Date: 2022-03-31T04:48:21+00:00

Actual source code: ex70.c

      1: static char help[] = "------------------------------------------------------------------------------------------------------------------------------ \n\
      2:   Solves the time-dependent incompressible, variable viscosity Stokes equation in 2D driven by buouyancy variations. \n\
      3:   Time-dependence is introduced by evolving the density (rho) and viscosity (eta) according to \n\
      4:     D \\rho / Dt = 0    and    D \\eta / Dt = 0 \n\
      5:   The Stokes problem is discretized using Q1-Q1 finite elements, stabilized with Bochev's polynomial projection method. \n\
      6:   The hyperbolic evolution equation for density is discretized using a variant of the Particle-In-Cell (PIC) method. \n\
      7:   The DMDA object is used to define the FE problem, whilst DMSwarm provides support for the PIC method. \n\
      8:   Material points (particles) store density and viscosity. The particles are advected with the fluid velocity using RK1. \n\
      9:   At each time step, the value of density and viscosity stored on each particle are projected into a Q1 function space \n\
     10:   and then interpolated onto the Gauss quadrature points. \n\
     11:   The model problem defined in this example is the iso-viscous Rayleigh-Taylor instability (case 1a) from: \n\
     12:     \"A comparison of methods for the modeling of thermochemical convection\" \n\
     13:     P.E. van Keken, S.D. King, H. Schmeling, U.R. Christensen, D. Neumeister and M.-P. Doin, \n\
     14:     Journal of Geophysical Research, vol 102 (B10), 477--499 (1997) \n\
     15:   Note that whilst the model problem defined is for an iso-viscous, the implementation in this example supports \n\
     16:   variable viscoity formulations. \n\
     17:   This example is based on src/ksp/ksp/tutorials/ex43.c \n\
     18:   Options: \n\
     19:     -mx        : Number of elements in the x-direction \n\
     20:     -my        : Number of elements in the y-direction \n\
     21:     -mxy       : Number of elements in the x- and y-directions \n\
     22:     -nt        : Number of time steps \n\
     23:     -dump_freq : Frequency of output file creation \n\
     24:     -ppcell    : Number of times the reference cell is sub-divided \n\
     25:     -randomize_coords : Apply a random shift to each particle coordinate in the range [-fac*dh,0.fac*dh] \n\
     26:     -randomize_fac    : Set the scaling factor for the random shift (default = 0.25)\n";

     28: /* Contributed by Dave May */

     30: #include <petscksp.h>
     31: #include <petscdm.h>
     32: #include <petscdmda.h>
     33: #include <petscdmswarm.h>
     34: #include <petsc/private/dmimpl.h>

     36: static PetscErrorCode DMDAApplyBoundaryConditions(DM,Mat,Vec);

     38: #define NSD            2 /* number of spatial dimensions */
     39: #define NODES_PER_EL   4 /* nodes per element */
     40: #define U_DOFS         2 /* degrees of freedom per velocity node */
     41: #define P_DOFS         1 /* degrees of freedom per pressure node */
     42: #define GAUSS_POINTS   4

     44: static void EvaluateBasis_Q1(PetscScalar _xi[],PetscScalar N[])
     45: {
     46:   PetscScalar xi  = _xi[0];
     47:   PetscScalar eta = _xi[1];

     49:   N[0] = 0.25*(1.0-xi)*(1.0-eta);
     50:   N[1] = 0.25*(1.0+xi)*(1.0-eta);
     51:   N[2] = 0.25*(1.0+xi)*(1.0+eta);
     52:   N[3] = 0.25*(1.0-xi)*(1.0+eta);
     53: }

     55: static void EvaluateBasisDerivatives_Q1(PetscScalar _xi[],PetscScalar dN[][NODES_PER_EL])
     56: {
     57:   PetscScalar xi  = _xi[0];
     58:   PetscScalar eta = _xi[1];

     60:   dN[0][0] = -0.25*(1.0-eta);
     61:   dN[0][1] =  0.25*(1.0-eta);
     62:   dN[0][2] =  0.25*(1.0+eta);
     63:   dN[0][3] = -0.25*(1.0+eta);

     65:   dN[1][0] = -0.25*(1.0-xi);
     66:   dN[1][1] = -0.25*(1.0+xi);
     67:   dN[1][2] =  0.25*(1.0+xi);
     68:   dN[1][3] =  0.25*(1.0-xi);
     69: }

     71: static void EvaluateDerivatives(PetscScalar dN[][NODES_PER_EL],PetscScalar dNx[][NODES_PER_EL],PetscScalar coords[],PetscScalar *det_J)
     72: {
     73:   PetscScalar J00,J01,J10,J11,J;
     74:   PetscScalar iJ00,iJ01,iJ10,iJ11;
     75:   PetscInt    i;

     77:   J00 = J01 = J10 = J11 = 0.0;
     78:   for (i = 0; i < NODES_PER_EL; i++) {
     79:     PetscScalar cx = coords[2*i];
     80:     PetscScalar cy = coords[2*i+1];

     82:     J00 += dN[0][i]*cx;      /* J_xx = dx/dxi */
     83:     J01 += dN[0][i]*cy;      /* J_xy = dy/dxi */
     84:     J10 += dN[1][i]*cx;      /* J_yx = dx/deta */
     85:     J11 += dN[1][i]*cy;      /* J_yy = dy/deta */
     86:   }
     87:   J = (J00*J11)-(J01*J10);

     89:   iJ00 =  J11/J;
     90:   iJ01 = -J01/J;
     91:   iJ10 = -J10/J;
     92:   iJ11 =  J00/J;

     94:   for (i = 0; i < NODES_PER_EL; i++) {
     95:     dNx[0][i] = dN[0][i]*iJ00+dN[1][i]*iJ01;
     96:     dNx[1][i] = dN[0][i]*iJ10+dN[1][i]*iJ11;
     97:   }

     99:   if (det_J) *det_J = J;
    100: }

    102: static void CreateGaussQuadrature(PetscInt *ngp,PetscScalar gp_xi[][2],PetscScalar gp_weight[])
    103: {
    104:   *ngp         = 4;
    105:   gp_xi[0][0]  = -0.57735026919; gp_xi[0][1] = -0.57735026919;
    106:   gp_xi[1][0]  = -0.57735026919; gp_xi[1][1] =  0.57735026919;
    107:   gp_xi[2][0]  =  0.57735026919; gp_xi[2][1] =  0.57735026919;
    108:   gp_xi[3][0]  =  0.57735026919; gp_xi[3][1] = -0.57735026919;
    109:   gp_weight[0] = 1.0;
    110:   gp_weight[1] = 1.0;
    111:   gp_weight[2] = 1.0;
    112:   gp_weight[3] = 1.0;
    113: }

    115: static PetscErrorCode DMDAGetElementEqnums_up(const PetscInt element[],PetscInt s_u[],PetscInt s_p[])
    116: {
    117:   PetscInt i;
    119:   for (i=0; i<NODES_PER_EL; i++) {
    120:     /* velocity */
    121:     s_u[NSD*i+0] = 3*element[i];
    122:     s_u[NSD*i+1] = 3*element[i]+1;
    123:     /* pressure */
    124:     s_p[i] = 3*element[i]+2;
    125:   }
    126:   return 0;
    127: }

    129: static PetscInt map_wIwDI_uJuDJ(PetscInt wi,PetscInt wd,PetscInt w_NPE,PetscInt w_dof,PetscInt ui,PetscInt ud,PetscInt u_NPE,PetscInt u_dof)
    130: {
    131:   PetscInt ij,r,c,nc;

    133:   nc = u_NPE*u_dof;
    134:   r = w_dof*wi+wd;
    135:   c = u_dof*ui+ud;
    136:   ij = r*nc+c;
    137:   return(ij);
    138: }

    140: static void BForm_DivT(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
    141: {
    142:   PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
    143:   PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
    144:   PetscScalar J_p,tildeD[3];
    145:   PetscScalar B[3][U_DOFS*NODES_PER_EL];
    146:   PetscInt    p,i,j,k,ngp;

    148:   /* define quadrature rule */
    149:   CreateGaussQuadrature(&ngp,gp_xi,gp_weight);

    151:   /* evaluate bilinear form */
    152:   for (p = 0; p < ngp; p++) {
    153:     EvaluateBasisDerivatives_Q1(gp_xi[p],GNi_p);
    154:     EvaluateDerivatives(GNi_p,GNx_p,coords,&J_p);

    156:     for (i = 0; i < NODES_PER_EL; i++) {
    157:       PetscScalar d_dx_i = GNx_p[0][i];
    158:       PetscScalar d_dy_i = GNx_p[1][i];

    160:       B[0][2*i] = d_dx_i;B[0][2*i+1] = 0.0;
    161:       B[1][2*i] = 0.0;B[1][2*i+1] = d_dy_i;
    162:       B[2][2*i] = d_dy_i;B[2][2*i+1] = d_dx_i;
    163:     }

    165:     tildeD[0] = 2.0*gp_weight[p]*J_p*eta[p];
    166:     tildeD[1] = 2.0*gp_weight[p]*J_p*eta[p];
    167:     tildeD[2] =       gp_weight[p]*J_p*eta[p];

