Actual source code: ex70.c

petsc-master 2018-07-20
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  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/examples/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


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

 50:   N[0] = 0.25*(1.0-xi)*(1.0-eta);
 51:   N[1] = 0.25*(1.0+xi)*(1.0-eta);
 52:   N[2] = 0.25*(1.0+xi)*(1.0+eta);
 53:   N[3] = 0.25*(1.0-xi)*(1.0+eta);
 54: }

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

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

 66:   dN[1][0] = -0.25*(1.0-xi);
 67:   dN[1][1] = -0.25*(1.0+xi);
 68:   dN[1][2] =  0.25*(1.0+xi);
 69:   dN[1][3] =  0.25*(1.0-xi);
 70: }

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

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

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

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

 95:   for (i = 0; i < NODES_PER_EL; i++) {
 96:     dNx[0][i] = dN[0][i]*iJ00+dN[1][i]*iJ01;
 97:     dNx[1][i] = dN[0][i]*iJ10+dN[1][i]*iJ11;
 98:   }

100:   if (det_J) *det_J = J;
101: }

103: static void CreateGaussQuadrature(PetscInt *ngp,PetscScalar gp_xi[][2],PetscScalar gp_weight[])
104: {
105:   *ngp         = 4;
106:   gp_xi[0][0]  = -0.57735026919; gp_xi[0][1] = -0.57735026919;
107:   gp_xi[1][0]  = -0.57735026919; gp_xi[1][1] =  0.57735026919;
108:   gp_xi[2][0]  =  0.57735026919; gp_xi[2][1] =  0.57735026919;
109:   gp_xi[3][0]  =  0.57735026919; gp_xi[3][1] = -0.57735026919;
110:   gp_weight[0] = 1.0;
111:   gp_weight[1] = 1.0;
112:   gp_weight[2] = 1.0;
113:   gp_weight[3] = 1.0;
114: }

116: static PetscErrorCode DMDAGetElementEqnums_up(const PetscInt element[],PetscInt s_u[],PetscInt s_p[])
117: {
118:   PetscInt i;
120:   for (i=0; i<NODES_PER_EL; i++) {
121:     /* velocity */
122:     s_u[NSD*i+0] = 3*element[i];
123:     s_u[NSD*i+1] = 3*element[i]+1;
124:     /* pressure */
125:     s_p[i] = 3*element[i]+2;
126:   }
127:   return(0);
128: }

130: 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)
131: {
132:   PetscInt ij,r,c,nc;

134:   nc = u_NPE*u_dof;
135:   r = w_dof*wi+wd;
136:   c = u_dof*ui+ud;
137:   ij = r*nc+c;
138:   return(ij);
139: }

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

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

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

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

161:       B[0][2*i] = d_dx_i;B[0][2*i+1] = 0.0;
162:       B[1][2*i] = 0.0;B[1][2*i+1] = d_dy_i;
163:       B[2][2*i] = d_dy_i;B[2][2*i+1] = d_dx_i;
164:     }

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

170:     /* form Bt tildeD B */
171:     /*
172:     Ke_ij = Bt_ik . D_kl . B_lj
173:           = B_ki . D_kl . B_lj
174:           = B_ki . D_kk . B_kj
175:     */
176:     for (i = 0; i < 8; i++) {
177:       for (j = 0; j < 8; j++) {
178:         for (k = 0; k < 3; k++) { /* Note D is diagonal for stokes */
179:           Ke[i+8*j] += B[k][i]*tildeD[k]*B[k][j];
180:         }
181:       }
182:     }
183:   }
184: }

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

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

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

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

209:           Ke[IJ] -= GNx_p[di][i]*Ni_p[j]*fac;
210:         }
211:       }
212:     }
213:   }
214: }

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

221:   PetscMemzero(Ge,sizeof(PetscScalar)*U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL);
222:   BForm_Grad(Ge,coords);

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

227:   for (i = 0; i < nr_g; i++) {
228:     for (j = 0; j < nc_g; j++) {
229:       De[nr_g*j+i] = Ge[nc_g*i+j];
230:     }
231:   }
232: }

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

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

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

251:     for (i = 0; i < NODES_PER_EL; i++) {
252:       for (j = 0; j < NODES_PER_EL; j++) {
253:         Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.0625);
254:       }
255:     }
256:   }

