-1];
    154:     else               fu[i]   = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h);
    155:   }

    157:   VecRestoreArray(vw,&w);
    158:   VecRestoreArray(vfw,&fw);
    159:   DMDAVecRestoreArray(user->da1,vu,&u);
    160:   DMDAVecRestoreArray(user->da1,vfu,&fu);
    161:   DMDAVecRestoreArray(user->da1,vlambda,&lambda);
    162:   DMDAVecRestoreArray(user->da1,vflambda,&flambda);

    164:   DMCompositeGather(user->packer,INSERT_VALUES,FU,vfw,vfu,vflambda);
    165:   DMCompositeRestoreLocalVectors(user->packer,&vw,&vu,&vlambda);
    166:   DMCompositeRestoreLocalVectors(user->packer,&vfw,&vfu,&vflambda);
    167:   return(0);
    168: }

    170: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
    171: {
    172:   UserCtx        *user = (UserCtx*)dummy;
    174:   Vec            w,u,lambda,U,F;

    177:   SNESGetSolution(snes,&U);
    178:   DMCompositeGetAccess(user->packer,U,&w,&u,&lambda);
    179:   VecView(u,user->u_viewer);
    180:   VecView(lambda,user->lambda_viewer);
    181:   DMCompositeRestoreAccess(user->packer,U,&w,&u,&lambda);

    183:   SNESGetFunction(snes,&F,0,0);
    184:   DMCompositeGetAccess(user->packer,F,&w,&u,&lambda);
    185:   VecView(u,user->fu_viewer);
    186:   VecView(lambda,user->flambda_viewer);
    187:   DMCompositeRestoreAccess(user->packer,F,&w,&u,&lambda);
    188:   return(0);
    189: }

    191: /*TEST

    193:    test:
    194:       nsize: 4
    195:       args: -snes_linesearch_monitor -snes_mf -pc_type none -snes_monitor_short -nox -ksp_monitor_short -snes_converged_reason
    196:       requires: !single

    198: TEST*/