Date: 2022-08-02T03:15:03+00:00

Actual source code: ex12.c

      1: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";
      2: /*
      3:   Solves the equation

      5:     u_tt - \Delta u = 0

      7:   which we split into two first-order systems

      9:     u_t -     v    = 0    so that     F(u,v).u = v
     10:     v_t - \Delta u = 0    so that     F(u,v).v = Delta u

     12:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     13:    Include "petscts.h" so that we can use SNES solvers.  Note that this
     14:    file automatically includes:
     15:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     16:      petscmat.h - matrices
     17:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     18:      petscviewer.h - viewers               petscpc.h  - preconditioners
     19:      petscksp.h   - linear solvers
     20: */
     21: #include <petscdm.h>
     22: #include <petscdmda.h>
     23: #include <petscts.h>

     25: /*
     26:    User-defined routines
     27: */
     28: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
     29: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
     30: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,PetscViewerAndFormat*);

     32: int main(int argc,char **argv)
     33: {
     34:   TS                   ts;                         /* nonlinear solver */
     35:   Vec                  x,r;                        /* solution, residual vectors */
     36:   PetscInt             steps;                      /* iterations for convergence */
     37:   DM                   da;
     38:   PetscReal            ftime;
     39:   SNES                 ts_snes;
     40:   PetscBool            usemonitor = PETSC_TRUE;
     41:   PetscViewerAndFormat *vf;

     43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     44:      Initialize program
     45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     46:   PetscInitialize(&argc,&argv,(char*)0,help);
     47:   PetscOptionsGetBool(NULL,NULL,"-usemonitor",&usemonitor,NULL);

     49:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     50:      Create distributed array (DMDA) to manage parallel grid and vectors
     51:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     52:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,NULL,&da);
     53:   DMSetFromOptions(da);
     54:   DMSetUp(da);
     55:   DMDASetFieldName(da,0,"u");
     56:   DMDASetFieldName(da,1,"v");

     58:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:      Extract global vectors from DMDA; then duplicate for remaining
     60:      vectors that are the same types
     61:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     62:   DMCreateGlobalVector(da,&x);
     63:   VecDuplicate(x,&r);

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:      Create timestepping solver context
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     68:   TSCreate(PETSC_COMM_WORLD,&ts);
     69:   TSSetDM(ts,da);
     70:   TSSetProblemType(ts,TS_NONLINEAR);
     71:   TSSetRHSFunction(ts,NULL,FormFunction,da);

     73:   TSSetMaxTime(ts,1.0);
     74:   if (usemonitor) {
     75:     TSMonitorSet(ts,MyTSMonitor,0,0);
     76:   }

     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:      Customize nonlinear solver
     80:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     81:   TSSetType(ts,TSBEULER);
     82:   TSGetSNES(ts,&ts_snes);
     83:   if (usemonitor) {
     84:     PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
     85:     SNESMonitorSet(ts_snes,(PetscErrorCode (*)(SNES,PetscInt,PetscReal,void *))MySNESMonitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);
     86:   }
     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:      Set initial conditions
     89:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     90:   FormInitialSolution(da,x);
     91:   TSSetTimeStep(ts,.0001);
     92:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
     93:   TSSetSolution(ts,x);

     95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96:      Set runtime options
     97:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     98:   TSSetFromOptions(ts);

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:      Solve nonlinear system
    102:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    103:   TSSolve(ts,x);
    104:   TSGetSolveTime(ts,&ftime);
    105:   TSGetStepNumber(ts,&steps);
    106:   VecViewFromOptions(x,NULL,"-final_sol");

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:      Free work space.  All PETSc objects should be destroyed when they
    110:      are no longer needed.
    111:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    112:   VecDestroy(&x);
    113:   VecDestroy(&r);
    114:   TSDestroy(&ts);
    115:   DMDestroy(&da);

    117:   PetscFinalize();
    118:   return 0;
    119: }
    120: /* ------------------------------------------------------------------- */
    121: /*
    122:    FormFunction - Evaluates nonlinear function, F(x).

    124:    Input Parameters:
    125: .  ts - the TS context
    126: .  X - input vector
    127: .  ptr - optional user-defined context, as set by SNESSetFunction()

    129:    Output Parameter:
    130: .  F - function vector
    131:  */
    132: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
    133: {
    134:   DM             da = (DM)ptr;
    135:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
    136:   PetscReal      hx,hy,/*hxdhy,hydhx,*/ sx,sy;
    137:   PetscScalar    u,uxx,uyy,v,***x,***f;
    138:   Vec            localX;

    141:   DMGetLocalVector(da,&localX);
    142:   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);

    144:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
    145:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
    146:   /*hxdhy  = hx/hy;*/
    147:   /*hydhx  = hy/hx;*/