258:   /* scale */
259:   eta_avg = 0.0;
260:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
261:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
262:   fac     = 1.0/eta_avg;
263:   for (i = 0; i < NODES_PER_EL; i++) {
264:     for (j = 0; j < NODES_PER_EL; j++) {
265:       Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
266:     }
267:   }
268: }

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

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

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

287:     for (i = 0; i < NODES_PER_EL; i++) {
288:       for (j = 0; j < NODES_PER_EL; j++) {
289:         Ke[NODES_PER_EL*i+j] -= fac*Ni_p[i]*Ni_p[j];
290:       }
291:     }
292:   }

294:   /* scale */
295:   eta_avg = 0.0;
296:   for (p = 0; p < ngp; p++) eta_avg += eta[p];
297:   eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
298:   fac     = 1.0/eta_avg;
299:   for (i = 0; i < NODES_PER_EL; i++) {
300:     for (j = 0; j < NODES_PER_EL; j++) {
301:       Ke[NODES_PER_EL*i+j] *= fac;
302:     }
303:   }
304: }

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

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

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

323:     for (i = 0; i < NODES_PER_EL; i++) {
324:       Fe[NSD*i]    = 0.0;
325:       Fe[NSD*i+1] -= fac*Ni_p[i]*fy[p];
326:     }
327:   }
328: }

330: static PetscErrorCode GetElementCoords(const PetscScalar _coords[],const PetscInt e2n[],PetscScalar el_coords[])
331: {
332:   PetscInt i,d;
334:   /* get coords for the element */
335:   for (i=0; i<4; i++) {
336:     for (d=0; d<NSD; d++) {
337:       el_coords[NSD*i+d] = _coords[NSD * e2n[i] + d];
338:     }
339:   }
340:   return(0);
341: }

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

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

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

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

374:     /* get coords for the element */
375:     GetElementCoords(_coords,element,el_coords);

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

380:     /* initialise element stiffness matrix */
381:     PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
382:     PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
383:     PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
384:     PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);

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

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

402:   DMSwarmRestoreField(quadrature,"eta_q",NULL,NULL,(void**)&q_eta);
403:   VecRestoreArrayRead(coords,&_coords);
404:   return(0);
405: }

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

425:   MatZeroEntries(A);
426:   /* setup for coords */
427:   DMGetCoordinateDM(stokes_da,&cda);
428:   DMGetCoordinatesLocal(stokes_da,&coords);
429:   VecGetArrayRead(coords,&_coords);

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

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

438:     /* get coords for the element */
439:     GetElementCoords(_coords,element,el_coords);

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

444:     /* initialise element stiffness matrix */
445:     PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
446:     PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
447:     PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
448:     PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);

450:     /* form element stiffness matrix */
451:     BForm_DivT(Ae,el_coords,prop_eta);
452:     BForm_Grad(Ge,el_coords);
453:     BForm_ScaledMassMatrix(Ce,el_coords,prop_eta);

455:     /* insert element matrix into global matrix */
456:     DMDAGetElementEqnums_up(element,u_eqn,p_eqn);
457:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
458:     MatSetValuesLocal(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
459:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);
460:     MatSetValuesLocal(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
461:   }
462:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
463:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

468:   return(0);
469: }

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

489:   VecZeroEntries(F);
490:   /* setup for coords */
491:   DMGetCoordinateDM(stokes_da,&cda);
492:   DMGetCoordinatesLocal(stokes_da,&coords);
493:   VecGetArrayRead(coords,&_coords);

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

498:   /* get acces to the vector */
499:   DMGetLocalVector(stokes_da,&local_F);
500:   VecZeroEntries(local_F);
501:   VecGetArray(local_F,&LA_F);

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

507:     /* get coords for the element */
508:     GetElementCoords(_coords,element,el_coords);

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

513:     /* initialise element stiffness matrix */
514:     PetscMemzero(Fe,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS);
515:     PetscMemzero(He,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS);

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

520:     /* insert element matrix into global matrix */
521:     DMDAGetElementEqnums_up(element,u_eqn,p_eqn);

523:     for (i=0; i<NODES_PER_EL*U_DOFS; i++) {
524:       LA_F[ u_eqn[i] ] += Fe[i];
525:     }
526:   }
527:   DMSwarmRestoreField(quadrature,"rho_q",NULL,NULL,(void**)&q_rhs);
528:   VecRestoreArrayRead(coords,&_coords);