    169:     /* form Bt tildeD B */
    170:     /*
    171:     Ke_ij = Bt_ik . D_kl . B_lj
    172:           = B_ki . D_kl . B_lj
    173:           = B_ki . D_kk . B_kj
    174:     */
    175:     for (i = 0; i < 8; i++) {
    176:       for (j = 0; j < 8; j++) {
    177:         for (k = 0; k < 3; k++) { /* Note D is diagonal for stokes */
    178:           Ke[i+8*j] += B[k][i]*tildeD[k]*B[k][j];
    179:         }
    180:       }
    181:     }
    182:   }
    183: }

    185: static void BForm_Grad(PetscScalar Ke[],PetscScalar coords[])
    186: {
    187:   PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
    188:   PetscScalar Ni_p[NODES_PER_EL],GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
    189:   PetscScalar J_p,fac;
    190:   PetscInt    p,i,j,di,ngp;

    192:   /* define quadrature rule */
    193:   CreateGaussQuadrature(&ngp,gp_xi,gp_weight);

    195:   /* evaluate bilinear form */
    196:   for (p = 0; p < ngp; p++) {
    197:     EvaluateBasis_Q1(gp_xi[p],Ni_p);
    198:     EvaluateBasisDerivatives_Q1(gp_xi[p],GNi_p);
    199:     EvaluateDerivatives(GNi_p,GNx_p,coords,&J_p);
    200:     fac = gp_weight[p]*J_p;

    202:     for (i = 0; i < NODES_PER_EL; i++) { /* u nodes */
    203:       for (di = 0; di < NSD; di++) { /* u dofs */
    204:         for (j = 0; j < 4; j++) {  /* p nodes, p dofs = 1 (ie no loop) */
    205:           PetscInt IJ;
    206:           IJ = map_wIwDI_uJuDJ(i,di,NODES_PER_EL,2,j,0,NODES_PER_EL,1);

    208:           Ke[IJ] -= GNx_p[di][i]*Ni_p[j]*fac;
    209:         }
    210:       }
    211:     }
    212:   }
    213: }

    215: static void BForm_Div(PetscScalar De[],PetscScalar coords[])
    216: {
    217:   PetscScalar Ge[U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL];
    218:   PetscInt    i,j,nr_g,nc_g;

    220:   PetscMemzero(Ge,sizeof(Ge));
    221:   BForm_Grad(Ge,coords);

    223:   nr_g = U_DOFS*NODES_PER_EL;
    224:   nc_g = P_DOFS*NODES_PER_EL;

    226:   for (i = 0; i < nr_g; i++) {
    227:     for (j = 0; j < nc_g; j++) {
    228:       De[nr_g*j+i] = Ge[nc_g*i+j];
    229:     }
    230:   }
    231: }

    233: static void BForm_Stabilisation(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
    234: {
    235:   PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
    236:   PetscScalar Ni_p[NODES_PER_EL],GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
    237:   PetscScalar J_p,fac,eta_avg;
    238:   PetscInt    p,i,j,ngp;

    240:   /* define quadrature rule */
    241:   CreateGaussQuadrature(&ngp,gp_xi,gp_weight);

    243:   /* evaluate bilinear form */
    244:   for (p = 0; p < ngp; p++) {
    245:     EvaluateBasis_Q1(gp_xi[p],Ni_p);
    246:     EvaluateBasisDerivatives_Q1(gp_xi[p],GNi_p);
    247:     EvaluateDerivatives(GNi_p,GNx_p,coords,&J_p);
    248:     fac = gp_weight[p]*J_p;

    250:     for (i = 0; i < NODES_PER_EL; i++) {
    251:       for (j = 0; j < NODES_PER_EL; j++) {
    252:         Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.0625);
    253:       }
    254:     }
    255:   }

    257:   /* scale */
    258:   eta_avg = 0.0;
    259:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
    260:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
    261:   fac     = 1.0/eta_avg;
    262:   for (i = 0; i < NODES_PER_EL; i++) {
    263:     for (j = 0; j < NODES_PER_EL; j++) {
    264:       Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
    265:     }
    266:   }
    267: }

    269: static void BForm_ScaledMassMatrix(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
    270: {
    271:   PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
    272:   PetscScalar Ni_p[NODES_PER_EL],GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
    273:   PetscScalar J_p,fac,eta_avg;
    274:   PetscInt    p,i,j,ngp;

    276:   /* define quadrature rule */
    277:   CreateGaussQuadrature(&ngp,gp_xi,gp_weight);

    279:   /* evaluate bilinear form */
    280:   for (p = 0; p < ngp; p++) {
    281:     EvaluateBasis_Q1(gp_xi[p],Ni_p);
    282:     EvaluateBasisDerivatives_Q1(gp_xi[p],GNi_p);
    283:     EvaluateDerivatives(GNi_p,GNx_p,coords,&J_p);
    284:     fac = gp_weight[p]*J_p;

    286:     for (i = 0; i < NODES_PER_EL; i++) {
    287:       for (j = 0; j < NODES_PER_EL; j++) {
    288:         Ke[NODES_PER_EL*i+j] -= fac*Ni_p[i]*Ni_p[j];
    289:       }
    290:     }
    291:   }

    293:   /* scale */
    294:   eta_avg = 0.0;
    295:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
    296:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
    297:   fac     = 1.0/eta_avg;
    298:   for (i = 0; i < NODES_PER_EL; i++) {
    299:     for (j = 0; j < NODES_PER_EL; j++) {
    300:       Ke[NODES_PER_EL*i+j] *= fac;
    301:     }
    302:   }
    303: }

    305: static void LForm_MomentumRHS(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[])
    306: {
    307:   PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
    308:   PetscScalar Ni_p[NODES_PER_EL],GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
    309:   PetscScalar J_p,fac;
    310:   PetscInt    p,i,ngp;

    312:   /* define quadrature rule */
    313:   CreateGaussQuadrature(&ngp,gp_xi,gp_weight);

    315:   /* evaluate linear form */
    316:   for (p = 0; p < ngp; p++) {
    317:     EvaluateBasis_Q1(gp_xi[p],Ni_p);
    318:     EvaluateBasisDerivatives_Q1(gp_xi[p],GNi_p);
    319:     EvaluateDerivatives(GNi_p,GNx_p,coords,&J_p);
    320:     fac = gp_weight[p]*J_p;

    322:     for (i = 0; i < NODES_PER_EL; i++) {
    323:       Fe[NSD*i]    = 0.0;
    324:       Fe[NSD*i+1] -= fac*Ni_p[i]*fy[p];
    325:     }
    326:   }
    327: }

    329: static PetscErrorCode GetElementCoords(const PetscScalar _coords[],const PetscInt e2n[],PetscScalar el_coords[])
    330: {
    331:   PetscInt i,d;
    333:   /* get coords for the element */
    334:   for (i=0; i<4; i++) {
    335:     for (d=0; d<NSD; d++) {
    336:       el_coords[NSD*i+d] = _coords[NSD * e2n[i] + d];
    337:     }
    338:   }
    339:   return 0;
    340: }

    342: static PetscErrorCode AssembleStokes_A(Mat A,DM stokes_da,DM quadrature)
    343: {
    344:   DM                     cda;
    345:   Vec                    coords;
    346:   const PetscScalar      *_coords;
    347:   PetscInt               u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
    348:   PetscInt               p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
    349:   PetscInt               nel,npe,eidx;
    350:   const PetscInt         *element_list;
    351:   PetscScalar            Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
    352:   PetscScalar            Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
    353:   PetscScalar            De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
    354:   PetscScalar            Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
    355:   PetscScalar            el_coords[NODES_PER_EL*NSD];
    356:   PetscScalar            *q_eta,*prop_eta;

    359:   MatZeroEntries(A);
    360:   /* setup for coords */
    361:   DMGetCoordinateDM(stokes_da,&cda);
    362:   DMGetCoordinatesLocal(stokes_da,&coords);
    363:   VecGetArrayRead(coords,&_coords);

    365:   /* setup for coefficients */
    366:   DMSwarmGetField(quadrature,"eta_q",NULL,NULL,(void**)&q_eta);

    368:   DMDAGetElements(stokes_da,&nel,&npe,&element_list);
    369:   for (eidx = 0; eidx < nel; eidx++) {
    370:     const PetscInt *element = &element_list[npe*eidx];

    372:     /* get coords for the element */
    373:     GetElementCoords(_coords,element,el_coords);

    375:     /* get coefficients for the element */
    376:     prop_eta = &q_eta[GAUSS_POINTS * eidx];

    378:     /* initialise element stiffness matrix */
    379:     PetscMemzero(Ae,sizeof(Ae));
    380:     PetscMemzero(Ge,sizeof(Ge));
    381:     PetscMemzero(De,sizeof(De));
    382:     PetscMemzero(Ce,sizeof(Ce));

    384:     /* form element stiffness matrix */
    385:     BForm_DivT(Ae,el_coords,prop_eta);
    386:     BForm_Grad(Ge,el_coords);
    387:     BForm_Div(De,el_coords);
    388:     BForm_Stabilisation(Ce,el_coords,prop_eta);

    390:     /* insert element matrix into global matrix */
    391:     DMDAGetElementEqnums_up(element,u_eqn,p_eqn);
    392:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
    393:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
    394:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);
    395:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
    396:   }
    397:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    398:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    400:   DMSwarmRestoreField(quadrature,"eta_q",NULL,NULL,(void**)&q_eta);
    401:   VecRestoreArrayRead(coords,&_coords);
    402:   return 0;
    403: }

