Date: 2021-03-03T22:28:09+00:00

Actual source code: eptorsion2.c
petsc-3.14.5 2021-03-03
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      1: /* Program usage: mpiexec -n <proc> eptorsion2 [-help] [all TAO options] */

      3: /* ----------------------------------------------------------------------

      5:   Elastic-plastic torsion problem.

      7:   The elastic plastic torsion problem arises from the determination
      8:   of the stress field on an infinitely long cylindrical bar, which is
      9:   equivalent to the solution of the following problem:

     11:   min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}

     13:   where C is the torsion angle per unit length.

     15:   The uniprocessor version of this code is eptorsion1.c; the Fortran
     16:   version of this code is eptorsion2f.F.

     18:   This application solves the problem without calculating hessians
     19: ---------------------------------------------------------------------- */

     21: /*
     22:   Include "petsctao.h" so that we can use TAO solvers.  Note that this
     23:   file automatically includes files for lower-level support, such as those
     24:   provided by the PETSc library:
     25:      petsc.h       - base PETSc routines   petscvec.h - vectors
     26:      petscsys.h    - sysem routines        petscmat.h - matrices
     27:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     28:      petscviewer.h - viewers               petscpc.h  - preconditioners
     29:   Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
     30:   the parallel mesh.
     31: */

     33: #include <petsctao.h>
     34: #include <petscdmda.h>

     36: static  char help[] =
     37: "Demonstrates use of the TAO package to solve \n\
     38: unconstrained minimization problems in parallel.  This example is based on \n\
     39: the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.\n\
     40: The command line options are:\n\
     41:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
     42:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
     43:   -par <param>, where <param> = angle of twist per unit length\n\n";

     45: /*T
     46:    Concepts: TAO^Solving an unconstrained minimization problem
     47:    Routines: TaoCreate(); TaoSetType();
     48:    Routines: TaoSetInitialVector();
     49:    Routines: TaoSetObjectiveAndGradientRoutine();
     50:    Routines: TaoSetHessianRoutine(); TaoSetFromOptions();
     51:    Routines: TaoSolve();
     52:    Routines: TaoDestroy();
     53:    Processors: n
     54: T*/

     56: /*
     57:    User-defined application context - contains data needed by the
     58:    application-provided call-back routines, FormFunction() and
     59:    FormGradient().
     60: */
     61: typedef struct {
     62:   /* parameters */
     63:    PetscInt      mx, my;         /* global discretization in x- and y-directions */
     64:    PetscReal     param;          /* nonlinearity parameter */

     66:   /* work space */
     67:    Vec           localX;         /* local vectors */
     68:    DM            dm;             /* distributed array data structure */
     69: } AppCtx;

     72: PetscErrorCode FormInitialGuess(AppCtx*, Vec);
     73: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
     74: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);

     77: int main(int argc, char **argv)
     78: {
     79:     PetscErrorCode     ierr;
     80:     Vec                x;
     81:     Mat                H;
     82:     PetscInt           Nx, Ny;
     83:     Tao                tao;
     84:     PetscBool          flg;
     85:     KSP                ksp;
     86:     PC                 pc;
     87:     AppCtx             user;

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

     91:     /* Specify default dimension of the problem */
     92:     user.param = 5.0; user.mx = 10; user.my = 10;
     93:     Nx = Ny = PETSC_DECIDE;

     95:     /* Check for any command line arguments that override defaults */
     96:     PetscOptionsGetReal(NULL,NULL,"-par",&user.param,&flg);
     97:     PetscOptionsGetInt(NULL,NULL,"-my",&user.my,&flg);
     98:     PetscOptionsGetInt(NULL,NULL,"-mx",&user.mx,&flg);

    100:     PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
    101:     PetscPrintf(PETSC_COMM_WORLD,"mx: %D     my: %D   \n\n",user.mx,user.my);

    103:     /* Set up distributed array */
    104:     DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.mx,user.my,Nx,Ny,1,1,NULL,NULL,&user.dm);
    105:     DMSetFromOptions(user.dm);
    106:     DMSetUp(user.dm);

    108:     /* Create vectors */
    109:     DMCreateGlobalVector(user.dm,&x);

    111:     DMCreateLocalVector(user.dm,&user.localX);

    113:     /* Create Hessian */
    114:     DMCreateMatrix(user.dm,&H);
    115:     MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE);

    117:     /* The TAO code begins here */

    119:     /* Create TAO solver and set desired solution method */
    120:     TaoCreate(PETSC_COMM_WORLD,&tao);
    121:     TaoSetType(tao,TAOCG);

    123:     /* Set initial solution guess */
    124:     FormInitialGuess(&user,x);
    125:     TaoSetInitialVector(tao,x);

    127:     /* Set routine for function and gradient evaluation */
    128:     TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);

    130:     TaoSetHessianRoutine(tao,H,H,FormHessian,(void*)&user);

    133:     /* Check for any TAO command line options */
    134:     TaoSetFromOptions(tao);