530:   VecRestoreArray(local_F,&LA_F);
531:   DMLocalToGlobalBegin(stokes_da,local_F,ADD_VALUES,F);
532:   DMLocalToGlobalEnd(stokes_da,local_F,ADD_VALUES,F);
533:   DMRestoreLocalVector(stokes_da,&local_F);

535:   return(0);
536: }

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

550:   DMGetDimension(dm,&dim);
551:   DMDAGetElements(dmc,&nel,&npe,&element_list);

553:   PetscMalloc1(dim*npoints,&xp);
554:   PetscMalloc1(dim*npe,&elcoor);
555:   PetscMalloc1(npoints,&basis);
556:   for (q=0; q<npoints; q++) {
557:     PetscMalloc1(npe,&basis[q]);

559:     switch (dim) {
560:       case 1:
561:         basis[q][0] = 0.5*(1.0 - xi[dim*q+0]);
562:         basis[q][1] = 0.5*(1.0 + xi[dim*q+0]);
563:         break;
564:       case 2:
565:         basis[q][0] = 0.25*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1]);
566:         basis[q][1] = 0.25*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1]);
567:         basis[q][2] = 0.25*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1]);
568:         basis[q][3] = 0.25*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1]);
569:         break;

571:       case 3:
572:         basis[q][0] = 0.125*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 - xi[dim*q+2]);
573:         basis[q][1] = 0.125*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 - xi[dim*q+2]);
574:         basis[q][2] = 0.125*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 - xi[dim*q+2]);
575:         basis[q][3] = 0.125*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 - xi[dim*q+2]);
576:         basis[q][4] = 0.125*(1.0 - xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 + xi[dim*q+2]);
577:         basis[q][5] = 0.125*(1.0 + xi[dim*q+0])*(1.0 - xi[dim*q+1])*(1.0 + xi[dim*q+2]);
578:         basis[q][6] = 0.125*(1.0 + xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 + xi[dim*q+2]);
579:         basis[q][7] = 0.125*(1.0 - xi[dim*q+0])*(1.0 + xi[dim*q+1])*(1.0 + xi[dim*q+2]);
580:         break;
581:     }
582:   }

584:   DMGetCoordinatesLocal(dmc,&coor);
585:   VecGetArrayRead(coor,&_coor);
586:   /* compute and store the coordinates for the new points */
587:   {
588:     const PetscInt *element = &element_list[npe*e];

590:     for (k=0; k<npe; k++) {
591:       for (d=0; d<dim; d++) {
592:         elcoor[dim*k+d] = PetscRealPart(_coor[ dim*element[k] + d ]);
593:       }
594:     }
595:     for (q=0; q<npoints; q++) {
596:       for (d=0; d<dim; d++) {
597:         xp[dim*q+d] = 0.0;
598:       }
599:       for (k=0; k<npe; k++) {
600:         for (d=0; d<dim; d++) {
601:           xp[dim*q+d] += basis[q][k] * elcoor[dim*k+d];
602:         }
603:       }
604:     }
605:   }
606:   VecRestoreArrayRead(coor,&_coor);
607:   DMDARestoreElements(dmc,&nel,&npe,&element_list);

609:   DMSwarmGetLocalSize(dm,&ncurr);
610:   DMSwarmAddNPoints(dm,npoints);

612:   if (proximity_initialization) {
613:     PetscInt  *nnlist;
614:     PetscReal *coor_q,*coor_qn;
615:     PetscInt  npoints_e,*plist_e;

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

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

627:       coor_q = &xp[dim*q];
628:       for (qn=0; qn<npoints_e; qn++) {
629:         coor_qn = &swarm_coor[dim*plist_e[qn]];
630:         sep = 0.0;
631:         for (d=0; d<dim; d++) {
632:           sep += (coor_q[d]-coor_qn[d])*(coor_q[d]-coor_qn[d]);
633:         }
634:         if (sep < min_sep) {
635:           nearest_neighour = plist_e[qn];
636:           min_sep = sep;
637:         }
638:       }
639:       if (nearest_neighour == -1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_USER,"Cell %D is empty - cannot initalize using nearest neighbours",e);
640:       nnlist[q] = nearest_neighour;
641:     }
642:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
643:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);