    405: static PetscErrorCode AssembleStokes_PC(Mat A,DM stokes_da,DM quadrature)
    406: {
    407:   DM                     cda;
    408:   Vec                    coords;
    409:   const PetscScalar      *_coords;
    410:   PetscInt               u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
    411:   PetscInt               p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
    412:   PetscInt               nel,npe,eidx;
    413:   const PetscInt         *element_list;
    414:   PetscScalar            Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
    415:   PetscScalar            Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
    416:   PetscScalar            De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
    417:   PetscScalar            Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
    418:   PetscScalar            el_coords[NODES_PER_EL*NSD];
    419:   PetscScalar            *q_eta,*prop_eta;

    422:   MatZeroEntries(A);
    423:   /* setup for coords */
    424:   DMGetCoordinateDM(stokes_da,&cda);
    425:   DMGetCoordinatesLocal(stokes_da,&coords);
    426:   VecGetArrayRead(coords,&_coords);

    428:   /* setup for coefficients */
    429:   DMSwarmGetField(quadrature,"eta_q",NULL,NULL,(void**)&q_eta);

    431:   DMDAGetElements(stokes_da,&nel,&npe,&element_list);
    432:   for (eidx = 0; eidx < nel; eidx++) {
    433:     const PetscInt *element = &element_list[npe*eidx];

    435:     /* get coords for the element */
    436:     GetElementCoords(_coords,element,el_coords);

    438:     /* get coefficients for the element */
    439:     prop_eta = &q_eta[GAUSS_POINTS * eidx];

    441:     /* initialise element stiffness matrix */
    442:     PetscMemzero(Ae,sizeof(Ae));
    443:     PetscMemzero(Ge,sizeof(Ge));
    444:     PetscMemzero(De,sizeof(De));
    445:     PetscMemzero(Ce,sizeof(Ce));

    447:     /* form element stiffness matrix */
    448:     BForm_DivT(Ae,el_coords,prop_eta);
    449:     BForm_Grad(Ge,el_coords);
    450:     BForm_ScaledMassMatrix(Ce,el_coords,prop_eta);

    452:     /* insert element matrix into global matrix */
    453:     DMDAGetElementEqnums_up(element,u_eqn,p_eqn);
    454:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
    455:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
    456:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);
    457:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
    458:   }
    459:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    460:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    462:   DMSwarmRestoreField(quadrature,"eta_q",NULL,NULL,(void**)&q_eta);
    463:   VecRestoreArrayRead(coords,&_coords);

    465:   return 0;
    466: }

    468: static PetscErrorCode AssembleStokes_RHS(Vec F,DM stokes_da,DM quadrature)
    469: {
    470:   DM                     cda;
    471:   Vec                    coords;
    472:   const PetscScalar      *_coords;
    473:   PetscInt               u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
    474:   PetscInt               p_eqn[NODES_PER_EL*P_DOFS]; /* 1 degrees of freedom */
    475:   PetscInt               nel,npe,eidx,i;
    476:   const PetscInt         *element_list;
    477:   PetscScalar            Fe[NODES_PER_EL*U_DOFS];
    478:   PetscScalar            He[NODES_PER_EL*P_DOFS];
    479:   PetscScalar            el_coords[NODES_PER_EL*NSD];
    480:   PetscScalar            *q_rhs,*prop_fy;
    481:   Vec                    local_F;
    482:   PetscScalar            *LA_F;

    485:   VecZeroEntries(F);
    486:   /* setup for coords */
    487:   DMGetCoordinateDM(stokes_da,&cda);
    488:   DMGetCoordinatesLocal(stokes_da,&coords);
    489:   VecGetArrayRead(coords,&_coords);

    491:   /* setup for coefficients */
    492:   DMSwarmGetField(quadrature,"rho_q",NULL,NULL,(void**)&q_rhs);

    494:   /* get access to the vector */
    495:   DMGetLocalVector(stokes_da,&local_F);
    496:   VecZeroEntries(local_F);
    497:   VecGetArray(local_F,&LA_F);

    499:   DMDAGetElements(stokes_da,&nel,&npe,&element_list);
    500:   for (eidx = 0; eidx < nel; eidx++) {
    501:     const PetscInt *element = &element_list[npe*eidx];

    503:     /* get coords for the element */
    504:     GetElementCoords(_coords,element,el_coords);

    506:     /* get coefficients for the element */
    507:     prop_fy = &q_rhs[GAUSS_POINTS * eidx];

    509:     /* initialise element stiffness matrix */
    510:     PetscMemzero(Fe,sizeof(Fe));
    511:     PetscMemzero(He,sizeof(He));

    513:     /* form element stiffness matrix */
    514:     LForm_MomentumRHS(Fe,el_coords,NULL,prop_fy);

    516:     /* insert element matrix into global matrix */
    517:     DMDAGetElementEqnums_up(element,u_eqn,p_eqn);

    519:     for (i=0; i<NODES_PER_EL*U_DOFS; i++) {
    520:       LA_F[ u_eqn[i] ] += Fe[i];
    521:     }
    522:   }
    523:   DMSwarmRestoreField(quadrature,"rho_q",NULL,NULL,(void**)&q_rhs);
    524:   VecRestoreArrayRead(coords,&_coords);

    526:   VecRestoreArray(local_F,&LA_F);
    527:   DMLocalToGlobalBegin(stokes_da,local_F,ADD_VALUES,F);
    528:   DMLocalToGlobalEnd(stokes_da,local_F,ADD_VALUES,F);
    529:   DMRestoreLocalVector(stokes_da,&local_F);

    531:   return 0;
    532: }

    534: PetscErrorCode DMSwarmPICInsertPointsCellwise(DM dm,DM dmc,PetscInt e,PetscInt npoints,PetscReal xi[],PetscBool proximity_initialization)
    535: {
    536:   PetscInt          dim,nel,npe,q,k,d,ncurr;
    537:   const PetscInt    *element_list;
    538:   Vec               coor;
    539:   const PetscScalar *_coor;
    540:   PetscReal         **basis,*elcoor,*xp;
    541:   PetscReal         *swarm_coor;
    542:   PetscInt          *swarm_cellid;

    545:   DMGetDimension(dm,&dim);
    546:   DMDAGetElements(dmc,&nel,&npe,&element_list);

    548:   PetscMalloc1(dim*npoints,&xp);
    549:   PetscMalloc1(dim*npe,&elcoor);
    550:   PetscMalloc1(npoints,&basis);
    551:   for (q=0; q<npoints; q++) {
    552:     PetscMalloc1(npe,&basis[q]);

    554:     switch (dim) {
    555:       case 1:
    556:         basis[q][0] = 0.5*(1.0 - xi[dim*q+0]);
    557:         basis[q][1] = 0.5*(1.0 + xi[dim*q+0]);
    558:         break;
    559:       case 2:
    560:         basis[q][0] = 0.25*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1]);
    561:         basis[q][1] = 0.25*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1]);
    562:         basis[q][2] = 0.25*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1]);
    563:         basis[q][3] = 0.25*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1]);
    564:         break;

    566:       case 3:
    567:         basis[q][0] = 0.125*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 - xi[dim*q+2]);
    568:         basis[q][1] = 0.125*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 - xi[dim*q+2]);
    569:         basis[q][2] = 0.125*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 - xi[dim*q+2]);
    570:         basis[q][3] = 0.125*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 - xi[dim*q+2]);
    571:         basis[q][4] = 0.125*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 + xi[dim*q+2]);
    572:         basis[q][5] = 0.125*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 + xi[dim*q+2]);
    573:         basis[q][6] = 0.125*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 + xi[dim*q+2]);
    574:         basis[q][7] = 0.125*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 + xi[dim*q+2]);
    575:         break;
    576:     }
    577:   }

    579:   DMGetCoordinatesLocal(dmc,&coor);
    580:   VecGetArrayRead(coor,&_coor);
    581:   /* compute and store the coordinates for the new points */
    582:   {
    583:     const PetscInt *element = &element_list[npe*e];

    585:     for (k=0; k<npe; k++) {
    586:       for (d=0; d<dim; d++) {
    587:         elcoor[dim*k+d] = PetscRealPart(_coor[ dim*element[k] + d ]);
    588:       }
    589:     }
    590:     for (q=0; q<npoints; q++) {
    591:       for (d=0; d<dim; d++) {
    592:         xp[dim*q+d] = 0.0;
    593:       }
    594:       for (k=0; k<npe; k++) {
    595:         for (d=0; d<dim; d++) {
    596:           xp[dim*q+d] += basis[q][k] * elcoor[dim*k+d];
    597:         }
    598:       }
    599:     }
    600:   }
    601:   VecRestoreArrayRead(coor,&_coor);
    602:   DMDARestoreElements(dmc,&nel,&npe,&element_list);

    604:   DMSwarmGetLocalSize(dm,&ncurr);
    605:   DMSwarmAddNPoints(dm,npoints);

    607:   if (proximity_initialization) {
    608:     PetscInt  *nnlist;
    609:     PetscReal *coor_q,*coor_qn;
    610:     PetscInt  npoints_e,*plist_e;