    136:     TaoGetKSP(tao,&ksp);
    137:     if (ksp) {
    138:       KSPGetPC(ksp,&pc);
    139:       PCSetType(pc,PCNONE);
    140:     }

    142:     /* SOLVE THE APPLICATION */
    143:     TaoSolve(tao);

    145:     /* Free TAO data structures */
    146:     TaoDestroy(&tao);

    148:     /* Free PETSc data structures */
    149:     VecDestroy(&x);
    150:     MatDestroy(&H);

    152:     VecDestroy(&user.localX);
    153:     DMDestroy(&user.dm);

    155:     PetscFinalize();
    156:     return 0;
    157: }

    160: /* ------------------------------------------------------------------- */
    161: /*
    162:     FormInitialGuess - Computes an initial approximation to the solution.

    164:     Input Parameters:
    165: .   user - user-defined application context
    166: .   X    - vector

    168:     Output Parameters:
    169:     X    - vector
    170: */
    171: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
    172: {
    174:   PetscInt       i, j, k, mx = user->mx, my = user->my;
    175:   PetscInt       xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
    176:   PetscReal      hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;

    179:   /* Get local mesh boundaries */
    180:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    181:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

    183:   /* Compute initial guess over locally owned part of mesh */
    184:   xe = xs+xm;
    185:   ye = ys+ym;
    186:   for (j=ys; j<ye; j++) {  /*  for (j=0; j<my; j++) */
    187:     temp = PetscMin(j+1,my-j)*hy;
    188:     for (i=xs; i<xe; i++) {  /*  for (i=0; i<mx; i++) */
    189:       k   = (j-gys)*gxm + i-gxs;
    190:       val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
    191:       VecSetValuesLocal(X,1,&k,&val,ADD_VALUES);
    192:     }
    193:   }
    194:   VecAssemblyBegin(X);
    195:   VecAssemblyEnd(X);
    196:   return(0);
    197: }

    200: /* ------------------------------------------------------------------ */
    201: /*
    202:    FormFunctionGradient - Evaluates the function and corresponding gradient.

    204:    Input Parameters:
    205:    tao - the Tao context
    206:    X   - the input vector
    207:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

    209:    Output Parameters:
    210:    f   - the newly evaluated function
    211:    G   - the newly evaluated gradient
    212: */
    213: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f,Vec G,void *ptr){

    215:   AppCtx         *user = (AppCtx *)ptr;
    217:   PetscInt       i,j,k,ind;
    218:   PetscInt       xe,ye,xsm,ysm,xep,yep;
    219:   PetscInt       xs, ys, xm, ym, gxm, gym, gxs, gys;
    220:   PetscInt       mx = user->mx, my = user->my;
    221:   PetscReal      three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
    222:   PetscReal      p5 = 0.5, area, val, flin, fquad;
    223:   PetscReal      v,vb,vl,vr,vt,dvdx,dvdy;
    224:   PetscReal      hx = 1.0/(user->mx + 1);
    225:   PetscReal      hy = 1.0/(user->my + 1);
    226:   Vec            localX = user->localX;

    229:   /* Initialize */
    230:   flin = fquad = zero;

    232:   VecSet(G, zero);
    233:   /*
    234:      Scatter ghost points to local vector,using the 2-step process
    235:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    236:      By placing code between these two statements, computations can be
    237:      done while messages are in transition.
    238:   */
    239:   DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
    240:   DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);

    242:   /* Get pointer to vector data */
    243:   VecGetArray(localX,&x);

    245:   /* Get local mesh boundaries */
    246:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    247:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

    249:   /* Set local loop dimensions */
    250:   xe = xs+xm;
    251:   ye = ys+ym;
    252:   if (xs == 0)  xsm = xs-1;
    253:   else          xsm = xs;
    254:   if (ys == 0)  ysm = ys-1;
    255:   else          ysm = ys;
    256:   if (xe == mx) xep = xe+1;
    257:   else          xep = xe;
    258:   if (ye == my) yep = ye+1;
    259:   else          yep = ye;

    261:   /* Compute local gradient contributions over the lower triangular elements */
    262:   for (j=ysm; j<ye; j++) {  /*  for (j=-1; j<my; j++) */
    263:     for (i=xsm; i<xe; i++) {  /*   for (i=-1; i<mx; i++) */
    264:       k = (j-gys)*gxm + i-gxs;
    265:       v = zero;
    266:       vr = zero;
    267:       vt = zero;
    268:       if (i >= 0 && j >= 0) v = x[k];
    269:       if (i < mx-1 && j > -1) vr = x[k+1];
    270:       if (i > -1 && j < my-1) vt = x[k+gxm];
    271:       dvdx = (vr-v)/hx;
    272:       dvdy = (vt-v)/hy;
    273:       if (i != -1 && j != -1) {
    274:         ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
    275:         VecSetValuesLocal(G,1,&k,&val,ADD_VALUES);
    276:       }
    277:       if (i != mx-1 && j != -1) {
    278:         ind = k+1; val =  dvdx/hx - cdiv3;
    279:         VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
    280:       }
    281:       if (i != -1 && j != my-1) {
    282:         ind = k+gxm; val = dvdy/hy - cdiv3;
    283:         VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
    284:       }
    285:       fquad += dvdx*dvdx + dvdy*dvdy;
    286:       flin -= cdiv3 * (v + vr + vt);
    287:     }
    288:   }