645:     /* copies the nearest neighbour (nnlist[q]) into the new slot (ncurr+q) */
646:     for (q=0; q<npoints; q++) {
647:       DMSwarmCopyPoint(dm,nnlist[q],ncurr+q);
648:     }
649:     DMSwarmGetField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
650:     DMSwarmGetField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
651:     for (q=0; q<npoints; q++) {
652:       /* set the coordinates */
653:       for (d=0; d<dim; d++) {
654:         swarm_coor[dim*(ncurr+q)+d] = xp[dim*q+d];
655:       }
656:       /* set the cell index */
657:       swarm_cellid[ncurr+q] = e;
658:     }
659:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
660:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);

662:     PetscFree(plist_e);
663:     PetscFree(nnlist);
664:   } else {
665:     DMSwarmGetField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
666:     DMSwarmGetField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
667:     for (q=0; q<npoints; q++) {
668:       /* set the coordinates */
669:       for (d=0; d<dim; d++) {
670:         swarm_coor[dim*(ncurr+q)+d] = xp[dim*q+d];
671:       }
672:       /* set the cell index */
673:       swarm_cellid[ncurr+q] = e;
674:     }
675:     DMSwarmRestoreField(dm,DMSwarmPICField_cellid,NULL,NULL,(void**)&swarm_cellid);
676:     DMSwarmRestoreField(dm,DMSwarmPICField_coor,NULL,NULL,(void**)&swarm_coor);
677:   }

679:   PetscFree(xp);
680:   PetscFree(elcoor);
681:   for (q=0; q<npoints; q++) {
682:     PetscFree(basis[q]);
683:   }
684:   PetscFree(basis);
685:   return(0);
686: }

688: PetscErrorCode MaterialPoint_PopulateCell(DM dm_vp,DM dm_mpoint)
689: {
690:   PetscInt        _npe,_nel,e,nel;
691:   const PetscInt  *element;
692:   DM              dmc;
693:   PetscQuadrature quadrature;
694:   const PetscReal *xi;
695:   PetscInt        npoints_q,cnt,cnt_g;
696:   PetscErrorCode  ierr;

699:   DMDAGetElements(dm_vp,&_nel,&_npe,&element);
700:   nel = _nel;
701:   DMDARestoreElements(dm_vp,&_nel,&_npe,&element);

703:   PetscDTGaussTensorQuadrature(2,1,4,-1.0,1.0,&quadrature);
704:   PetscQuadratureGetData(quadrature,NULL,NULL,&npoints_q,&xi,NULL);
705:   DMSwarmGetCellDM(dm_mpoint,&dmc);

707:   DMSwarmSortGetAccess(dm_mpoint);

709:   cnt = 0;
710:   for (e=0; e<nel; e++) {
711:     PetscInt npoints_per_cell;

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

715:     if (npoints_per_cell < 12) {
716:       DMSwarmPICInsertPointsCellwise(dm_mpoint,dm_vp,e,npoints_q,(PetscReal*)xi,PETSC_TRUE);
717:       cnt++;
718:     }
719:   }
720:   MPI_Allreduce(&cnt,&cnt_g,1,MPIU_INT,MPI_SUM,PETSC_COMM_WORLD);
721:   if (cnt_g > 0) {
722:     PetscPrintf(PETSC_COMM_WORLD,".... ....pop cont: adjusted %D cells\n",cnt_g);
723:   }

725:   DMSwarmSortRestoreAccess(dm_mpoint);
726:   PetscQuadratureDestroy(&quadrature);
727:   return(0);
728: }

730: PetscErrorCode MaterialPoint_AdvectRK1(DM dm_vp,Vec vp,PetscReal dt,DM dm_mpoint)
731: {
732:   PetscErrorCode    ierr;
733:   Vec               vp_l,coor_l;
734:   const PetscScalar *LA_vp;
735:   PetscInt          i,p,e,npoints,nel,npe;
736:   PetscInt          *mpfield_cell;
737:   PetscReal         *mpfield_coor;
738:   const PetscInt    *element_list;
739:   const PetscInt    *element;
740:   PetscScalar       xi_p[NSD],Ni[NODES_PER_EL];
741:   const PetscScalar *LA_coor;
742:   PetscScalar       dx[NSD];

745:   DMGetCoordinatesLocal(dm_vp,&coor_l);
746:   VecGetArrayRead(coor_l,&LA_coor);

748:   DMGetLocalVector(dm_vp,&vp_l);
749:   DMGlobalToLocalBegin(dm_vp,vp,INSERT_VALUES,vp_l);
750:   DMGlobalToLocalEnd(dm_vp,vp,INSERT_VALUES,vp_l);
751:   VecGetArrayRead(vp_l,&LA_vp);