    612:     DMSwarmSortGetPointsPerCell(dm,e,&npoints_e,&plist_e);

    614:     PetscMalloc1(npoints,&nnlist);
    615:     /* find nearest neighour points in this cell */
    616:     DMSwarmGetField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
    617:     DMSwarmGetField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    618:     for (q=0; q<npoints; q++) {
    619:       PetscInt  qn,nearest_neighour = -1;
    620:       PetscReal sep,min_sep = PETSC_MAX_REAL;

    622:       coor_q = &xp[dim*q];
    623:       for (qn=0; qn<npoints_e; qn++) {
    624:         coor_qn = &swarm_coor[dim*plist_e[qn]];
    625:         sep = 0.0;
    626:         for (d=0; d<dim; d++) {
    627:           sep += (coor_q[d]-coor_qn[d])*(coor_q[d]-coor_qn[d]);
    628:         }
    629:         if (sep < min_sep) {
    630:           nearest_neighour = plist_e[qn];
    631:           min_sep = sep;
    632:         }
    633:       }
    635:       nnlist[q] = nearest_neighour;
    636:     }
    637:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    638:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);

    640:     /* copies the nearest neighbour (nnlist[q]) into the new slot (ncurr+q) */
    641:     for (q=0; q<npoints; q++) {
    642:       DMSwarmCopyPoint(dm,nnlist[q],ncurr+q);
    643:     }
    644:     DMSwarmGetField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
    645:     DMSwarmGetField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    646:     for (q=0; q<npoints; q++) {
    647:       /* set the coordinates */
    648:       for (d=0; d<dim; d++) {
    649:         swarm_coor[dim*(ncurr+q)+d] = xp[dim*q+d];
    650:       }
    651:       /* set the cell index */
    652:       swarm_cellid[ncurr+q] = e;
    653:     }
    654:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    655:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);

    657:     PetscFree(plist_e);
    658:     PetscFree(nnlist);
    659:   } else {
    660:     DMSwarmGetField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
    661:     DMSwarmGetField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    662:     for (q=0; q<npoints; q++) {
    663:       /* set the coordinates */
    664:       for (d=0; d<dim; d++) {
    665:         swarm_coor[dim*(ncurr+q)+d] = xp[dim*q+d];
    666:       }
    667:       /* set the cell index */
    668:       swarm_cellid[ncurr+q] = e;
    669:     }
    670:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
    671:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
    672:   }

    674:   PetscFree(xp);
    675:   PetscFree(elcoor);
    676:   for (q=0; q<npoints; q++) {
    677:     PetscFree(basis[q]);
    678:   }
    679:   PetscFree(basis);
    680:   return 0;
    681: }

    683: PetscErrorCode MaterialPoint_PopulateCell(DM dm_vp,DM dm_mpoint)
    684: {
    685:   PetscInt        _npe,_nel,e,nel;
    686:   const PetscInt  *element;
    687:   DM              dmc;
    688:   PetscQuadrature quadrature;
    689:   const PetscReal *xi;
    690:   PetscInt        npoints_q,cnt,cnt_g;

    693:   DMDAGetElements(dm_vp,&_nel,&_npe,&element);
    694:   nel = _nel;
    695:   DMDARestoreElements(dm_vp,&_nel,&_npe,&element);

    697:   PetscDTGaussTensorQuadrature(2,1,4,-1.0,1.0,&quadrature);
    698:   PetscQuadratureGetData(quadrature,NULL,NULL,&npoints_q,&xi,NULL);
    699:   DMSwarmGetCellDM(dm_mpoint,&dmc);

    701:   DMSwarmSortGetAccess(dm_mpoint);

    703:   cnt = 0;
    704:   for (e=0; e<nel; e++) {
    705:     PetscInt npoints_per_cell;

    707:     DMSwarmSortGetNumberOfPointsPerCell(dm_mpoint,e,&npoints_per_cell);

    709:     if (npoints_per_cell < 12) {
    710:       DMSwarmPICInsertPointsCellwise(dm_mpoint,dm_vp,e,npoints_q,(PetscReal*)xi,PETSC_TRUE);
    711:       cnt++;
    712:     }
    713:   }
    714:   MPI_Allreduce(&cnt,&cnt_g,1,MPIU_INT,MPI_SUM,PETSC_COMM_WORLD);
    715:   if (cnt_g > 0) {
    716:     PetscPrintf(PETSC_COMM_WORLD,".... ....pop cont: adjusted %D cells\n",cnt_g);
    717:   }

    719:   DMSwarmSortRestoreAccess(dm_mpoint);
    720:   PetscQuadratureDestroy(&quadrature);
    721:   return 0;
    722: }

    724: PetscErrorCode MaterialPoint_AdvectRK1(DM dm_vp,Vec vp,PetscReal dt,DM dm_mpoint)
    725: {
    726:   Vec               vp_l,coor_l;
    727:   const PetscScalar *LA_vp;
    728:   PetscInt          i,p,e,npoints,nel,npe;
    729:   PetscInt          *mpfield_cell;
    730:   PetscReal         *mpfield_coor;
    731:   const PetscInt    *element_list;
    732:   const PetscInt    *element;
    733:   PetscScalar       xi_p[NSD],Ni[NODES_PER_EL];
    734:   const PetscScalar *LA_coor;
    735:   PetscScalar       dx[NSD];

    738:   DMGetCoordinatesLocal(dm_vp,&coor_l);
    739:   VecGetArrayRead(coor_l,&LA_coor);

    741:   DMGetLocalVector(dm_vp,&vp_l);
    742:   DMGlobalToLocalBegin(dm_vp,vp,INSERT_VALUES,vp_l);
    743:   DMGlobalToLocalEnd(dm_vp,vp,INSERT_VALUES,vp_l);
    744:   VecGetArrayRead(vp_l,&LA_vp);

    746:   DMDAGetElements(dm_vp,&nel,&npe,&element_list);
    747:   DMSwarmGetLocalSize(dm_mpoint,&npoints);
    748:   DMSwarmGetField(dm_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&mpfield_coor);
    749:   DMSwarmGetField(dm_mpoint,DMSwarmPICField_cellid,NULL,NULL,(void**)&mpfield_cell);
    750:   for (p=0; p<npoints; p++) {
    751:     PetscReal         *coor_p;
    752:     PetscScalar       vel_n[NSD*NODES_PER_EL],vel_p[NSD];
    753:     const PetscScalar *x0;
    754:     const PetscScalar *x2;

    756:     e       = mpfield_cell[p];
    757:     coor_p  = &mpfield_coor[NSD*p];
    758:     element = &element_list[NODES_PER_EL*e];

    760:     /* compute local coordinates: (xp-x0)/dx = (xip+1)/2 */
    761:     x0 = &LA_coor[NSD*element[0]];
    762:     x2 = &LA_coor[NSD*element[2]];

    764:     dx[0] = x2[0] - x0[0];
    765:     dx[1] = x2[1] - x0[1];

    767:     xi_p[0] = 2.0 * (coor_p[0] - x0[0])/dx[0] - 1.0;
    768:     xi_p[1] = 2.0 * (coor_p[1] - x0[1])/dx[1] - 1.0;

    774:     /* evaluate basis functions */
    775:     EvaluateBasis_Q1(xi_p,Ni);

    777:     /* get cell nodal velocities */
    778:     for (i=0; i<NODES_PER_EL; i++) {
    779:       PetscInt nid;

    781:       nid = element[i];
    782:       vel_n[NSD*i+0] = LA_vp[(NSD+1)*nid+0];
    783:       vel_n[NSD*i+1] = LA_vp[(NSD+1)*nid+1];
    784:     }

    786:     /* interpolate velocity */
    787:     vel_p[0] = vel_p[1] = 0.0;
    788:     for (i=0; i<NODES_PER_EL; i++) {
    789:       vel_p[0] += Ni[i] * vel_n[NSD*i+0];
    790:       vel_p[1] += Ni[i] * vel_n[NSD*i+1];
    791:     }

    793:     coor_p[0] += dt * PetscRealPart(vel_p[0]);
    794:     coor_p[1] += dt * PetscRealPart(vel_p[1]);
    795:   }

    797:   DMSwarmRestoreField(dm_mpoint,DMSwarmPICField_cellid,NULL,NULL,(void**)&mpfield_cell);
    798:   DMSwarmRestoreField(dm_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&mpfield_coor);
    799:   DMDARestoreElements(dm_vp,&nel,&npe,&element_list);
    800:   VecRestoreArrayRead(vp_l,&LA_vp);
    801:   DMRestoreLocalVector(dm_vp,&vp_l);
    802:   VecRestoreArrayRead(coor_l,&LA_coor);
    803:   return 0;
    804: }

    806: PetscErrorCode MaterialPoint_Interpolate(DM dm,Vec eta_v,Vec rho_v,DM dm_quadrature)
    807: {
    808:   Vec            eta_l,rho_l;
    809:   PetscScalar    *_eta_l,*_rho_l;
    810:   PetscInt       nqp,npe,nel;
    811:   PetscScalar    qp_xi[GAUSS_POINTS][NSD];
    812:   PetscScalar    qp_weight[GAUSS_POINTS];
    813:   PetscInt       q,k,e;
    814:   PetscScalar    Ni[GAUSS_POINTS][NODES_PER_EL];
    815:   const PetscInt *element_list;
    816:   PetscReal      *q_eta,*q_rhs;

