Date: 2013-07-02T14:51:38+00:00

Actual source code: ex15.c
petsc-3.4.2 2013-07-02

      2: static char help[] = "Time-dependent PDE in 2d. Modified from ex13.c for illustrating how to solve DAEs. \n";
      3: /*
      4:    u_t = uxx + uyy
      5:    0 < x < 1, 0 < y < 1;
      6:    At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125
      7:            u(x,y) = 0.0           if r >= .125

     10:    Boundary conditions:
     11:    Drichlet BC:
     12:    At x=0, x=1, y=0, y=1: u = 0.0

     14:    Neumann BC:
     15:    At x=0, x=1: du(x,y,t)/dx = 0
     16:    At y=0, y=1: du(x,y,t)/dy = 0

     18:    mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
     19:          ./ex15 -da_grid_x 40 -da_grid_y 40  -draw_pause .1 -boundary 1 -ts_monitor_draw_solution
     20:          ./ex15 -da_grid_x 40 -da_grid_y 40  -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9

     22: */

     24: #include <petscdmda.h>
     25: #include <petscts.h>

     27: /*
     28:    User-defined data structures and routines
     29: */

     31: /* AppCtx: used by FormIFunction() and FormIJacobian() */
     32: typedef struct {
     33:   DM        da;
     34:   PetscInt  nstencilpts;         /* number of stencil points: 5 or 9 */
     35:   PetscReal c;
     36:   PetscInt  boundary;            /* Type of boundary condition */
     37:   PetscBool viewJacobian;
     38: } AppCtx;

     40: extern PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
     41: extern PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat*,Mat*,MatStructure*,void*);
     42: extern PetscErrorCode FormInitialSolution(Vec,void*);

     46: int main(int argc,char **argv)
     47: {
     48:   TS             ts;                   /* nonlinear solver */
     49:   Vec            u,r;                  /* solution, residual vectors */
     50:   Mat            J,Jmf = NULL;   /* Jacobian matrices */
     51:   PetscInt       maxsteps = 1000;      /* iterations for convergence */
     53:   DM             da;
     54:   PetscReal      dt;
     55:   AppCtx         user;              /* user-defined work context */
     56:   SNES           snes;
     57:   PetscInt       Jtype; /* Jacobian type
     58:                             0: user provide Jacobian;
     59:                             1: slow finite difference;
     60:                             2: fd with coloring; */

     62:   PetscInitialize(&argc,&argv,(char*)0,help);
     63:   /* Initialize user application context */
     64:   user.da           = NULL;
     65:   user.nstencilpts  = 5;
     66:   user.c            = -30.0;
     67:   user.boundary     = 0;  /* 0: Drichlet BC; 1: Neumann BC */
     68:   user.viewJacobian = PETSC_FALSE;

     70:   PetscOptionsGetInt(NULL,"-nstencilpts",&user.nstencilpts,NULL);
     71:   PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);
     72:   PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian);

     74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     75:      Create distributed array (DMDA) to manage parallel grid and vectors
     76:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     77:   if (user.nstencilpts == 5) {
     78:     DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     79:   } else if (user.nstencilpts == 9) {
     80:     DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     81:   } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
     82:   user.da = da;

     84:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:      Extract global vectors from DMDA;
     86:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     87:   DMCreateGlobalVector(da,&u);
     88:   VecDuplicate(u,&r);

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:      Create timestepping solver context
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     93:   TSCreate(PETSC_COMM_WORLD,&ts);
     94:   TSSetProblemType(ts,TS_NONLINEAR);
     95:   TSSetType(ts,TSBEULER);
     96:   TSSetDM(ts,da);
     97:   TSSetIFunction(ts,r,FormIFunction,&user);
     98:   TSSetDuration(ts,maxsteps,1.0);

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:      Set initial conditions
    102:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    103:   FormInitialSolution(u,&user);
    104:   TSSetSolution(ts,u);
    105:   dt   = .01;
    106:   TSSetInitialTimeStep(ts,0.0,dt);

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:    Set Jacobian evaluation routine
    110:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    111:   DMCreateMatrix(da,MATAIJ,&J);
    112:   Jtype = 0;
    113:   PetscOptionsGetInt(NULL, "-Jtype",&Jtype,NULL);
    114:   if (Jtype == 0) { /* use user provided Jacobian evaluation routine */
    115:     if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts);
    116:     TSSetIJacobian(ts,J,J,FormIJacobian,&user);
    117:   } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */
    118:     TSGetSNES(ts,&snes);
    119:     MatCreateSNESMF(snes,&Jmf);
    120:     if (Jtype == 1) { /* slow finite difference J; */
    121:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);
    122:     } else if (Jtype == 2) { /* Use coloring to compute  finite difference J efficiently */
    123:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);
    124:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported");
    125:   }

