Date: 2022-08-02T03:14:56+00:00

Actual source code: ex78.c

      2: static char help[] = "Newton methods to solve u''  = f in parallel with periodic boundary conditions.\n\n";

      4: /*
      5:    Compare this example to ex3.c that handles Dirichlet boundary conditions

      7:    Though this is a linear problem it is treated as a nonlinear problem in this example to demonstrate
      8:    handling periodic boundary conditions for nonlinear problems.

     10:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     11:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     12:    file automatically includes:
     13:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     14:      petscmat.h - matrices
     15:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     16:      petscviewer.h - viewers               petscpc.h  - preconditioners
     17:      petscksp.h   - linear solvers
     18: */

     20: #include <petscdm.h>
     21: #include <petscdmda.h>
     22: #include <petscsnes.h>

     24: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
     25: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);

     27: int main(int argc,char **argv)
     28: {
     29:   SNES           snes;                 /* SNES context */
     30:   Mat            J;                    /* Jacobian matrix */
     31:   DM             da;
     32:   Vec            x,r;              /* vectors */
     33:   PetscInt       N = 5;
     34:   MatNullSpace   constants;

     36:   PetscInitialize(&argc,&argv,(char*)0,help);
     37:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);

     39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     40:      Create nonlinear solver context
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     43:   SNESCreate(PETSC_COMM_WORLD,&snes);

     45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     46:      Create vector data structures; set function evaluation routine
     47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     49:   /*
     50:      Create distributed array (DMDA) to manage parallel grid and vectors
     51:   */
     52:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,N,1,1,NULL,&da);
     53:   DMSetFromOptions(da);
     54:   DMSetUp(da);

     56:   /*
     57:      Extract global and local vectors from DMDA; then duplicate for remaining
     58:      vectors that are the same types
     59:   */
     60:   DMCreateGlobalVector(da,&x);
     61:   VecDuplicate(x,&r);

     63:   /*
     64:      Set function evaluation routine and vector.  Whenever the nonlinear
     65:      solver needs to compute the nonlinear function, it will call this
     66:      routine.
     67:       - Note that the final routine argument is the user-defined
     68:         context that provides application-specific data for the
     69:         function evaluation routine.
     70:   */
     71:   SNESSetFunction(snes,r,FormFunction,da);

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:      Create matrix data structure; set Jacobian evaluation routine
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     76:   DMCreateMatrix(da,&J);
     77:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&constants);
     78:   MatSetNullSpace(J,constants);
     79:   SNESSetJacobian(snes,J,J,FormJacobian,da);

     81:   SNESSetFromOptions(snes);
     82:   SNESSolve(snes,NULL,x);

     84:   VecDestroy(&x);
     85:   VecDestroy(&r);
     86:   MatDestroy(&J);
     87:   MatNullSpaceDestroy(&constants);
     88:   SNESDestroy(&snes);
     89:   DMDestroy(&da);
     90:   PetscFinalize();
     91:   return 0;
     92: }

     94: /*
     95:    FormFunction - Evaluates nonlinear function, F(x).

     97:    Input Parameters:
     98: .  snes - the SNES context
     99: .  x - input vector
    100: .  ctx - optional user-defined context, as set by SNESSetFunction()

    102:    Output Parameter:
    103: .  f - function vector

    105:    Note:
    106:    The user-defined context can contain any application-specific
    107:    data needed for the function evaluation.
    108: */
    109: PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *ctx)
    110: {
    111:   DM             da    = (DM) ctx;
    112:   PetscScalar    *xx,*ff;
    113:   PetscReal      h;
    114:   PetscInt       i,M,xs,xm;
    115:   Vec            xlocal;

    118:   /* Get local work vector */
    119:   DMGetLocalVector(da,&xlocal);

    121:   /*
    122:      Scatter ghost points to local vector, using the 2-step process
    123:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
    124:      By placing code between these two statements, computations can
    125:      be done while messages are in transition.
    126:   */
    127:   DMGlobalToLocalBegin(da,x,INSERT_VALUES,xlocal);
    128:   DMGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);

    130:   /*
    131:      Get pointers to vector data.
    132:        - The vector xlocal includes ghost point; the vectors x and f do
    133:          NOT include ghost points.
    134:        - Using DMDAVecGetArray() allows accessing the values using global ordering
    135:   */
    136:   DMDAVecGetArray(da,xlocal,&xx);
    137:   DMDAVecGetArray(da,f,&ff);

    139:   /*
    140:      Get local grid boundaries (for 1-dimensional DMDA):
    141:        xs, xm  - starting grid index, width of local grid (no ghost points)
    142:   */
    143:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
    144:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

    146:   /*
    147:      Compute function over locally owned part of the grid
    148:      Note the [i-1] and [i+1] will automatically access the ghost points from other processes or the periodic points.
    149:   */
    150:   h = 1.0/M;
    151:   for (i=xs; i<xs+xm; i++) ff[i] = (xx[i-1] - 2.0*xx[i] + xx[i+1])/(h*h)  - PetscSinReal(2.0*PETSC_PI*i*h);

    153:   /*
    154:      Restore vectors
    155:   */
    156:   DMDAVecRestoreArray(da,xlocal,&xx);
    157:   DMDAVecRestoreArray(da,f,&ff);
    158:   DMRestoreLocalVector(da,&xlocal);
    159:   return 0;
    160: }
    161: /* ------------------------------------------------------------------- */
    162: /*
    163:    FormJacobian - Evaluates Jacobian matrix.

    165:    Input Parameters:
    166: .  snes - the SNES context
    167: .  x - input vector
    168: .  dummy - optional user-defined context (not used here)

    170:    Output Parameters:
    171: .  jac - Jacobian matrix
    172: .  B - optionally different preconditioning matrix
    173: .  flag - flag indicating matrix structure
    174: */
    175: PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *ctx)
    176: {
    177:   PetscScalar    *xx,A[3];
    178:   PetscInt       i,M,xs,xm;
    179:   DM             da = (DM) ctx;
    180:   MatStencil     row,cols[3];
    181:   PetscReal      h;

    184:   /*
    185:      Get pointer to vector data
    186:   */
    187:   DMDAVecGetArrayRead(da,x,&xx);
    188:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

    190:   /*
    191:     Get range of locally owned matrix
    192:   */
    193:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

    195:   MatZeroEntries(jac);
    196:   h = 1.0/M;
    197:   /* because of periodic boundary conditions we can simply loop over all local nodes and access to the left and right */
    198:   for (i=xs; i<xs+xm; i++) {
    199:     row.i = i;
    200:     cols[0].i = i - 1;
    201:     cols[1].i = i;
    202:     cols[2].i = i + 1;
    203:     A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
    204:     MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);
    205:   }

    207:   DMDAVecRestoreArrayRead(da,x,&xx);
    208:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    209:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    210:   return 0;
    211: }

    213: /*TEST

    215:    test:
    216:       args: -snes_monitor_short -ksp_monitor_short -pc_type sor -snes_converged_reason -da_refine 3
    217:       requires: !single

    219:    test:
    220:       suffix: 2
    221:       args: -snes_monitor_short -ksp_monitor_short -pc_type sor -snes_converged_reason -da_refine 3 -snes_type newtontrdc
    222:       requires: !single

    224:    test:
    225:       suffix: 3
    226:       args: -snes_monitor_short -ksp_monitor_short -pc_type sor -snes_converged_reason -da_refine 3 -snes_type newtontrdc -snes_trdc_use_cauchy false
    227:       requires: !single

    229: TEST*/