Actual source code: ex5s.c

      2: static char help[] = "2d Bratu problem in shared memory parallel with SNES.\n\
      3: We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
      4: domain, uses SHARED MEMORY to evaluate the user function.\n\
      5: The command line options include:\n\
      6:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
      7:      problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
      8:   -mx <xg>, where <xg> = number of grid points in the x-direction\n\
      9:   -my <yg>, where <yg> = number of grid points in the y-direction\n\
     10:   -use_fortran_function: use Fortran coded function, rather than C\n";

     12: /*
     13:              This code compiles ONLY on SGI systems
     14:             ========================================
     15: */
     16: /*T
     17:    Concepts: SNES^parallel Bratu example
     18:    Concepts: shared memory
     19:    Processors: n
     20: T*/

     22: /*

     24:      Programming model: Combination of
     25:         1) MPI message passing for PETSc routines
     26:         2) automatic loop parallism (using shared memory) for user
     27:            provided function.

     29:        While the user function is being evaluated all MPI processes except process
     30:      0 blocks. Process zero spawns nt threads to evaluate the user function. Once
     31:      the user function is complete, the worker threads are suspended and all the MPI processes
     32:      continue.

     34:      Other useful options:

     36:        -snes_mf : use matrix free operator and no preconditioner
     37:        -snes_mf_operator : use matrix free operator but compute Jacobian via
     38:                            finite differences to form preconditioner

     40:        Environmental variable:

     42:          setenv MPC_NUM_THREADS nt <- set number of threads processor 0 should
     43:                                       use to evaluate user provided function

     45:        Note: The number of MPI processes (set with the mpirun option -np) can
     46:        be set completely independently from the number of threads process 0
     47:        uses to evaluate the function (though usually one would make them the same).
     48: */
     49:
     50: /* ------------------------------------------------------------------------

     52:     Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     53:     the partial differential equation
     54:
     55:             -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
     56:
     57:     with boundary conditions
     58:
     59:              u = 0  for  x = 0, x = 1, y = 0, y = 1.
     60:
     61:     A finite difference approximation with the usual 5-point stencil
     62:     is used to discretize the boundary value problem to obtain a nonlinear
     63:     system of equations.

     65:     The uniprocessor version of this code is snes/examples/tutorials/ex4.c
     66:     A parallel distributed memory version is snes/examples/tutorials/ex5.c and ex5f.F

     68:   ------------------------------------------------------------------------- */

     70: /*
     71:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     72:    file automatically includes:
     73:      petsc.h       - base PETSc routines   petscvec.h - vectors
     74:      petscsys.h    - system routines       petscmat.h - matrices
     75:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     76:      petscviewer.h - viewers               petscpc.h  - preconditioners
     77:      petscksp.h   - linear solvers
     78: */
     79:  #include petscsnes.h

     81: /*
     82:    User-defined application context - contains data needed by the
     83:    application-provided call-back routines   FormFunction().
     84: */
     85: typedef struct {
     86:    PetscReal   param;          /* test problem parameter */
     87:    int         mx,my;          /* discretization in x, y directions */
     88:    int         rank;           /* processor rank */
     89: } AppCtx;

     91: /*
     92:    User-defined routines
     93: */

     99: /*
    100:     The main program is written in C while the user provided function
    101:  is given in both Fortran and C. The main program could also be written
    102:  in Fortran; the ONE PROBLEM is that VecGetArray() cannot be called from
    103:  Fortran on the SGI machines; thus the routine FormFunctionFortran() must
    104:  be written in C.
    105: */
    106: int main(int argc,char **argv)
    107: {
    108:   SNES           snes;                /* nonlinear solver */
    109:   Vec            x,r;                 /* solution, residual vectors */
    110:   AppCtx         user;                /* user-defined work context */
    111:   int            its;                 /* iterations for convergence */
    112:   int            N,ierr,rstart,rend,*colors,i,ii,ri,rj;
    113:   PetscErrorCode (*fnc)(SNES,Vec,Vec,void*);
    114:   PetscReal      bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
    115:   MatFDColoring  fdcoloring;
    116:   ISColoring     iscoloring;
    117:   Mat            J;
    118:   PetscScalar    zero = 0.0;
    119:   PetscTruth     flg;