753:   DMDAGetElements(dm_vp,&nel,&npe,&element_list);
754:   DMSwarmGetLocalSize(dm_mpoint,&npoints);
755:   DMSwarmGetField(dm_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&mpfield_coor);
756:   DMSwarmGetField(dm_mpoint,DMSwarmPICField_cellid,NULL,NULL,(void**)&mpfield_cell);
757:   for (p=0; p<npoints; p++) {
758:     PetscReal         *coor_p;
759:     PetscScalar       vel_n[NSD*NODES_PER_EL],vel_p[NSD];
760:     const PetscScalar *x0;
761:     const PetscScalar *x2;

763:     e       = mpfield_cell[p];
764:     coor_p  = &mpfield_coor[NSD*p];
765:     element = &element_list[NODES_PER_EL*e];

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

771:     dx[0] = x2[0] - x0[0];
772:     dx[1] = x2[1] - x0[1];

774:     xi_p[0] = 2.0 * (coor_p[0] - x0[0])/dx[0] - 1.0;
775:     xi_p[1] = 2.0 * (coor_p[1] - x0[1])/dx[1] - 1.0;
776:     if (PetscRealPart(xi_p[0]) < -1.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"value (xi) too small %1.4e [e=%D]\n",(double)PetscRealPart(xi_p[0]),e);
777:     if (PetscRealPart(xi_p[0]) >  1.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"value (xi) too large %1.4e [e=%D]\n",(double)PetscRealPart(xi_p[0]),e);
778:     if (PetscRealPart(xi_p[1]) < -1.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"value (eta) too small %1.4e [e=%D]\n",(double)PetscRealPart(xi_p[1]),e);
779:     if (PetscRealPart(xi_p[1]) >  1.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"value (eta) too large %1.4e [e=%D]\n",(double)PetscRealPart(xi_p[1]),e);

781:     /* evaluate basis functions */
782:     EvaluateBasis_Q1(xi_p,Ni);

784:     /* get cell nodal velocities */
785:     for (i=0; i<NODES_PER_EL; i++) {
786:       PetscInt nid;

788:       nid = element[i];
789:       vel_n[NSD*i+0] = LA_vp[(NSD+1)*nid+0];
790:       vel_n[NSD*i+1] = LA_vp[(NSD+1)*nid+1];
791:     }

793:     /* interpolate velocity */
794:     vel_p[0] = vel_p[1] = 0.0;
795:     for (i=0; i<NODES_PER_EL; i++) {
796:       vel_p[0] += Ni[i] * vel_n[NSD*i+0];
797:       vel_p[1] += Ni[i] * vel_n[NSD*i+1];
798:     }

800:     coor_p[0] += dt * PetscRealPart(vel_p[0]);
801:     coor_p[1] += dt * PetscRealPart(vel_p[1]);
802:   }

804:   DMSwarmRestoreField(dm_mpoint,DMSwarmPICField_cellid,NULL,NULL,(void**)&mpfield_cell);
805:   DMSwarmRestoreField(dm_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&mpfield_coor);
806:   DMDARestoreElements(dm_vp,&nel,&npe,&element_list);
807:   VecRestoreArrayRead(vp_l,&LA_vp);
808:   DMRestoreLocalVector(dm_vp,&vp_l);
809:   VecRestoreArrayRead(coor_l,&LA_coor);
810:   return(0);
811: }

813: PetscErrorCode MaterialPoint_Interpolate(DM dm,Vec eta_v,Vec rho_v,DM dm_quadrature)
814: {
815:   Vec            eta_l,rho_l;
816:   PetscScalar    *_eta_l,*_rho_l;
817:   PetscInt       nqp,npe,nel;
818:   PetscScalar    qp_xi[GAUSS_POINTS][NSD];
819:   PetscScalar    qp_weight[GAUSS_POINTS];
820:   PetscInt       q,k,e;
821:   PetscScalar    Ni[GAUSS_POINTS][NODES_PER_EL];
822:   const PetscInt *element_list;
823:   PetscReal      *q_eta,*q_rhs;

827:   /* define quadrature rule */
828:   CreateGaussQuadrature(&nqp,qp_xi,qp_weight);
829:   for (q=0; q<nqp; q++) {
830:     EvaluateBasis_Q1(qp_xi[q],Ni[q]);
831:   }

