Date: 2022-03-04T17:39:26+00:00

Actual source code: ex46.c

      1: static char help[] = "Surface processes in geophysics.\n\n";

      3: /*T
      4:    Concepts: SNES^parallel Surface process example
      5:    Concepts: DMDA^using distributed arrays;
      6:    Concepts: IS coloirng types;
      7:    Processors: n
      8: T*/

     10: #include <petscsnes.h>
     11: #include <petscdm.h>
     12: #include <petscdmda.h>

     14: /*
     15:    User-defined application context - contains data needed by the
     16:    application-provided call-back routines, FormJacobianLocal() and
     17:    FormFunctionLocal().
     18: */
     19: typedef struct {
     20:   PetscReal   D;  /* The diffusion coefficient */
     21:   PetscReal   K;  /* The advection coefficient */
     22:   PetscInt    m;  /* Exponent for A */
     23: } AppCtx;

     25: /*
     26:    User-defined routines
     27: */
     28: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
     29: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);

     31: int main(int argc,char **argv)
     32: {
     33:   SNES           snes;                         /* nonlinear solver */
     34:   AppCtx         user;                         /* user-defined work context */
     35:   PetscInt       its;                          /* iterations for convergence */
     37:   DM             da;

     39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     40:      Initialize program
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     43:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     46:      Initialize problem parameters
     47:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     48:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
     49:   user.D = 1.0;
     50:   PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
     51:   user.K = 1.0;
     52:   PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
     53:   user.m = 1;
     54:   PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
     55:   PetscOptionsEnd();

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:      Create distributed array (DMDA) to manage parallel grid and vectors
     59:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     60:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     61:   DMSetFromOptions(da);
     62:   DMSetUp(da);
     63:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
     64:   DMSetApplicationContext(da,&user);
     65:   SNESCreate(PETSC_COMM_WORLD, &snes);
     66:   SNESSetDM(snes, da);

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:      Set local function evaluation routine
     70:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     71:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:      Customize solver; set runtime options
     75:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     76:   SNESSetFromOptions(snes);

     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:      Solve nonlinear system
     80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     81:   SNESSolve(snes,0,0);
     82:   SNESGetIterationNumber(snes,&its);

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     86:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:      Free work space.  All PETSc objects should be destroyed when they
     90:      are no longer needed.
     91:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     93:   SNESDestroy(&snes);
     94:   DMDestroy(&da);

     96:   PetscFinalize();
     97:   return ierr;
     98: }

    100: PetscScalar funcU(DMDACoor2d *coords)
    101: {
    102:   return coords->x + coords->y;
    103: }

    105: PetscScalar funcA(PetscScalar z, AppCtx *user)
    106: {
    107:   PetscScalar v = 1.0;
    108:   PetscInt    i;

    110:   for (i = 0; i < user->m; ++i) v *= z;
    111:   return v;
    112: }

    114: PetscScalar funcADer(PetscScalar z, AppCtx *user)
    115: {
    116:   PetscScalar v = 1.0;
    117:   PetscInt    i;

    119:   for (i = 0; i < user->m-1; ++i) v *= z;
    120:   return (PetscScalar)user->m*v;
    121: }

    123: /*
    124:    FormFunctionLocal - Evaluates nonlinear function, F(x).
    125: */
    126: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
    127: {
    128:   DM             coordDA;
    129:   Vec            coordinates;
    130:   DMDACoor2d     **coords;
    131:   PetscScalar    u, ux, uy, uxx, uyy;
    132:   PetscReal      D, K, hx, hy, hxdhy, hydhx;
    133:   PetscInt       i,j;

    137:   D     = user->D;
    138:   K     = user->K;
    139:   hx    = 1.0/(PetscReal)(info->mx-1);
    140:   hy    = 1.0/(PetscReal)(info->my-1);
    141:   hxdhy = hx/hy;
    142:   hydhx = hy/hx;
    143:   /*
    144:      Compute function over the locally owned part of the grid
    145:   */
    146:   DMGetCoordinateDM(info->da, &coordDA);
    147:   DMGetCoordinates(info->da, &coordinates);
    148:   DMDAVecGetArray(coordDA, coordinates, &coords);
    149:   for (j=info->ys; j<info->ys+info->ym; j++) {
    150:     for (i=info->xs; i<info->xs+info->xm; i++) {
    151:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
    152:       else {
    153:         u       = x[j][i];
    154:         ux      = (x[j][i+1] - x[j][i])/hx;
    155:         uy      = (x[j+1][i] - x[j][i])/hy;
    156:         uxx     = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
    157:         uyy     = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
    158:         f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
    159:         if (PetscIsInfOrNanScalar(f[j][i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(f[j][i]));
    160:       }
    161:     }
    162:   }
    163:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
    164:   PetscLogFlops(11.0*info->ym*info->xm);
    165:   return(0);
    166: }