    819:   /* define quadrature rule */
    820:   CreateGaussQuadrature(&nqp,qp_xi,qp_weight);
    821:   for (q=0; q<nqp; q++) {
    822:     EvaluateBasis_Q1(qp_xi[q],Ni[q]);
    823:   }

    825:   DMGetLocalVector(dm,&eta_l);
    826:   DMGetLocalVector(dm,&rho_l);

    828:   DMGlobalToLocalBegin(dm,eta_v,INSERT_VALUES,eta_l);
    829:   DMGlobalToLocalEnd(dm,eta_v,INSERT_VALUES,eta_l);
    830:   DMGlobalToLocalBegin(dm,rho_v,INSERT_VALUES,rho_l);
    831:   DMGlobalToLocalEnd(dm,rho_v,INSERT_VALUES,rho_l);

    833:   VecGetArray(eta_l,&_eta_l);
    834:   VecGetArray(rho_l,&_rho_l);

    836:   DMSwarmGetField(dm_quadrature,"eta_q",NULL,NULL,(void**)&q_eta);
    837:   DMSwarmGetField(dm_quadrature,"rho_q",NULL,NULL,(void**)&q_rhs);

    839:   DMDAGetElements(dm,&nel,&npe,&element_list);
    840:   for (e=0; e<nel; e++) {
    841:     PetscScalar    eta_field_e[NODES_PER_EL];
    842:     PetscScalar    rho_field_e[NODES_PER_EL];
    843:     const PetscInt *element = &element_list[4*e];

    845:     for (k=0; k<NODES_PER_EL; k++) {
    846:       eta_field_e[k] = _eta_l[ element[k] ];
    847:       rho_field_e[k] = _rho_l[ element[k] ];
    848:     }

    850:     for (q=0; q<nqp; q++) {
    851:       PetscScalar eta_q,rho_q;

    853:       eta_q = rho_q = 0.0;
    854:       for (k=0; k<NODES_PER_EL; k++) {
    855:         eta_q += Ni[q][k] * eta_field_e[k];
    856:         rho_q += Ni[q][k] * rho_field_e[k];
    857:       }

    859:       q_eta[nqp*e+q] = PetscRealPart(eta_q);
    860:       q_rhs[nqp*e+q] = PetscRealPart(rho_q);
    861:     }
    862:   }
    863:   DMDARestoreElements(dm,&nel,&npe,&element_list);

    865:   DMSwarmRestoreField(dm_quadrature,"rho_q",NULL,NULL,(void**)&q_rhs);
    866:   DMSwarmRestoreField(dm_quadrature,"eta_q",NULL,NULL,(void**)&q_eta);

    868:   VecRestoreArray(rho_l,&_rho_l);
    869:   VecRestoreArray(eta_l,&_eta_l);
    870:   DMRestoreLocalVector(dm,&rho_l);
    871:   DMRestoreLocalVector(dm,&eta_l);
    872:   return 0;
    873: }

    875: static PetscErrorCode SolveTimeDepStokes(PetscInt mx,PetscInt my)
    876: {
    877:   DM                     dm_stokes,dm_coeff;
    878:   PetscInt               u_dof,p_dof,dof,stencil_width;
    879:   Mat                    A,B;
    880:   PetscInt               nel_local;
    881:   Vec                    eta_v,rho_v;
    882:   Vec                    f,X;
    883:   KSP                    ksp;
    884:   PC                     pc;
    885:   char                   filename[PETSC_MAX_PATH_LEN];
    886:   DM                     dms_quadrature,dms_mpoint;
    887:   PetscInt               nel,npe,npoints;
    888:   const PetscInt         *element_list;
    889:   PetscInt               tk,nt,dump_freq;
    890:   PetscReal              dt,dt_max = 0.0;
    891:   PetscReal              vx[2],vy[2],max_v = 0.0,max_v_step,dh;
    892:   const char             *fieldnames[] = { "eta" , "rho" };
    893:   Vec                    *pfields;
    894:   PetscInt               ppcell = 1;
    895:   PetscReal              time,delta_eta = 1.0;
    896:   PetscBool              randomize_coords = PETSC_FALSE;
    897:   PetscReal              randomize_fac = 0.25;
    898:   PetscBool              no_view = PETSC_FALSE;
    899:   PetscBool              isbddc;

    902:   /*
    903:     Generate the DMDA for the velocity and pressure spaces.
    904:     We use Q1 elements for both fields.
    905:     The Q1 FE basis on a regular mesh has a 9-point stencil (DMDA_STENCIL_BOX)
    906:     The number of nodes in each direction is mx+1, my+1
    907:   */
    908:   u_dof         = U_DOFS; /* Vx, Vy - velocities */
    909:   p_dof         = P_DOFS; /* p - pressure */
    910:   dof           = u_dof + p_dof;
    911:   stencil_width = 1;
    912:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx+1,my+1,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,NULL,NULL,&dm_stokes);
    913:   DMDASetElementType(dm_stokes,DMDA_ELEMENT_Q1);
    914:   DMSetMatType(dm_stokes,MATAIJ);
    915:   DMSetFromOptions(dm_stokes);
    916:   DMSetUp(dm_stokes);
    917:   DMDASetFieldName(dm_stokes,0,"ux");
    918:   DMDASetFieldName(dm_stokes,1,"uy");
    919:   DMDASetFieldName(dm_stokes,2,"p");

    921:   /* unit box [0,0.9142] x [0,1] */
    922:   DMDASetUniformCoordinates(dm_stokes,0.0,0.9142,0.0,1.0,0.,0.);
    923:   dh = 1.0/((PetscReal)(mx));

    925:   /* Get local number of elements */
    926:   {
    927:     DMDAGetElements(dm_stokes,&nel,&npe,&element_list);

    929:     nel_local = nel;

    931:     DMDARestoreElements(dm_stokes,&nel,&npe,&element_list);
    932:   }

    934:   /* Create DMDA for representing scalar fields */
    935:   DMDACreateCompatibleDMDA(dm_stokes,1,&dm_coeff);

    937:   /* Create the swarm for storing quadrature point values */
    938:   DMCreate(PETSC_COMM_WORLD,&dms_quadrature);
    939:   DMSetType(dms_quadrature,DMSWARM);
    940:   DMSetDimension(dms_quadrature,2);

    942:   /* Register fields for viscosity and density on the quadrature points */
    943:   DMSwarmRegisterPetscDatatypeField(dms_quadrature,"eta_q",1,PETSC_REAL);
    944:   DMSwarmRegisterPetscDatatypeField(dms_quadrature,"rho_q",1,PETSC_REAL);
    945:   DMSwarmFinalizeFieldRegister(dms_quadrature);
    946:   DMSwarmSetLocalSizes(dms_quadrature,nel_local * GAUSS_POINTS,0);

    948:   /* Create the material point swarm */
    949:   DMCreate(PETSC_COMM_WORLD,&dms_mpoint);
    950:   DMSetType(dms_mpoint,DMSWARM);
    951:   DMSetDimension(dms_mpoint,2);

    953:   /* Configure the material point swarm to be of type Particle-In-Cell */
    954:   DMSwarmSetType(dms_mpoint,DMSWARM_PIC);

    956:   /*
    957:      Specify the DM to use for point location and projections
    958:      within the context of a PIC scheme
    959:   */
    960:   DMSwarmSetCellDM(dms_mpoint,dm_coeff);

    962:   /* Register fields for viscosity and density */
    963:   DMSwarmRegisterPetscDatatypeField(dms_mpoint,"eta",1,PETSC_REAL);
    964:   DMSwarmRegisterPetscDatatypeField(dms_mpoint,"rho",1,PETSC_REAL);
    965:   DMSwarmFinalizeFieldRegister(dms_mpoint);

    967:   PetscOptionsGetInt(NULL,NULL,"-ppcell",&ppcell,NULL);
    968:   DMSwarmSetLocalSizes(dms_mpoint,nel_local * ppcell,100);

    970:   /*
    971:     Layout the material points in space using the cell DM.
    972:     Particle coordinates are defined by cell wise using different methods.
    973:     - DMSWARMPIC_LAYOUT_GAUSS defines particles coordinates at the positions
    974:                               corresponding to a Gauss quadrature rule with
    975:                               ppcell points in each direction.
    976:     - DMSWARMPIC_LAYOUT_REGULAR defines particle coordinates at the centoid of
    977:                                 ppcell x ppcell quadralaterals defined within the
    978:                                 reference element.
    979:     - DMSWARMPIC_LAYOUT_SUBDIVISION defines particles coordinates at the centroid
    980:                                     of each quadralateral obtained by sub-dividing
    981:                                     the reference element cell ppcell times.
    982:   */
    983:   DMSwarmInsertPointsUsingCellDM(dms_mpoint,DMSWARMPIC_LAYOUT_SUBDIVISION,ppcell);

    985:   /*
    986:     Defne a high resolution layer of material points across the material interface
    987:   */
    988:   {
    989:     PetscInt  npoints_dir_x[2];
    990:     PetscReal min[2],max[2];