    290:   /* Compute local gradient contributions over the upper triangular elements */
    291:   for (j=ys; j<yep; j++) { /*  for (j=0; j<=my; j++) */
    292:     for (i=xs; i<xep; i++) {  /*   for (i=0; i<=mx; i++) */
    293:       k = (j-gys)*gxm + i-gxs;
    294:       vb = zero;
    295:       vl = zero;
    296:       v  = zero;
    297:       if (i < mx && j > 0) vb = x[k-gxm];
    298:       if (i > 0 && j < my) vl = x[k-1];
    299:       if (i < mx && j < my) v = x[k];
    300:       dvdx = (v-vl)/hx;
    301:       dvdy = (v-vb)/hy;
    302:       if (i != mx && j != 0) {
    303:         ind = k-gxm; val = - dvdy/hy - cdiv3;
    304:         VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
    305:       }
    306:       if (i != 0 && j != my) {
    307:         ind = k-1; val =  - dvdx/hx - cdiv3;
    308:         VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
    309:       }
    310:       if (i != mx && j != my) {
    311:         ind = k; val =  dvdx/hx + dvdy/hy - cdiv3;
    312:         VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES);
    313:       }
    314:       fquad += dvdx*dvdx + dvdy*dvdy;
    315:       flin -= cdiv3 * (vb + vl + v);
    316:     }
    317:   }

    320:   /* Restore vector */
    321:   VecRestoreArray(localX,&x);

    323:   /* Assemble gradient vector */
    324:   VecAssemblyBegin(G);
    325:   VecAssemblyEnd(G);

    327:   /* Scale the gradient */
    328:   area = p5*hx*hy;
    329:   floc = area * (p5 * fquad + flin);
    330:   VecScale(G, area);

    332:   /* Sum function contributions from all processes */
    333:   (PetscErrorCode)MPI_Allreduce((void*)&floc,(void*)f,1,MPIU_REAL,MPIU_SUM,MPI_COMM_WORLD);

    335:   ierr=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16);

    337:   return(0);
    338: }

    342: PetscErrorCode FormHessian(Tao tao, Vec X, Mat A, Mat Hpre, void*ctx)
    343: {
    344:   AppCtx         *user= (AppCtx*) ctx;
    346:   PetscInt       i,j,k;
    347:   PetscInt       col[5],row;
    348:   PetscInt       xs,xm,gxs,gxm,ys,ym,gys,gym;
    349:   PetscReal      v[5];
    350:   PetscReal      hx=1.0/(user->mx+1), hy=1.0/(user->my+1), hxhx=1.0/(hx*hx), hyhy=1.0/(hy*hy), area=0.5*hx*hy;

    352:   /* Compute the quadratic term in the objective function */

    354:   /*
    355:      Get local grid boundaries
    356:   */

    359:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    360:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

    362:   for (j=ys; j<ys+ym; j++){

    364:     for (i=xs; i< xs+xm; i++){

    366:       row=(j-gys)*gxm + (i-gxs);

    368:       k=0;
    369:       if (j>gys){
    370:         v[k]=-2*hyhy; col[k]=row - gxm; k++;
    371:       }

    373:       if (i>gxs){
    374:         v[k]= -2*hxhx; col[k]=row - 1; k++;
    375:       }

    377:       v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;

    379:       if (i+1 < gxs+gxm){
    380:         v[k]= -2.0*hxhx; col[k]=row+1; k++;
    381:       }

    383:       if (j+1 <gys+gym){
    384:         v[k]= -2*hyhy; col[k] = row+gxm; k++;
    385:       }

    387:       MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES);

    389:     }
    390:   }
    391:   /*
    392:      Assemble matrix, using the 2-step process:
    393:      MatAssemblyBegin(), MatAssemblyEnd().
    394:      By placing code between these two statements, computations can be
    395:      done while messages are in transition.
    396:   */
    397:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    398:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    399:   /*
    400:     Tell the matrix we will never add a new nonzero location to the
    401:     matrix. If we do it will generate an error.
    402:   */
    403:   MatScale(A,area);
    404:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    405:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
    406:   PetscLogFlops(9*xm*ym+49*xm);
    407:   return(0);
    408: }

    411: /*TEST

    413:    build:
    414:       requires: !complex

    416:    test:
    417:       suffix: 1
    418:       nsize: 2
    419:       args: -tao_smonitor -tao_type nls -mx 16 -my 16 -tao_gatol 1.e-4

    421: TEST*/