    121:   PetscInitialize(&argc,&argv,(char *)0,help);
    122:   MPI_Comm_rank(PETSC_COMM_WORLD,&user.rank);

    124:   /*
    125:      Initialize problem parameters
    126:   */
    127:   user.mx = 4; user.my = 4; user.param = 6.0;
    128:   PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,PETSC_NULL);
    129:   PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,PETSC_NULL);
    130:   PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
    131:   if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
    132:     SETERRQ(1,"Lambda is out of range");
    133:   }
    134:   N = user.mx*user.my;

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:      Create nonlinear solver context
    138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    140:   SNESCreate(PETSC_COMM_WORLD,&snes);

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:      Create vector data structures; set function evaluation routine
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    146:   /*
    147:       The routine VecCreateShared() creates a parallel vector with each processor
    148:     assigned its own segment, BUT, in addition, the first processor has access to the
    149:     entire array. This is to allow the users function to be based on loop level
    150:     parallelism rather than MPI.
    151:   */
    152:   VecCreateShared(PETSC_COMM_WORLD,PETSC_DECIDE,N,&x);
    153:   VecDuplicate(x,&r);

    155:   PetscOptionsHasName(PETSC_NULL,"-use_fortran_function",&flg);
    156:   if (flg) {
    157:     fnc = FormFunctionFortran;
    158:   } else {
    159:     fnc = FormFunction;
    160:   }

    162:   /*
    163:      Set function evaluation routine and vector
    164:   */
    165:   SNESSetFunction(snes,r,fnc,&user);

    167:   /*
    168:        Currently when using VecCreateShared() and using loop level parallelism
    169:     to automatically parallelise the user function it makes no sense for the
    170:     Jacobian to be computed via loop level parallelism, because all the threads
    171:     would be simultaneously calling MatSetValues() causing a bottle-neck.

    173:     Thus this example uses the PETSc Jacobian calculations via finite differencing
    174:     to approximate the Jacobian
    175:   */

    177:   /*

    179:   */
    180:   VecGetOwnershipRange(r,&rstart,&rend);
    181:   PetscMalloc((rend-rstart)*sizeof(PetscInt),&colors);
    182:   for (i=rstart; i<rend; i++) {
    183:     colors[i - rstart] = 3*((i/user.mx) % 3) + (i % 3);
    184:   }
    185:   ISColoringCreate(PETSC_COMM_WORLD,rend-rstart,colors,&iscoloring);
    186:   PetscFree(colors);

    188:   /*
    189:      Create and set the nonzero pattern for the Jacobian: This is not done
    190:      particularly efficiently. One should process the boundary nodes seperately and
    191:      then use a simple loop for the interior nodes.
    192:        Note that for this code we use the "natural" number of the nodes on the
    193:      grid (since that is what is good for the user provided function). In the
    194:      DA examples we must use the DA numbering where each processor is assigned a
    195:      chunk of data.
    196:   */
    197:   MatCreateMPIAIJ(PETSC_COMM_WORLD,rend-rstart,rend-rstart,N,
    198:                          N,5,0,0,0,&J);
    199:   for (i=rstart; i<rend; i++) {
    200:     rj = i % user.mx;         /* column in grid */
    201:     ri = i / user.mx;         /* row in grid */
    202:     if (ri != 0) {     /* first row does not have neighbor below */
    203:       ii   = i - user.mx;
    204:       MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
    205:     }
    206:     if (ri != user.my - 1) { /* last row does not have neighbors above */
    207:       ii   = i + user.mx;
    208:       MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
    209:     }
    210:     if (rj != 0) {     /* first column does not have neighbor to left */
    211:       ii   = i - 1;
    212:       MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
    213:     }
    214:     if (rj != user.mx - 1) {     /* last column does not have neighbor to right */
    215:       ii   = i + 1;
    216:       MatSetValues(J,1,&i,1,&ii,&zero,INSERT_VALUES);
    217:     }
    218:     MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);
    219:   }
    220:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    221:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