    168: /*
    169:    FormJacobianLocal - Evaluates Jacobian matrix.
    170: */
    171: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
    172: {
    173:   MatStencil     col[5], row;
    174:   PetscScalar    D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
    175:   PetscReal      normGradZ;
    176:   PetscInt       i, j,k;

    180:   D     = user->D;
    181:   K     = user->K;
    182:   hx    = 1.0/(PetscReal)(info->mx-1);
    183:   hy    = 1.0/(PetscReal)(info->my-1);
    184:   hxdhy = hx/hy;
    185:   hydhx = hy/hx;

    187:   /*
    188:      Compute entries for the locally owned part of the Jacobian.
    189:       - Currently, all PETSc parallel matrix formats are partitioned by
    190:         contiguous chunks of rows across the processors.
    191:       - Each processor needs to insert only elements that it owns
    192:         locally (but any non-local elements will be sent to the
    193:         appropriate processor during matrix assembly).
    194:       - Here, we set all entries for a particular row at once.
    195:       - We can set matrix entries either using either
    196:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    197:   */
    198:   for (j=info->ys; j<info->ys+info->ym; j++) {
    199:     for (i=info->xs; i<info->xs+info->xm; i++) {
    200:       row.j = j; row.i = i;
    201:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    202:         /* boundary points */
    203:         v[0] = 1.0;
    204:         MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    205:       } else {
    206:         /* interior grid points */
    207:         ux        = (x[j][i+1] - x[j][i])/hx;
    208:         uy        = (x[j+1][i] - x[j][i])/hy;
    209:         normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
    210:         if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
    211:         A = funcA(x[j][i], user);

    213:         v[0] = -D*hxdhy;                                                                          col[0].j = j - 1; col[0].i = i;
    214:         v[1] = -D*hydhx;                                                                          col[1].j = j;     col[1].i = i-1;
    215:         v[2] = D*2.0*(hydhx + hxdhy) + K*(funcADer(x[j][i], user)*normGradZ - A/normGradZ)*hx*hy; col[2].j = row.j; col[2].i = row.i;
    216:         v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ);                                              col[3].j = j;     col[3].i = i+1;
    217:         v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ);                                              col[4].j = j + 1; col[4].i = i;
    218:         for (k = 0; k < 5; ++k) {
    219:           if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(v[k]));
    220:         }
    221:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    222:       }
    223:     }
    224:   }

    226:   /*
    227:      Assemble matrix, using the 2-step process:
    228:        MatAssemblyBegin(), MatAssemblyEnd().
    229:   */
    230:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    231:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    232:   /*
    233:      Tell the matrix we will never add a new nonzero location to the
    234:      matrix. If we do, it will generate an error.
    235:   */
    236:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    237:   return(0);
    238: }

    240: /*TEST

    242:    test:
    243:       args: -snes_view -snes_monitor_short -da_refine 1 -pc_type mg -ksp_type fgmres -pc_mg_type full -mg_levels_ksp_chebyshev_esteig 0.5,1.1

    245:    test:
    246:       suffix: ew_1
    247:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 1
    248:       requires: !single

    250:    test:
    251:       suffix: ew_2
    252:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 2

    254:    test:
    255:       suffix: ew_3
    256:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 3
    257:       requires: !single

    259:    test:
    260:       suffix: fm_rise_2
    261:       args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 1 -snes_ngmres_restart_fm_rise
    262:       requires: !single

    264:    test:
    265:       suffix: fm_rise_4
    266:       args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 2 -snes_ngmres_restart_fm_rise -snes_rtol 1.e-2 -snes_max_it 5

    268: TEST*/