833:   DMGetLocalVector(dm,&eta_l);
834:   DMGetLocalVector(dm,&rho_l);

836:   DMGlobalToLocalBegin(dm,eta_v,INSERT_VALUES,eta_l);
837:   DMGlobalToLocalEnd(dm,eta_v,INSERT_VALUES,eta_l);
838:   DMGlobalToLocalBegin(dm,rho_v,INSERT_VALUES,rho_l);
839:   DMGlobalToLocalEnd(dm,rho_v,INSERT_VALUES,rho_l);

841:   VecGetArray(eta_l,&_eta_l);
842:   VecGetArray(rho_l,&_rho_l);

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

847:   DMDAGetElements(dm,&nel,&npe,&element_list);
848:   for (e=0; e<nel; e++) {
849:     PetscScalar    eta_field_e[NODES_PER_EL];
850:     PetscScalar    rho_field_e[NODES_PER_EL];
851:     const PetscInt *element = &element_list[4*e];

853:     for (k=0; k<NODES_PER_EL; k++) {
854:       eta_field_e[k] = _eta_l[ element[k] ];
855:       rho_field_e[k] = _rho_l[ element[k] ];
856:     }

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

861:       eta_q = rho_q = 0.0;
862:       for (k=0; k<NODES_PER_EL; k++) {
863:         eta_q += Ni[q][k] * eta_field_e[k];
864:         rho_q += Ni[q][k] * rho_field_e[k];
865:       }

867:       q_eta[nqp*e+q] = PetscRealPart(eta_q);
868:       q_rhs[nqp*e+q] = PetscRealPart(rho_q);
869:     }
870:   }
871:   DMDARestoreElements(dm,&nel,&npe,&element_list);

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

876:   VecRestoreArray(rho_l,&_rho_l);
877:   VecRestoreArray(eta_l,&_eta_l);
878:   DMRestoreLocalVector(dm,&rho_l);
879:   DMRestoreLocalVector(dm,&eta_l);
880:   return(0);
881: }

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

911:   /*
912:     Generate the DMDA for the velocity and pressure spaces.
913:     We use Q1 elements for both fields.
914:     The Q1 FE basis on a regular mesh has a 9-point stencil (DMDA_STENCIL_BOX)
915:     The number of nodes in each direction is mx+1, my+1
916:   */
917:   u_dof         = U_DOFS; /* Vx, Vy - velocities */
918:   p_dof         = P_DOFS; /* p - pressure */
919:   dof           = u_dof + p_dof;
920:   stencil_width = 1;
921:   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);
922:   DMDASetElementType(dm_stokes,DMDA_ELEMENT_Q1);
923:   DMSetMatType(dm_stokes,MATAIJ);
924:   DMSetFromOptions(dm_stokes);
925:   DMSetUp(dm_stokes);
926:   DMDASetFieldName(dm_stokes,0,"ux");
927:   DMDASetFieldName(dm_stokes,1,"uy");
928:   DMDASetFieldName(dm_stokes,2,"p");

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

934:   /* Get local number of elements */
935:   {
936:     DMDAGetElements(dm_stokes,&nel,&npe,&element_list);

938:     nel_local = nel;

940:     DMDARestoreElements(dm_stokes,&nel,&npe,&element_list);
941:   }

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

946:   /* Create the swarm for storing quadrature point values */
947:   DMCreate(PETSC_COMM_WORLD,&dms_quadrature);
948:   DMSetType(dms_quadrature,DMSWARM);
949:   DMSetDimension(dms_quadrature,2);

951:   /* Register fields for viscosity and density on the quadrature points */
952:   DMSwarmRegisterPetscDatatypeField(dms_quadrature,"eta_q",1,PETSC_REAL);
953:   DMSwarmRegisterPetscDatatypeField(dms_quadrature,"rho_q",1,PETSC_REAL);
954:   DMSwarmFinalizeFieldRegister(dms_quadrature);
955:   DMSwarmSetLocalSizes(dms_quadrature,nel_local * GAUSS_POINTS,0);

957:   /* Create the material point swarm */
958:   DMCreate(PETSC_COMM_WORLD,&dms_mpoint);
959:   DMSetType(dms_mpoint,DMSWARM);
960:   DMSetDimension(dms_mpoint,2);

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

965:   /*
966:      Specify the DM to use for point location and projections
967:      within the context of a PIC scheme
968:   */
969:   DMSwarmSetCellDM(dms_mpoint,dm_coeff);