    992:     npoints_dir_x[0] = (PetscInt)(0.9142/(0.05*dh));
    993:     npoints_dir_x[1] = (PetscInt)((0.25-0.15)/(0.05*dh));
    994:     min[0] = 0.0;  max[0] = 0.9142;
    995:     min[1] = 0.05; max[1] = 0.35;
    996:     DMSwarmSetPointsUniformCoordinates(dms_mpoint,min,max,npoints_dir_x,ADD_VALUES);
    997:   }

    999:   /*
    1000:     Define a high resolution layer of material points near the surface of the domain
    1001:     to deal with weakly compressible Q1-Q1 elements. These elements "self compact"
    1002:     when applied to buouyancy driven flow. The error in div(u) is O(h).
    1003:   */
    1004:   {
    1005:     PetscInt  npoints_dir_x[2];
    1006:     PetscReal min[2],max[2];

    1008:     npoints_dir_x[0] = (PetscInt)(0.9142/(0.25*dh));
    1009:     npoints_dir_x[1] = (PetscInt)(3.0*dh/(0.25*dh));
    1010:     min[0] = 0.0;          max[0] = 0.9142;
    1011:     min[1] = 1.0 - 3.0*dh; max[1] = 1.0-0.0001;
    1012:     DMSwarmSetPointsUniformCoordinates(dms_mpoint,min,max,npoints_dir_x,ADD_VALUES);
    1013:   }

    1015:   DMView(dms_mpoint,PETSC_VIEWER_STDOUT_WORLD);

    1017:   /* Define initial material properties on each particle in the material point swarm */
    1018:   PetscOptionsGetReal(NULL,NULL,"-delta_eta",&delta_eta,NULL);
    1019:   PetscOptionsGetBool(NULL,NULL,"-randomize_coords",&randomize_coords,NULL);
    1020:   PetscOptionsGetReal(NULL,NULL,"-randomize_fac",&randomize_fac,NULL);
    1022:   {
    1023:     PetscReal   *array_x,*array_e,*array_r;
    1024:     PetscInt    p;
    1025:     PetscRandom r;
    1026:     PetscMPIInt rank;

    1028:     MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

    1030:     PetscRandomCreate(PETSC_COMM_SELF,&r);
    1031:     PetscRandomSetInterval(r,-randomize_fac*dh,randomize_fac*dh);
    1032:     PetscRandomSetSeed(r,(unsigned long)rank);
    1033:     PetscRandomSeed(r);

    1035:     DMDAGetElements(dm_stokes,&nel,&npe,&element_list);

    1037:     /*
    1038:        Fetch the registered data from the material point DMSwarm.
    1039:        The fields "eta" and "rho" were registered by this example.
    1040:        The field identified by the the variable DMSwarmPICField_coor
    1041:        was registered by the DMSwarm implementation when the function
    1042:          DMSwarmSetType(dms_mpoint,DMSWARM_PIC)
    1043:        was called. The returned array defines the coordinates of each
    1044:        material point in the point swarm.
    1045:     */
    1046:     DMSwarmGetField(dms_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&array_x);
    1047:     DMSwarmGetField(dms_mpoint,"eta",               NULL,NULL,(void**)&array_e);
    1048:     DMSwarmGetField(dms_mpoint,"rho",               NULL,NULL,(void**)&array_r);

    1050:     DMSwarmGetLocalSize(dms_mpoint,&npoints);
    1051:     for (p = 0; p < npoints; p++) {
    1052:       PetscReal x_p[2],rr[2];

    1054:       if (randomize_coords) {
    1055:         PetscRandomGetValueReal(r,&rr[0]);
    1056:         PetscRandomGetValueReal(r,&rr[1]);
    1057:         array_x[2*p + 0] += rr[0];
    1058:         array_x[2*p + 1] += rr[1];
    1059:       }

    1061:       /* Get the coordinates of point, p */
    1062:       x_p[0] = array_x[2*p + 0];
    1063:       x_p[1] = array_x[2*p + 1];

    1065:        if (x_p[1] < (0.2 + 0.02*PetscCosReal(PETSC_PI*x_p[0]/0.9142))) {
    1066:          /* Material properties below the interface */
    1067:          array_e[p] = 1.0 * (1.0/delta_eta);
    1068:          array_r[p] = 0.0;
    1069:        } else {
    1070:          /* Material properties above the interface */
    1071:          array_e[p] = 1.0;
    1072:          array_r[p] = 1.0;
    1073:        }
    1074:     }

    1076:     /*
    1077:        Restore the fetched data fields from the material point DMSwarm.
    1078:        Calling the Restore function invalidates the points array_r, array_e, array_x
    1079:        by setting them to NULL.
    1080:     */
    1081:     DMSwarmRestoreField(dms_mpoint,"rho",NULL,NULL,(void**)&array_r);
    1082:     DMSwarmRestoreField(dms_mpoint,"eta",NULL,NULL,(void**)&array_e);
    1083:     DMSwarmRestoreField(dms_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&array_x);

    1085:     DMDARestoreElements(dm_stokes,&nel,&npe,&element_list);
    1086:     PetscRandomDestroy(&r);
    1087:   }

    1089:   /*
    1090:      If the particle coordinates where randomly shifted, they may have crossed into another
    1091:      element, or into another sub-domain. To account for this we call the Migrate function.
    1092:   */
    1093:   if (randomize_coords) {
    1094:     DMSwarmMigrate(dms_mpoint,PETSC_TRUE);
    1095:   }

    1097:   PetscOptionsGetBool(NULL,NULL,"-no_view",&no_view,NULL);
    1098:   if (!no_view) {
    1099:     DMSwarmViewXDMF(dms_mpoint,"ic_coeff_dms.xmf");
    1100:   }

    1102:   /* project the swarm properties */
    1103:   DMSwarmProjectFields(dms_mpoint,2,fieldnames,&pfields,PETSC_FALSE);
    1104:   eta_v = pfields[0];
    1105:   rho_v = pfields[1];
    1106:   PetscObjectSetName((PetscObject)eta_v,"eta");
    1107:   PetscObjectSetName((PetscObject)rho_v,"rho");
    1108:   MaterialPoint_Interpolate(dm_coeff,eta_v,rho_v,dms_quadrature);

    1110:   /* view projected coefficients eta and rho */
    1111:   if (!no_view) {
    1112:     PetscViewer viewer;

    1114:     PetscViewerCreate(PETSC_COMM_WORLD,&viewer);
    1115:     PetscViewerSetType(viewer,PETSCVIEWERVTK);
    1116:     PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
    1117:     PetscViewerFileSetName(viewer,"ic_coeff_dmda.vts");
    1118:     VecView(eta_v,viewer);
    1119:     VecView(rho_v,viewer);
    1120:     PetscViewerDestroy(&viewer);
    1121:   }

    1123:   DMCreateMatrix(dm_stokes,&A);
    1124:   DMCreateMatrix(dm_stokes,&B);
    1125:   DMCreateGlobalVector(dm_stokes,&f);
    1126:   DMCreateGlobalVector(dm_stokes,&X);

    1128:   AssembleStokes_A(A,dm_stokes,dms_quadrature);
    1129:   AssembleStokes_PC(B,dm_stokes,dms_quadrature);
    1130:   AssembleStokes_RHS(f,dm_stokes,dms_quadrature);

    1132:   DMDAApplyBoundaryConditions(dm_stokes,A,f);
    1133:   DMDAApplyBoundaryConditions(dm_stokes,B,NULL);

    1135:   KSPCreate(PETSC_COMM_WORLD,&ksp);
    1136:   KSPSetOptionsPrefix(ksp,"stokes_");
    1137:   KSPSetDM(ksp,dm_stokes);
    1138:   KSPSetDMActive(ksp,PETSC_FALSE);
    1139:   KSPSetOperators(ksp,A,B);
    1140:   KSPSetFromOptions(ksp);
    1141:   KSPGetPC(ksp,&pc);
    1142:   PetscObjectTypeCompare((PetscObject)pc,PCBDDC,&isbddc);
    1143:   if (isbddc) {
    1144:     KSPSetOperators(ksp,A,A);
    1145:   }

    1147:   /* Define u-v-p indices for fieldsplit */
    1148:   {
    1149:     PC             pc;
    1150:     const PetscInt ufields[] = {0,1},pfields[1] = {2};

    1152:     KSPGetPC(ksp,&pc);
    1153:     PCFieldSplitSetBlockSize(pc,3);
    1154:     PCFieldSplitSetFields(pc,"u",2,ufields,ufields);
    1155:     PCFieldSplitSetFields(pc,"p",1,pfields,pfields);
    1156:   }

    1158:   /* If using a fieldsplit preconditioner, attach a DMDA to the velocity split so that geometric multigrid can be used */
    1159:   {
    1160:     PC        pc,pc_u;
    1161:     KSP       *sub_ksp,ksp_u;
    1162:     PetscInt  nsplits;
    1163:     DM        dm_u;
    1164:     PetscBool is_pcfs;

    1166:     KSPGetPC(ksp,&pc);

    1168:     is_pcfs = PETSC_FALSE;
    1169:     PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&is_pcfs);

    1171:     if (is_pcfs) {
    1172:       KSPSetUp(ksp);
    1173:       KSPGetPC(ksp,&pc);
    1174:       PCFieldSplitGetSubKSP(pc,&nsplits,&sub_ksp);
    1175:       ksp_u = sub_ksp[0];
    1176:       PetscFree(sub_ksp);

