Actual source code: ex7.c

      2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";

      5: /*
      6:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
      7:    Include "petscts.h" so that we can use SNES solvers.  Note that this
      8:    file automatically includes:
      9:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     10:      petscmat.h - matrices
     11:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     12:      petscviewer.h - viewers               petscpc.h  - preconditioners
     13:      petscksp.h   - linear solvers
     14: */
     15: #include <petscdm.h>
     16: #include <petscdmda.h>
     17: #include <petscts.h>

     20: /*
     21:    User-defined routines
     22: */
     23: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
     24: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
     25: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,PetscViewerAndFormat*);

     27: int main(int argc,char **argv)
     28: {
     29:   TS                   ts;                         /* time integrator */
     30:   SNES                 snes;
     31:   Vec                  x,r;                        /* solution, residual vectors */
     32:   PetscErrorCode       ierr;
     33:   DM                   da;
     34:   PetscViewerAndFormat *vf;

     36:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     37:      Initialize program
     38:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     39:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     41:      Create distributed array (DMDA) to manage parallel grid and vectors
     42:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     43:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     44:   DMSetFromOptions(da);
     45:   DMSetUp(da);

     47:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     48:      Extract global vectors from DMDA; then duplicate for remaining
     49:      vectors that are the same types
     50:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     51:   DMCreateGlobalVector(da,&x);
     52:   VecDuplicate(x,&r);

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:      Create timestepping solver context
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     57:   TSCreate(PETSC_COMM_WORLD,&ts);
     58:   TSSetProblemType(ts,TS_NONLINEAR);
     59:   TSSetRHSFunction(ts,NULL,FormFunction,da);

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:      Create matrix data structure; set Jacobian evaluation routine

     64:      Set Jacobian matrix data structure and default Jacobian evaluation
     65:      routine. User can override with:
     66:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
     67:                 (unless user explicitly sets preconditioner)
     68:      -snes_mf_operator : form preconditioning matrix as set by the user,
     69:                          but use matrix-free approx for Jacobian-vector
     70:                          products within Newton-Krylov method

     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   TSSetMaxTime(ts,1.0);
     75:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
     76:   TSMonitorSet(ts,MyTSMonitor,PETSC_VIEWER_STDOUT_WORLD,NULL);
     77:   TSSetDM(ts,da);
     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:      Customize nonlinear solver
     80:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     81:   TSSetType(ts,TSBEULER);
     82:   TSGetSNES(ts,&snes);
     83:   PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
     84:   SNESMonitorSet(snes,(PetscErrorCode (*)(SNES,PetscInt,PetscReal,void*))MySNESMonitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:      Set initial conditions
     88:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     89:   FormInitialSolution(da,x);
     90:   TSSetTimeStep(ts,.0001);
     91:   TSSetSolution(ts,x);

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:      Set runtime options
     95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     96:   TSSetFromOptions(ts);

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:      Solve nonlinear system
    100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    101:   TSSolve(ts,x);

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:      Free work space.  All PETSc objects should be destroyed when they
    105:      are no longer needed.
    106:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    107:   VecDestroy(&x);
    108:   VecDestroy(&r);
    109:   TSDestroy(&ts);
    110:   DMDestroy(&da);

    112:   PetscFinalize();
    113:   return ierr;
    114: }
    115: /* ------------------------------------------------------------------- */
    116: /*
    117:    FormFunction - Evaluates nonlinear function, F(x).