    223:   /*
    224:        Create the data structure that SNESDefaultComputeJacobianColor() uses
    225:        to compute the actual Jacobians via finite differences.
    226:   */
    227:   MatFDColoringCreate(J,iscoloring,&fdcoloring);
    228:   MatFDColoringSetFunction(fdcoloring,(PetscErrorCode (*)(void))fnc,&user);
    229:   MatFDColoringSetFromOptions(fdcoloring);
    230:   /*
    231:         Tell SNES to use the routine SNESDefaultComputeJacobianColor()
    232:       to compute Jacobians.
    233:   */
    234:   SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor,fdcoloring);
    235:   ISColoringDestroy(iscoloring);

    238:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    239:      Customize nonlinear solver; set runtime options
    240:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    242:   /*
    243:      Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
    244:   */
    245:   SNESSetFromOptions(snes);

    247:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    248:      Evaluate initial guess; then solve nonlinear system
    249:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    250:   /*
    251:      Note: The user should initialize the vector, x, with the initial guess
    252:      for the nonlinear solver prior to calling SNESSolve().  In particular,
    253:      to employ an initial guess of zero, the user should explicitly set
    254:      this vector to zero by calling VecSet().
    255:   */
    256:   FormInitialGuess(&user,x);
    257:   SNESSolve(snes,PETSC_NULL,x);
    258:   SNESGetIterationNumber(snes,&its);
    259:   PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);

    261:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    262:      Free work space.  All PETSc objects should be destroyed when they
    263:      are no longer needed.
    264:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    265:   VecDestroy(x);
    266:   VecDestroy(r);
    267:   SNESDestroy(snes);
    268:   PetscFinalize();

    270:   return 0;
    271: }
    272: /* ------------------------------------------------------------------- */

    276: /*
    277:    FormInitialGuess - Forms initial approximation.

    279:    Input Parameters:
    280:    user - user-defined application context
    281:    X - vector

    283:    Output Parameter:
    284:    X - vector
    285:  */
    286: int FormInitialGuess(AppCtx *user,Vec X)
    287: {
    288:   int          i,j,row,mx,my,ierr;
    289:   PetscReal    one = 1.0,lambda,temp1,temp,hx,hy,hxdhy,hydhx,sc;
    290:   PetscScalar  *x;

    292:   /*
    293:       Process 0 has to wait for all other processes to get here
    294:    before proceeding to write in the shared vector
    295:   */
    296:   PetscBarrier((PetscObject)X);
    297:   if (user->rank) {
    298:      /*
    299:         All the non-busy processors have to wait here for process 0 to finish
    300:         evaluating the function; otherwise they will start using the vector values
    301:         before they have been computed
    302:      */
    303:      PetscBarrier((PetscObject)X);
    304:      return 0;
    305:   }

    307:   mx = user->mx;            my = user->my;            lambda = user->param;
    308:   hx = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
    309:   sc = hx*hy*lambda;        hxdhy = hx/hy;            hydhx = hy/hx;
    310:   temp1 = lambda/(lambda + one);

    312:   /*
    313:      Get a pointer to vector data.
    314:        - For default PETSc vectors, VecGetArray() returns a pointer to
    315:          the data array.  Otherwise, the routine is implementation dependent.
    316:        - You MUST call VecRestoreArray() when you no longer need access to
    317:          the array.
    318:   */
    319:   VecGetArray(X,&x);

    321:   /*
    322:      Compute initial guess over the locally owned part of the grid
    323:   */
    324: #pragma arl(4)
    325: #pragma distinct (*x,*f)
    326: #pragma no side effects (sqrt)
    327:   for (j=0; j<my; j++) {
    328:     temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
    329:     for (i=0; i<mx; i++) {
    330:       row = i + j*mx;
    331:       if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
    332:         x[row] = 0.0;
    333:         continue;
    334:       }
    335:       x[row] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
    336:     }
    337:   }

    339:   /*
    340:      Restore vector
    341:   */
    342:   VecRestoreArray(X,&x);

    344:   PetscBarrier((PetscObject)X);
    345:   return 0;
    346: }
    347: /* ------------------------------------------------------------------- */
    350: /*
    351:    FormFunction - Evaluates nonlinear function, F(x).