    1178:       if (nsplits == 2) {
    1179:         DMDACreateCompatibleDMDA(dm_stokes,2,&dm_u);

    1181:         KSPSetDM(ksp_u,dm_u);
    1182:         KSPSetDMActive(ksp_u,PETSC_FALSE);
    1183:         DMDestroy(&dm_u);

    1185:         /* enforce galerkin coarse grids be used */
    1186:         KSPGetPC(ksp_u,&pc_u);
    1187:         PCMGSetGalerkin(pc_u,PC_MG_GALERKIN_PMAT);
    1188:       }
    1189:     }
    1190:   }

    1192:   dump_freq = 10;
    1193:   PetscOptionsGetInt(NULL,NULL,"-dump_freq",&dump_freq,NULL);
    1194:   nt = 10;
    1195:   PetscOptionsGetInt(NULL,NULL,"-nt",&nt,NULL);
    1196:   time = 0.0;
    1197:   for (tk=1; tk<=nt; tk++) {

    1199:     PetscPrintf(PETSC_COMM_WORLD,".... assemble\n");
    1200:     AssembleStokes_A(A,dm_stokes,dms_quadrature);
    1201:     AssembleStokes_PC(B,dm_stokes,dms_quadrature);
    1202:     AssembleStokes_RHS(f,dm_stokes,dms_quadrature);

    1204:     PetscPrintf(PETSC_COMM_WORLD,".... bc imposition\n");
    1205:     DMDAApplyBoundaryConditions(dm_stokes,A,f);
    1206:     DMDAApplyBoundaryConditions(dm_stokes,B,NULL);

    1208:     PetscPrintf(PETSC_COMM_WORLD,".... solve\n");
    1209:     KSPSetOperators(ksp,A, isbddc ? A : B);
    1210:     KSPSolve(ksp,f,X);

    1212:     VecStrideMax(X,0,NULL,&vx[1]);
    1213:     VecStrideMax(X,1,NULL,&vy[1]);
    1214:     VecStrideMin(X,0,NULL,&vx[0]);
    1215:     VecStrideMin(X,1,NULL,&vy[0]);

    1217:     max_v_step = PetscMax(vx[0],vx[1]);
    1218:     max_v_step = PetscMax(max_v_step,vy[0]);
    1219:     max_v_step = PetscMax(max_v_step,vy[1]);
    1220:     max_v = PetscMax(max_v,max_v_step);

    1222:     dt_max = 2.0;
    1223:     dt = 0.5 * (dh / max_v_step);
    1224:     PetscPrintf(PETSC_COMM_WORLD,".... max v %1.4e , dt %1.4e : [total] max v %1.4e , dt_max %1.4e\n",(double)max_v_step,(double)dt,(double)max_v,(double)dt_max);
    1225:     dt = PetscMin(dt_max,dt);

    1227:     /* advect */
    1228:     PetscPrintf(PETSC_COMM_WORLD,".... advect\n");
    1229:     MaterialPoint_AdvectRK1(dm_stokes,X,dt,dms_mpoint);

    1231:     /* migrate */
    1232:     PetscPrintf(PETSC_COMM_WORLD,".... migrate\n");
    1233:     DMSwarmMigrate(dms_mpoint,PETSC_TRUE);

    1235:     /* update cell population */
    1236:     PetscPrintf(PETSC_COMM_WORLD,".... populate cells\n");
    1237:     MaterialPoint_PopulateCell(dm_stokes,dms_mpoint);

    1239:     /* update coefficients on quadrature points */
    1240:     PetscPrintf(PETSC_COMM_WORLD,".... project\n");
    1241:     DMSwarmProjectFields(dms_mpoint,2,fieldnames,&pfields,PETSC_TRUE);
    1242:     eta_v = pfields[0];
    1243:     rho_v = pfields[1];
    1244:     PetscPrintf(PETSC_COMM_WORLD,".... interp\n");
    1245:     MaterialPoint_Interpolate(dm_coeff,eta_v,rho_v,dms_quadrature);

    1247:     if (tk%dump_freq == 0) {
    1248:       PetscViewer viewer;

    1250:       PetscPrintf(PETSC_COMM_WORLD,".... write XDMF, VTS\n");
    1251:       PetscSNPrintf(filename,PETSC_MAX_PATH_LEN-1,"step%.4D_coeff_dms.xmf",tk);
    1252:       DMSwarmViewXDMF(dms_mpoint,filename);

    1254:       PetscSNPrintf(filename,PETSC_MAX_PATH_LEN-1,"step%.4D_vp_dm.vts",tk);
    1255:       PetscViewerCreate(PETSC_COMM_WORLD,&viewer);
    1256:       PetscViewerSetType(viewer,PETSCVIEWERVTK);
    1257:       PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
    1258:       PetscViewerFileSetName(viewer,filename);
    1259:       VecView(X,viewer);
    1260:       PetscViewerDestroy(&viewer);
    1261:     }
    1262:     time += dt;
    1263:     PetscPrintf(PETSC_COMM_WORLD,"step %D : time %1.2e \n",tk,(double)time);
    1264:   }

    1266:   KSPDestroy(&ksp);
    1267:   VecDestroy(&X);
    1268:   VecDestroy(&f);
    1269:   MatDestroy(&A);
    1270:   MatDestroy(&B);
    1271:   VecDestroy(&eta_v);
    1272:   VecDestroy(&rho_v);
    1273:   PetscFree(pfields);

    1275:   DMDestroy(&dms_mpoint);
    1276:   DMDestroy(&dms_quadrature);
    1277:   DMDestroy(&dm_coeff);
    1278:   DMDestroy(&dm_stokes);
    1279:   return 0;
    1280: }

    1282: /*
    1283:  <sequential run>
    1284:  ./ex70 -stokes_ksp_type fgmres -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_block_size 3 -stokes_pc_fieldsplit_type SYMMETRIC_MULTIPLICATIVE -stokes_pc_fieldsplit_0_fields 0,1 -stokes_pc_fieldsplit_1_fields 2 -stokes_fieldsplit_0_ksp_type preonly -stokes_fieldsplit_0_pc_type lu -stokes_fieldsplit_1_ksp_type preonly -stokes_fieldsplit_1_pc_type lu  -mx 80 -my 80  -stokes_ksp_converged_reason  -dump_freq 25  -stokes_ksp_rtol 1.0e-8 -build_twosided allreduce  -ppcell 2 -nt 4000 -delta_eta 1.0 -randomize_coords
    1285: */
    1286: int main(int argc,char **args)
    1287: {
    1288:   PetscInt       mx,my;
    1289:   PetscBool      set = PETSC_FALSE;

    1291:   PetscInitialize(&argc,&args,(char*)0,help);
    1292:   mx = my = 10;
    1293:   PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
    1294:   PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
    1295:   PetscOptionsGetInt(NULL,NULL,"-mxy",&mx,&set);
    1296:   if (set) {
    1297:     my = mx;
    1298:   }
    1299:   SolveTimeDepStokes(mx,my);
    1300:   PetscFinalize();
    1301:   return 0;
    1302: }

    1304: /* -------------------------- helpers for boundary conditions -------------------------------- */
    1305: static PetscErrorCode BCApplyZero_EAST(DM da,PetscInt d_idx,Mat A,Vec b)
    1306: {
    1307:   DM                     cda;
    1308:   Vec                    coords;
    1309:   PetscInt               si,sj,nx,ny,i,j;
    1310:   PetscInt               M,N;
    1311:   DMDACoor2d             **_coords;
    1312:   const PetscInt         *g_idx;
    1313:   PetscInt               *bc_global_ids;
    1314:   PetscScalar            *bc_vals;
    1315:   PetscInt               nbcs;
    1316:   PetscInt               n_dofs;
    1317:   ISLocalToGlobalMapping ltogm;

    1320:   DMGetLocalToGlobalMapping(da,&ltogm);
    1321:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

    1323:   DMGetCoordinateDM(da,&cda);
    1324:   DMGetCoordinatesLocal(da,&coords);
    1325:   DMDAVecGetArray(cda,coords,&_coords);
    1326:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
    1327:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

    1329:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
    1330:   PetscMalloc1(ny*n_dofs,&bc_vals);

    1332:   /* init the entries to -1 so VecSetValues will ignore them */
    1333:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

    1335:   i = nx-1;
    1336:   for (j = 0; j < ny; j++) {
    1337:     PetscInt local_id;

    1339:     local_id = i+j*nx;

    1341:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

    1343:     bc_vals[j] =  0.0;
    1344:   }
    1345:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
    1346:   nbcs = 0;
    1347:   if ((si+nx) == (M)) nbcs = ny;

    1349:   if (b) {
    1350:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
    1351:     VecAssemblyBegin(b);
    1352:     VecAssemblyEnd(b);
    1353:   }
    1354:   if (A) {
    1355:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
    1356:   }

    1358:   PetscFree(bc_vals);
    1359:   PetscFree(bc_global_ids);

    1361:   DMDAVecRestoreArray(cda,coords,&_coords);
    1362:   return 0;
    1363: }