971:   /* Register fields for viscosity and density */
972:   DMSwarmRegisterPetscDatatypeField(dms_mpoint,"eta",1,PETSC_REAL);
973:   DMSwarmRegisterPetscDatatypeField(dms_mpoint,"rho",1,PETSC_REAL);
974:   DMSwarmFinalizeFieldRegister(dms_mpoint);

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

979:   /*
980:     Layout the material points in space using the cell DM.
981:     Particle coordinates are defined by cell wise using different methods.
982:     - DMSWARMPIC_LAYOUT_GAUSS defines particles coordinates at the positions
983:                               corresponding to a Gauss quadrature rule with
984:                               ppcell points in each direction.
985:     - DMSWARMPIC_LAYOUT_REGULAR defines particle coordinates at the centoid of
986:                                 ppcell x ppcell quadralaterals defined within the
987:                                 reference element.
988:     - DMSWARMPIC_LAYOUT_SUBDIVISION defines particles coordinates at the centroid
989:                                     of each quadralateral obtained by sub-dividing
990:                                     the reference element cell ppcell times.
991:   */
992:   DMSwarmInsertPointsUsingCellDM(dms_mpoint,DMSWARMPIC_LAYOUT_SUBDIVISION,ppcell);

994:   /*
995:     Defne a high resolution layer of material points across the material interface
996:   */
997:   {
998:     PetscInt  npoints_dir_x[2];
999:     PetscReal min[2],max[2];

1001:     npoints_dir_x[0] = (PetscInt)(0.9142/(0.05*dh));
1002:     npoints_dir_x[1] = (PetscInt)((0.25-0.15)/(0.05*dh));
1003:     min[0] = 0.0;  max[0] = 0.9142;
1004:     min[1] = 0.05; max[1] = 0.35;
1005:     DMSwarmSetPointsUniformCoordinates(dms_mpoint,min,max,npoints_dir_x,ADD_VALUES);
1006:   }

1008:   /*
1009:     Define a high resolution layer of material points near the surface of the domain
1010:     to deal with weakly compressible Q1-Q1 elements. These elements "self compact"
1011:     when applied to buouyancy driven flow. The error in div(u) is O(h).
1012:   */
1013:   {
1014:     PetscInt  npoints_dir_x[2];
1015:     PetscReal min[2],max[2];

1017:     npoints_dir_x[0] = (PetscInt)(0.9142/(0.25*dh));
1018:     npoints_dir_x[1] = (PetscInt)(3.0*dh/(0.25*dh));
1019:     min[0] = 0.0;          max[0] = 0.9142;
1020:     min[1] = 1.0 - 3.0*dh; max[1] = 1.0-0.0001;
1021:     DMSwarmSetPointsUniformCoordinates(dms_mpoint,min,max,npoints_dir_x,ADD_VALUES);
1022:   }

1024:   DMView(dms_mpoint,PETSC_VIEWER_STDOUT_WORLD);

1026:   /* Define initial material properties on each particle in the material point swarm */
1027:   PetscOptionsGetReal(NULL,NULL,"-delta_eta",&delta_eta,NULL);
1028:   PetscOptionsGetBool(NULL,NULL,"-randomize_coords",&randomize_coords,NULL);
1029:   PetscOptionsGetReal(NULL,NULL,"-randomize_fac",&randomize_fac,NULL);
1030:   if (randomize_fac > 1.0) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"The value of -randomize_fac should be <= 1.0");
1031:   {
1032:     PetscReal   *array_x,*array_e,*array_r;
1033:     PetscInt    p;
1034:     PetscRandom r;
1035:     PetscMPIInt rank;

1037:     MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

1039:     PetscRandomCreate(PETSC_COMM_SELF,&r);
1040:     PetscRandomSetInterval(r,-randomize_fac*dh,randomize_fac*dh);
1041:     PetscRandomSetSeed(r,(unsigned long)rank);
1042:     PetscRandomSeed(r);

1044:     DMDAGetElements(dm_stokes,&nel,&npe,&element_list);