    149:   /*
    150:      Scatter ghost points to local vector,using the 2-step process
    151:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    152:      By placing code between these two statements, computations can be
    153:      done while messages are in transition.
    154:   */
    155:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    156:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    158:   /*
    159:      Get pointers to vector data
    160:   */
    161:   DMDAVecGetArrayDOF(da,localX,&x);
    162:   DMDAVecGetArrayDOF(da,F,&f);

    164:   /*
    165:      Get local grid boundaries
    166:   */
    167:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    169:   /*
    170:      Compute function over the locally owned part of the grid
    171:   */
    172:   for (j=ys; j<ys+ym; j++) {
    173:     for (i=xs; i<xs+xm; i++) {
    174:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    175:         f[j][i][0] = x[j][i][0];
    176:         f[j][i][1] = x[j][i][1];
    177:         continue;
    178:       }
    179:       u          = x[j][i][0];
    180:       v          = x[j][i][1];
    181:       uxx        = (-2.0*u + x[j][i-1][0] + x[j][i+1][0])*sx;
    182:       uyy        = (-2.0*u + x[j-1][i][0] + x[j+1][i][0])*sy;
    183:       f[j][i][0] = v;
    184:       f[j][i][1] = uxx + uyy;
    185:     }
    186:   }

    188:   /*
    189:      Restore vectors
    190:   */
    191:   DMDAVecRestoreArrayDOF(da,localX,&x);
    192:   DMDAVecRestoreArrayDOF(da,F,&f);
    193:   DMRestoreLocalVector(da,&localX);
    194:   PetscLogFlops(11.0*ym*xm);
    195:   return 0;
    196: }

    198: /* ------------------------------------------------------------------- */
    199: PetscErrorCode FormInitialSolution(DM da,Vec U)
    200: {
    201:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
    202:   PetscScalar    ***u;
    203:   PetscReal      hx,hy,x,y,r;

    206:   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);

    208:   hx = 1.0/(PetscReal)(Mx-1);
    209:   hy = 1.0/(PetscReal)(My-1);

    211:   /*
    212:      Get pointers to vector data
    213:   */
    214:   DMDAVecGetArrayDOF(da,U,&u);

    216:   /*
    217:      Get local grid boundaries
    218:   */
    219:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    221:   /*
    222:      Compute function over the locally owned part of the grid
    223:   */
    224:   for (j=ys; j<ys+ym; j++) {
    225:     y = j*hy;
    226:     for (i=xs; i<xs+xm; i++) {
    227:       x = i*hx;
    228:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
    229:       if (r < .125) {
    230:         u[j][i][0] = PetscExpReal(-30.0*r*r*r);
    231:         u[j][i][1] = 0.0;
    232:       } else {
    233:         u[j][i][0] = 0.0;
    234:         u[j][i][1] = 0.0;
    235:       }
    236:     }
    237:   }

    239:   /*
    240:      Restore vectors
    241:   */
    242:   DMDAVecRestoreArrayDOF(da,U,&u);
    243:   return 0;
    244: }

    246: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
    247: {
    248:   PetscReal      norm;
    249:   MPI_Comm       comm;

    252:   VecNorm(v,NORM_2,&norm);
    253:   PetscObjectGetComm((PetscObject)ts,&comm);
    254:   if (step > -1) { /* -1 is used to indicate an interpolated value */
    255:     PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
    256:   }
    257:   return 0;
    258: }

    260: /*
    261:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
    262:    Input Parameters:
    263:      snes - the SNES context
    264:      its - iteration number
    265:      fnorm - 2-norm function value (may be estimated)
    266:      ctx - optional user-defined context for private data for the
    267:          monitor routine, as set by SNESMonitorSet()
    268:  */
    269: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
    270: {
    272:   SNESMonitorDefaultShort(snes,its,fnorm,vf);
    273:   return 0;
    274: }
    275: /*TEST

    277:     test:
    278:       args: -da_grid_x 20 -ts_max_time 3 -ts_dt 1e-1 -ts_theta_initial_guess_extrapolate 0 -ts_monitor -ksp_monitor_short
    279:       requires: !single

    281:     test:
    282:       suffix: 2
    283:       args: -da_grid_x 20 -ts_max_time 0.11 -ts_dt 1e-1 -ts_type glle -ts_monitor -ksp_monitor_short
    284:       requires: !single

    286:     test:
    287:       suffix: glvis_da_2d_vect
    288:       args: -usemonitor 0 -da_grid_x 20 -ts_max_time 0.3 -ts_dt 1e-1 -ts_type glle -final_sol glvis: -viewer_glvis_dm_da_bs 2,0
    289:       requires: !single

    291:     test:
    292:       suffix: glvis_da_2d_vect_ll
    293:       args: -usemonitor 0 -da_grid_x 20 -ts_max_time 0.3 -ts_dt 1e-1 -ts_type glle -final_sol glvis: -viewer_glvis_dm_da_bs 2,0 -viewer_glvis_dm_da_ll
    294:       requires: !single

    296: TEST*/