    127:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:    Sets various TS parameters from user options
    129:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    130:   TSSetFromOptions(ts);

    132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133:      Solve nonlinear system
    134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    135:   TSSolve(ts,u);

    137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    138:      Free work space.
    139:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    140:   MatDestroy(&J);
    141:   MatDestroy(&Jmf);
    142:   VecDestroy(&u);
    143:   VecDestroy(&r);
    144:   TSDestroy(&ts);
    145:   DMDestroy(&da);

    147:   PetscFinalize();
    148:   return(0);
    149: }

    151: /* --------------------------------------------------------------------- */
    152: /*
    153:   FormIFunction = Udot - RHSFunction
    154: */
    157: PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
    158: {
    160:   AppCtx         *user=(AppCtx*)ctx;
    161:   DM             da   = (DM)user->da;
    162:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
    163:   PetscReal      hx,hy,sx,sy;
    164:   PetscScalar    u,uxx,uyy,**uarray,**f,**udot;
    165:   Vec            localU;

    168:   DMGetLocalVector(da,&localU);
    169:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
    170:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    172:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
    173:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
    174:   if (user->nstencilpts == 9 && hx != hy) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"hx must equal hy when nstencilpts = 9 for this example");

    176:   /*
    177:      Scatter ghost points to local vector,using the 2-step process
    178:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    179:      By placing code between these two statements, computations can be
    180:      done while messages are in transition.
    181:   */
    182:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
    183:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

    185:   /* Get pointers to vector data */
    186:   DMDAVecGetArray(da,localU,&uarray);
    187:   DMDAVecGetArray(da,F,&f);
    188:   DMDAVecGetArray(da,Udot,&udot);

    190:   /* Get local grid boundaries */
    191:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    193:   /* Compute function over the locally owned part of the grid */
    194:   for (j=ys; j<ys+ym; j++) {
    195:     for (i=xs; i<xs+xm; i++) {
    196:       /* Boundary conditions */
    197:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
    198:         if (user->boundary == 0) { /* Drichlet BC */
    199:           f[j][i] = uarray[j][i]; /* F = U */
    200:         } else {                  /* Neumann BC */
    201:           if (i == 0 && j == 0) {              /* SW corner */
    202:             f[j][i] = uarray[j][i] - uarray[j+1][i+1];
    203:           } else if (i == Mx-1 && j == 0) {    /* SE corner */
    204:             f[j][i] = uarray[j][i] - uarray[j+1][i-1];
    205:           } else if (i == 0 && j == My-1) {    /* NW corner */
    206:             f[j][i] = uarray[j][i] - uarray[j-1][i+1];
    207:           } else if (i == Mx-1 && j == My-1) { /* NE corner */
    208:             f[j][i] = uarray[j][i] - uarray[j-1][i-1];
    209:           } else if (i == 0) {                  /* Left */
    210:             f[j][i] = uarray[j][i] - uarray[j][i+1];
    211:           } else if (i == Mx-1) {               /* Right */
    212:             f[j][i] = uarray[j][i] - uarray[j][i-1];
    213:           } else if (j == 0) {                 /* Bottom */
    214:             f[j][i] = uarray[j][i] - uarray[j+1][i];
    215:           } else if (j == My-1) {               /* Top */
    216:             f[j][i] = uarray[j][i] - uarray[j-1][i];
    217:           }
    218:         }
    219:       } else { /* Interior */
    220:         u = uarray[j][i];
    221:         /* 5-point stencil */
    222:         uxx = (-2.0*u + uarray[j][i-1] + uarray[j][i+1]);
    223:         uyy = (-2.0*u + uarray[j-1][i] + uarray[j+1][i]);
    224:         if (user->nstencilpts == 9) {
    225:           /* 9-point stencil: assume hx=hy */
    226:           uxx = 2.0*uxx/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0;
    227:           uyy = 2.0*uyy/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0;
    228:         }
    229:         f[j][i] = udot[j][i] - (uxx*sx + uyy*sy);
    230:       }
    231:     }
    232:   }

