Date: 2021-03-03T22:27:56+00:00

Actual source code: ex15.c
petsc-3.14.5 2021-03-03
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      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 <petscdm.h>
     25: #include <petscdmda.h>
     26: #include <petscts.h>

     28: /*
     29:    User-defined data structures and routines
     30: */

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

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

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

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

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

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:      Create distributed array (DMDA) to manage parallel grid and vectors
     74:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     75:   if (user.nstencilpts == 5) {
     76:     DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     77:   } else if (user.nstencilpts == 9) {
     78:     DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     79:   } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
     80:   DMSetFromOptions(da);
     81:   DMSetUp(da);
     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:   TSSetMaxTime(ts,1.0);
     99:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);

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

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:    Set Jacobian evaluation routine
    111:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    112:   DMSetMatType(da,MATAIJ);
    113:   DMCreateMatrix(da,&J);
    114:   Jtype = 0;
    115:   PetscOptionsGetInt(NULL,NULL, "-Jtype",&Jtype,NULL);
    116:   if (Jtype == 0) { /* use user provided Jacobian evaluation routine */
    117:     if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts);
    118:     TSSetIJacobian(ts,J,J,FormIJacobian,&user);
    119:   } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */
    120:     TSGetSNES(ts,&snes);
    121:     MatCreateSNESMF(snes,&Jmf);
    122:     if (Jtype == 1) { /* slow finite difference J; */
    123:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);
    124:     } else if (Jtype == 2) { /* Use coloring to compute  finite difference J efficiently */
    125:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);
    126:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported");
    127:   }

    129:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:    Sets various TS parameters from user options
    131:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    132:   TSSetFromOptions(ts);

    134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    135:      Solve nonlinear system
    136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    137:   TSSolve(ts,u);

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

    149:   PetscFinalize();
    150:   return ierr;
    151: }

    153: /* --------------------------------------------------------------------- */
    154: /*
    155:   FormIFunction = Udot - RHSFunction
    156: */
    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,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

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

    175:   /*
    176:      Scatter ghost points to local vector,using the 2-step process
    177:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    178:      By placing code between these two statements, computations can be
    179:      done while messages are in transition.
    180:   */
    181:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
    182:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

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

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

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

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

    242: /* --------------------------------------------------------------------- */
    243: /*
    244:   FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot
    245:   This routine is not used with option '-use_coloring'
    246: */
    247: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
    248: {
    250:   PetscInt       i,j,Mx,My,xs,ys,xm,ym,nc;
    251:   AppCtx         *user = (AppCtx*)ctx;
    252:   DM             da    = (DM)user->da;
    253:   MatStencil     col[5],row;
    254:   PetscScalar    vals[5],hx,hy,sx,sy;

    257:   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);
    258:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

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

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

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

    299:   if (user->viewJacobian) {
    300:     PetscPrintf(PetscObjectComm((PetscObject)Jpre),"Jpre:\n");
    301:     MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);
    302:   }
    303:   return(0);
    304: }

    306: /* ------------------------------------------------------------------- */
    307: PetscErrorCode FormInitialSolution(Vec U,void *ptr)
    308: {
    309:   AppCtx         *user=(AppCtx*)ptr;
    310:   DM             da   =user->da;
    311:   PetscReal      c    =user->c;
    313:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
    314:   PetscScalar    **u;
    315:   PetscReal      hx,hy,x,y,r;

    318:   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);

    320:   hx = 1.0/(PetscReal)(Mx-1);
    321:   hy = 1.0/(PetscReal)(My-1);

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

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

    329:   /* Compute function over the locally owned part of the grid */
    330:   for (j=ys; j<ys+ym; j++) {
    331:     y = j*hy;
    332:     for (i=xs; i<xs+xm; i++) {
    333:       x = i*hx;
    334:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
    335:       if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
    336:       else u[j][i] = 0.0;
    337:     }
    338:   }

    340:   /* Restore vectors */
    341:   DMDAVecRestoreArray(da,U,&u);
    342:   return(0);
    343: }

    345: /*TEST

    347:     test:
    348:       args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -ts_monitor

    350:     test:
    351:       suffix: 2
    352:       args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 2 -ts_monitor

    354:     test:
    355:       suffix: 3
    356:       requires: !single
    357:       args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor

    359:     test:
    360:       suffix: 4
    361:       requires: !single
    362:       nsize: 2
    363:       args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor

    365:     test:
    366:       suffix: 5
    367:       nsize: 1
    368:       args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 1 -ts_monitor

    371: TEST*/