    353:    Input Parameters:
    354: .  snes - the SNES context
    355: .  X - input vector
    356: .  ptr - optional user-defined context, as set by SNESSetFunction()

    358:    Output Parameter:
    359: .  F - function vector
    360:  */
    361: int FormFunction(SNES snes,Vec X,Vec F,void *ptr)
    362: {
    363:   AppCtx       *user = (AppCtx*)ptr;
    364:   int          ierr,i,j,row,mx,my;
    365:   PetscReal    two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
    366:   PetscScalar  u,uxx,uyy,*x,*f;

    368:   /*
    369:       Process 0 has to wait for all other processes to get here
    370:    before proceeding to write in the shared vector
    371:   */
    372:   PetscBarrier((PetscObject)X);

    374:   if (user->rank) {
    375:      /*
    376:         All the non-busy processors have to wait here for process 0 to finish
    377:         evaluating the function; otherwise they will start using the vector values
    378:         before they have been computed
    379:      */
    380:      PetscBarrier((PetscObject)X);
    381:      return 0;
    382:   }

    384:   mx = user->mx;            my = user->my;            lambda = user->param;
    385:   hx = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
    386:   sc = hx*hy*lambda;        hxdhy = hx/hy;            hydhx = hy/hx;

    388:   /*
    389:      Get pointers to vector data
    390:   */
    391:   VecGetArray(X,&x);
    392:   VecGetArray(F,&f);

    394:   /*
    395:       The next line tells the SGI compiler that x and f contain no overlapping
    396:     regions and thus it can use addition optimizations.
    397:   */
    398: #pragma arl(4)
    399: #pragma distinct (*x,*f)
    400: #pragma no side effects (exp)

    402:   /*
    403:      Compute function over the entire  grid
    404:   */
    405:   for (j=0; j<my; j++) {
    406:     for (i=0; i<mx; i++) {
    407:       row = i + j*mx;
    408:       if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
    409:         f[row] = x[row];
    410:         continue;
    411:       }
    412:       u = x[row];
    413:       uxx = (two*u - x[row-1] - x[row+1])*hydhx;
    414:       uyy = (two*u - x[row-mx] - x[row+mx])*hxdhy;
    415:       f[row] = uxx + uyy - sc*exp(u);
    416:     }
    417:   }

    419:   /*
    420:      Restore vectors
    421:   */
    422:   VecRestoreArray(X,&x);
    423:   VecRestoreArray(F,&f);

    425:   PetscLogFlops(11*(mx-2)*(my-2))
    426:   PetscBarrier((PetscObject)X);
    427:   return 0;
    428: }

    430: #if defined(PETSC_HAVE_FORTRAN_CAPS)
    431: #define applicationfunctionfortran_ APPLICATIONFUNCTIONFORTRAN
    432: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
    433: #define applicationfunctionfortran_ applicationfunctionfortran
    434: #endif

    436: /* ------------------------------------------------------------------- */
    439: /*
    440:    FormFunctionFortran - Evaluates nonlinear function, F(x) in Fortran.

    442: */
    443: int FormFunctionFortran(SNES snes,Vec X,Vec F,void *ptr)
    444: {
    445:   AppCtx  *user = (AppCtx*)ptr;
    446:   int     ierr;
    447:   PetscScalar  *x,*f;

    449:   /*
    450:       Process 0 has to wait for all other processes to get here
    451:    before proceeding to write in the shared vector
    452:   */
    453:   PetscBarrier((PetscObject)snes);
    454:   if (!user->rank) {
    455:     VecGetArray(X,&x);
    456:     VecGetArray(F,&f);
    457:     applicationfunctionfortran_(&user->param,&user->mx,&user->my,x,f,&ierr);
    458:     VecRestoreArray(X,&x);
    459:     VecRestoreArray(F,&f);
    460:     PetscLogFlops(11*(user->mx-2)*(user->my-2))
    461:   }
    462:   /*
    463:       All the non-busy processors have to wait here for process 0 to finish
    464:       evaluating the function; otherwise they will start using the vector values
    465:       before they have been computed
    466:   */
    467:   PetscBarrier((PetscObject)snes);
    468:   return 0;
    469: }