    1365: static PetscErrorCode BCApplyZero_WEST(DM da,PetscInt d_idx,Mat A,Vec b)
    1366: {
    1367:   DM                     cda;
    1368:   Vec                    coords;
    1369:   PetscInt               si,sj,nx,ny,i,j;
    1370:   PetscInt               M,N;
    1371:   DMDACoor2d             **_coords;
    1372:   const PetscInt         *g_idx;
    1373:   PetscInt               *bc_global_ids;
    1374:   PetscScalar            *bc_vals;
    1375:   PetscInt               nbcs;
    1376:   PetscInt               n_dofs;
    1377:   ISLocalToGlobalMapping ltogm;

    1380:   DMGetLocalToGlobalMapping(da,&ltogm);
    1381:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

    1383:   DMGetCoordinateDM(da,&cda);
    1384:   DMGetCoordinatesLocal(da,&coords);
    1385:   DMDAVecGetArray(cda,coords,&_coords);
    1386:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
    1387:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

    1389:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
    1390:   PetscMalloc1(ny*n_dofs,&bc_vals);

    1392:   /* init the entries to -1 so VecSetValues will ignore them */
    1393:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

    1395:   i = 0;
    1396:   for (j = 0; j < ny; j++) {
    1397:     PetscInt local_id;

    1399:     local_id = i+j*nx;

    1401:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

    1403:     bc_vals[j] =  0.0;
    1404:   }
    1405:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
    1406:   nbcs = 0;
    1407:   if (si == 0) nbcs = ny;

    1409:   if (b) {
    1410:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
    1411:     VecAssemblyBegin(b);
    1412:     VecAssemblyEnd(b);
    1413:   }

    1415:   if (A) {
    1416:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
    1417:   }

    1419:   PetscFree(bc_vals);
    1420:   PetscFree(bc_global_ids);

    1422:   DMDAVecRestoreArray(cda,coords,&_coords);
    1423:   return 0;
    1424: }

    1426: static PetscErrorCode BCApplyZero_NORTH(DM da,PetscInt d_idx,Mat A,Vec b)
    1427: {
    1428:   DM                     cda;
    1429:   Vec                    coords;
    1430:   PetscInt               si,sj,nx,ny,i,j;
    1431:   PetscInt               M,N;
    1432:   DMDACoor2d             **_coords;
    1433:   const PetscInt         *g_idx;
    1434:   PetscInt               *bc_global_ids;
    1435:   PetscScalar            *bc_vals;
    1436:   PetscInt               nbcs;
    1437:   PetscInt               n_dofs;
    1438:   ISLocalToGlobalMapping ltogm;

    1441:   DMGetLocalToGlobalMapping(da,&ltogm);
    1442:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

    1444:   DMGetCoordinateDM(da,&cda);
    1445:   DMGetCoordinatesLocal(da,&coords);
    1446:   DMDAVecGetArray(cda,coords,&_coords);
    1447:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
    1448:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

    1450:   PetscMalloc1(nx,&bc_global_ids);
    1451:   PetscMalloc1(nx,&bc_vals);

    1453:   /* init the entries to -1 so VecSetValues will ignore them */
    1454:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

    1456:   j = ny-1;
    1457:   for (i = 0; i < nx; i++) {
    1458:     PetscInt local_id;

    1460:     local_id = i+j*nx;

    1462:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

    1464:     bc_vals[i] =  0.0;
    1465:   }
    1466:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
    1467:   nbcs = 0;
    1468:   if ((sj+ny) == (N)) nbcs = nx;

    1470:   if (b) {
    1471:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
    1472:     VecAssemblyBegin(b);
    1473:     VecAssemblyEnd(b);
    1474:   }
    1475:   if (A) {
    1476:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,NULL,NULL);
    1477:   }

    1479:   PetscFree(bc_vals);
    1480:   PetscFree(bc_global_ids);

    1482:   DMDAVecRestoreArray(cda,coords,&_coords);
    1483:   return 0;
    1484: }

    1486: static PetscErrorCode BCApplyZero_SOUTH(DM da,PetscInt d_idx,Mat A,Vec b)
    1487: {
    1488:   DM                     cda;
    1489:   Vec                    coords;
    1490:   PetscInt               si,sj,nx,ny,i,j;
    1491:   PetscInt               M,N;
    1492:   DMDACoor2d             **_coords;
    1493:   const PetscInt         *g_idx;
    1494:   PetscInt               *bc_global_ids;
    1495:   PetscScalar            *bc_vals;
    1496:   PetscInt               nbcs;
    1497:   PetscInt               n_dofs;
    1498:   ISLocalToGlobalMapping ltogm;

    1501:   DMGetLocalToGlobalMapping(da,&ltogm);
    1502:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

    1504:   DMGetCoordinateDM(da,&cda);
    1505:   DMGetCoordinatesLocal(da,&coords);
    1506:   DMDAVecGetArray(cda,coords,&_coords);
    1507:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
    1508:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

    1510:   PetscMalloc1(nx,&bc_global_ids);
    1511:   PetscMalloc1(nx,&bc_vals);

    1513:   /* init the entries to -1 so VecSetValues will ignore them */
    1514:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

    1516:   j = 0;
    1517:   for (i = 0; i < nx; i++) {
    1518:     PetscInt local_id;

    1520:     local_id = i+j*nx;

    1522:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

    1524:     bc_vals[i] =  0.0;
    1525:   }
    1526:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
    1527:   nbcs = 0;
    1528:   if (sj == 0) nbcs = nx;

    1530:   if (b) {
    1531:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
    1532:     VecAssemblyBegin(b);
    1533:     VecAssemblyEnd(b);
    1534:   }
    1535:   if (A) {
    1536:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
    1537:   }

    1539:   PetscFree(bc_vals);
    1540:   PetscFree(bc_global_ids);

    1542:   DMDAVecRestoreArray(cda,coords,&_coords);
    1543:   return 0;
    1544: }

    1546: /*
    1547:  Impose free slip boundary conditions on the left/right faces: u_i n_i = 0, tau_{ij} t_j = 0
    1548:  Impose no slip boundray conditions on the top/bottom faces:   u_i n_i = 0, u_i t_i = 0
    1549: */
    1550: static PetscErrorCode DMDAApplyBoundaryConditions(DM dm_stokes,Mat A,Vec f)
    1551: {
    1553:   BCApplyZero_NORTH(dm_stokes,0,A,f);
    1554:   BCApplyZero_NORTH(dm_stokes,1,A,f);
    1555:   BCApplyZero_EAST(dm_stokes,0,A,f);
    1556:   BCApplyZero_SOUTH(dm_stokes,0,A,f);
    1557:   BCApplyZero_SOUTH(dm_stokes,1,A,f);
    1558:   BCApplyZero_WEST(dm_stokes,0,A,f);
    1559:   return 0;
    1560: }

    1562: /*TEST

    1564:    test:
    1565:      suffix: 1
    1566:      args: -no_view
    1567:      requires: !complex double
    1568:      filter: grep -v atomic
    1569:      filter_output: grep -v atomic
    1570:    test:
    1571:      suffix: 1_matis
    1572:      requires: !complex double
    1573:      args: -no_view -dm_mat_type is
    1574:      filter: grep -v atomic
    1575:      filter_output: grep -v atomic
    1576:    testset:
    1577:      nsize: 4
    1578:      requires: !complex double
    1579:      args: -no_view -dm_mat_type is -stokes_ksp_type fetidp -mx 80 -my 80 -stokes_ksp_converged_reason -stokes_ksp_rtol 1.0e-8 -ppcell 2 -nt 4 -randomize_coords -stokes_ksp_error_if_not_converged
    1580:      filter: grep -v atomic
    1581:      filter_output: grep -v atomic
    1582:      test:
    1583:        suffix: fetidp
    1584:        args: -stokes_fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
    1585:      test:
    1586:        suffix: fetidp_lumped
    1587:        args: -stokes_fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd -stokes_fetidp_pc_lumped -stokes_fetidp_bddc_pc_bddc_dirichlet_pc_type none -stokes_fetidp_bddc_pc_bddc_switch_static
    1588:      test:
    1589:        suffix: fetidp_saddlepoint
    1590:        args: -stokes_ksp_fetidp_saddlepoint -stokes_fetidp_ksp_type cg -stokes_ksp_norm_type natural -stokes_fetidp_pc_fieldsplit_schur_fact_type diag -stokes_fetidp_fieldsplit_p_pc_type bjacobi -stokes_fetidp_fieldsplit_lag_ksp_type preonly -stokes_fetidp_fieldsplit_p_ksp_type preonly -stokes_ksp_fetidp_pressure_field 2 -stokes_fetidp_pc_fieldsplit_schur_scale -1
    1591:      test:
    1592:        suffix: fetidp_saddlepoint_lumped
    1593:        args: -stokes_ksp_fetidp_saddlepoint -stokes_fetidp_ksp_type cg -stokes_ksp_norm_type natural -stokes_fetidp_pc_fieldsplit_schur_fact_type diag -stokes_fetidp_fieldsplit_p_pc_type bjacobi -stokes_fetidp_fieldsplit_lag_ksp_type preonly -stokes_fetidp_fieldsplit_p_ksp_type preonly -stokes_ksp_fetidp_pressure_field 2 -stokes_fetidp_pc_fieldsplit_schur_scale -1 -stokes_fetidp_bddc_pc_bddc_dirichlet_pc_type none -stokes_fetidp_bddc_pc_bddc_switch_static -stokes_fetidp_pc_lumped
    1594: TEST*/