    234:   /* Restore vectors */
    235:   DMDAVecRestoreArray(da,localU,&uarray);
    236:   DMDAVecRestoreArray(da,F,&f);
    237:   DMDAVecRestoreArray(da,Udot,&udot);
    238:   DMRestoreLocalVector(da,&localU);
    239:   PetscLogFlops(11.0*ym*xm);
    240:   return(0);
    241: }

    243: /* --------------------------------------------------------------------- */
    244: /*
    245:   FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot
    246:   This routine is not used with option '-use_coloring'
    247: */
    250: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
    251: {
    253:   PetscInt       i,j,Mx,My,xs,ys,xm,ym,nc;
    254:   AppCtx         *user = (AppCtx*)ctx;
    255:   DM             da    = (DM)user->da;
    256:   MatStencil     col[5],row;
    257:   PetscScalar    vals[5],hx,hy,sx,sy;

    260:   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);
    261:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

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

    266:   for (j=ys; j<ys+ym; j++) {
    267:     for (i=xs; i<xs+xm; i++) {
    268:       nc    = 0;
    269:       row.j = j; row.i = i;
    270:       if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) {
    271:         col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;

    273:       } else if (user->boundary > 0 && i == 0) {  /* Left Neumann */
    274:         col[nc].j = j; col[nc].i = i;   vals[nc++] = 1.0;
    275:         col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0;
    276:       } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
    277:         col[nc].j = j; col[nc].i = i;   vals[nc++] = 1.0;
    278:         col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0;
    279:       } else if (user->boundary > 0 && j == 0) {  /* Bottom Neumann */
    280:         col[nc].j = j;   col[nc].i = i; vals[nc++] = 1.0;
    281:         col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0;
    282:       } else if (user->boundary > 0 && j == My-1) { /* Top Neumann */
    283:         col[nc].j = j;   col[nc].i = i;  vals[nc++] = 1.0;
    284:         col[nc].j = j-1; col[nc].i = i;  vals[nc++] = -1.0;
    285:       } else {   /* Interior */
    286:         col[nc].j = j-1; col[nc].i = i;   vals[nc++] = -sy;
    287:         col[nc].j = j;   col[nc].i = i-1; vals[nc++] = -sx;
    288:         col[nc].j = j;   col[nc].i = i;   vals[nc++] = 2.0*(sx + sy) + a;
    289:         col[nc].j = j;   col[nc].i = i+1; vals[nc++] = -sx;
    290:         col[nc].j = j+1; col[nc].i = i;   vals[nc++] = -sy;
    291:       }
    292:       MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,INSERT_VALUES);
    293:     }
    294:   }
    295:   MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);
    296:   MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);
    297:   if (*J != *Jpre) {
    298:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
    299:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
    300:   }

    302:   if (user->viewJacobian) {
    303:     PetscPrintf(PetscObjectComm((PetscObject)*Jpre),"Jpre:\n");
    304:     MatView(*Jpre,PETSC_VIEWER_STDOUT_WORLD);
    305:   }
    306:   return(0);
    307: }

    309: /* ------------------------------------------------------------------- */
    312: PetscErrorCode FormInitialSolution(Vec U,void *ptr)
    313: {
    314:   AppCtx         *user=(AppCtx*)ptr;
    315:   DM             da   =user->da;
    316:   PetscReal      c    =user->c;
    318:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
    319:   PetscScalar    **u;
    320:   PetscReal      hx,hy,x,y,r;

    323:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
    324:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    326:   hx = 1.0/(PetscReal)(Mx-1);
    327:   hy = 1.0/(PetscReal)(My-1);

    329:   /* Get pointers to vector data */
    330:   DMDAVecGetArray(da,U,&u);

    332:   /* Get local grid boundaries */
    333:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

    335:   /* Compute function over the locally owned part of the grid */
    336:   for (j=ys; j<ys+ym; j++) {
    337:     y = j*hy;
    338:     for (i=xs; i<xs+xm; i++) {
    339:       x = i*hx;
    340:       r = PetscSqrtScalar((x-.5)*(x-.5) + (y-.5)*(y-.5));
    341:       if (r < .125) u[j][i] = PetscExpScalar(c*r*r*r);
    342:       else u[j][i] = 0.0;
    343:     }
    344:   }

    346:   /* Restore vectors */
    347:   DMDAVecRestoreArray(da,U,&u);
    348:   return(0);
    349: }