    119:    Input Parameters:
    120: .  ts - the TS context
    121: .  X - input vector
    122: .  ptr - optional user-defined context, as set by SNESSetFunction()

    124:    Output Parameter:
    125: .  F - function vector
    126:  */
    127: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
    128: {
    129:   DM             da;
    131:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
    132:   PetscReal      two = 2.0,hx,hy,sx,sy;
    133:   PetscScalar    u,uxx,uyy,**x,**f;
    134:   Vec            localX;

    137:   TSGetDM(ts,&da);
    138:   DMGetLocalVector(da,&localX);
    139:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    141:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
    142:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);

    144:   /*
    145:      Scatter ghost points to local vector,using the 2-step process
    146:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    147:      By placing code between these two statements, computations can be
    148:      done while messages are in transition.
    149:   */
    150:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    151:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    153:   /*
    154:      Get pointers to vector data
    155:   */
    156:   DMDAVecGetArrayRead(da,localX,&x);
    157:   DMDAVecGetArray(da,F,&f);

    159:   /*
    160:      Get local grid boundaries
    161:   */
    162:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    164:   /*
    165:      Compute function over the locally owned part of the grid
    166:   */
    167:   for (j=ys; j<ys+ym; j++) {
    168:     for (i=xs; i<xs+xm; i++) {
    169:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    170:         f[j][i] = x[j][i];
    171:         continue;
    172:       }
    173:       u   = x[j][i];
    174:       uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
    175:       uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
    176:       /*      f[j][i] = -(uxx + uyy); */
    177:       f[j][i] = -u*(uxx + uyy) - (4.0 - 1.0)*((x[j][i+1] - x[j][i-1])*(x[j][i+1] - x[j][i-1])*.25*sx +
    178:                                               (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
    179:     }
    180:   }

    182:   /*
    183:      Restore vectors
    184:   */
    185:   DMDAVecRestoreArrayRead(da,localX,&x);
    186:   DMDAVecRestoreArray(da,F,&f);
    187:   DMRestoreLocalVector(da,&localX);
    188:   PetscLogFlops(11.0*ym*xm);
    189:   return(0);
    190: }

    192: /* ------------------------------------------------------------------- */
    193: PetscErrorCode FormInitialSolution(DM da,Vec U)
    194: {
    196:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
    197:   PetscScalar    **u;
    198:   PetscReal      hx,hy,x,y,r;

    201:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    203:   hx = 1.0/(PetscReal)(Mx-1);
    204:   hy = 1.0/(PetscReal)(My-1);

    206:   /*
    207:      Get pointers to vector data
    208:   */
    209:   DMDAVecGetArray(da,U,&u);

    211:   /*
    212:      Get local grid boundaries
    213:   */
    214:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    216:   /*
    217:      Compute function over the locally owned part of the grid
    218:   */
    219:   for (j=ys; j<ys+ym; j++) {
    220:     y = j*hy;
    221:     for (i=xs; i<xs+xm; i++) {
    222:       x = i*hx;
    223:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
    224:       if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
    225:       else          u[j][i] = 0.0;
    226:     }
    227:   }

    229:   /*
    230:      Restore vectors
    231:   */
    232:   DMDAVecRestoreArray(da,U,&u);
    233:   return(0);
    234: }

    236: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
    237: {
    239:   PetscReal      norm;
    240:   MPI_Comm       comm;

    243:   if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
    244:   VecNorm(v,NORM_2,&norm);
    245:   PetscObjectGetComm((PetscObject)ts,&comm);
    246:   PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
    247:   return(0);
    248: }

    250: /*
    251:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
    252:    Input Parameters:
    253:      snes - the SNES context
    254:      its - iteration number
    255:      fnorm - 2-norm function value (may be estimated)
    256:      ctx - optional user-defined context for private data for the
    257:          monitor routine, as set by SNESMonitorSet()
    258:  */
    259: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
    260: {

    264:   SNESMonitorDefaultShort(snes,its,fnorm,vf);
    265:   return(0);
    266: }

    268: /*TEST

    270:     test:
    271:       args: -ts_max_steps 5

    273:     test:
    274:       suffix: 2
    275:       args: -ts_max_steps 5  -snes_mf_operator

    277:     test:
    278:       suffix: 3
    279:       args: -ts_max_steps 5  -snes_mf -pc_type none

    281: TEST*/