1046:     /*
1047:        Fetch the registered data from the material point DMSwarm.
1048:        The fields "eta" and "rho" were registered by this example.
1049:        The field identified by the the variable DMSwarmPICField_coor
1050:        was registered by the DMSwarm implementation when the function
1051:          DMSwarmSetType(dms_mpoint,DMSWARM_PIC)
1052:        was called. The returned array defines the coordinates of each
1053:        material point in the point swarm.
1054:     */
1055:     DMSwarmGetField(dms_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&array_x);
1056:     DMSwarmGetField(dms_mpoint,"eta",               NULL,NULL,(void**)&array_e);
1057:     DMSwarmGetField(dms_mpoint,"rho",               NULL,NULL,(void**)&array_r);

1059:     DMSwarmGetLocalSize(dms_mpoint,&npoints);
1060:     for (p = 0; p < npoints; p++) {
1061:       PetscReal x_p[2],rr[2];

1063:       if (randomize_coords) {
1064:         PetscRandomGetValueReal(r,&rr[0]);
1065:         PetscRandomGetValueReal(r,&rr[1]);
1066:         array_x[2*p + 0] += rr[0];
1067:         array_x[2*p + 1] += rr[1];
1068:       }

1070:       /* Get the coordinates of point, p */
1071:       x_p[0] = array_x[2*p + 0];
1072:       x_p[1] = array_x[2*p + 1];

1074:        if (x_p[1] < (0.2 + 0.02*PetscCosReal(PETSC_PI*x_p[0]/0.9142))) {
1075:          /* Material properties below the interface */
1076:          array_e[p] = 1.0 * (1.0/delta_eta);
1077:          array_r[p] = 0.0;
1078:        } else {
1079:          /* Material properties above the interface */
1080:          array_e[p] = 1.0;
1081:          array_r[p] = 1.0;
1082:        }
1083:     }

1085:     /*
1086:        Restore the fetched data fields from the material point DMSwarm.
1087:        Calling the Restore function invalidates the points array_r, array_e, array_x
1088:        by setting them to NULL.
1089:     */
1090:     DMSwarmRestoreField(dms_mpoint,"rho",NULL,NULL,(void**)&array_r);
1091:     DMSwarmRestoreField(dms_mpoint,"eta",NULL,NULL,(void**)&array_e);
1092:     DMSwarmRestoreField(dms_mpoint,DMSwarmPICField_coor,NULL,NULL,(void**)&array_x);

1094:     DMDARestoreElements(dm_stokes,&nel,&npe,&element_list);
1095:     PetscRandomDestroy(&r);
1096:   }

1098:   /*
1099:      If the particle coordinates where randomly shifted, they may have crossed into another
1100:      element, or into another sub-domain. To account for this we call the Migrate function.
1101:   */
1102:   if (randomize_coords) {
1103:     DMSwarmMigrate(dms_mpoint,PETSC_TRUE);
1104:   }

1106:   PetscOptionsGetBool(NULL,NULL,"-no_view",&no_view,NULL);
1107:   if (!no_view) {
1108:     DMSwarmViewXDMF(dms_mpoint,"ic_coeff_dms.xmf");
1109:   }

1111:   /* project the swarm properties */
1112:   DMSwarmProjectFields(dms_mpoint,2,fieldnames,&pfields,PETSC_FALSE);
1113:   eta_v = pfields[0];
1114:   rho_v = pfields[1];
1115:   PetscObjectSetName((PetscObject)eta_v,"eta");
1116:   PetscObjectSetName((PetscObject)rho_v,"rho");
1117:   MaterialPoint_Interpolate(dm_coeff,eta_v,rho_v,dms_quadrature);

1119:   /* view projected coefficients eta and rho */
1120:   if (!no_view) {
1121:     PetscViewer viewer;

1123:     PetscViewerCreate(PETSC_COMM_WORLD,&viewer);
1124:     PetscViewerSetType(viewer,PETSCVIEWERVTK);
1125:     PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1126:     PetscViewerFileSetName(viewer,"ic_coeff_dmda.vts");
1127:     VecView(eta_v,viewer);
1128:     VecView(rho_v,viewer);
1129:     PetscViewerDestroy(&viewer);
1130:   }

1132:   DMCreateMatrix(dm_stokes,&A);
1133:   DMCreateMatrix(dm_stokes,&B);
1134:   DMCreateGlobalVector(dm_stokes,&f);
1135:   DMCreateGlobalVector(dm_stokes,&X);

1137:   AssembleStokes_A(A,dm_stokes,dms_quadrature);
1138:   AssembleStokes_PC(B,dm_stokes,dms_quadrature);
1139:   AssembleStokes_RHS(f,dm_stokes,dms_quadrature);

1141:   DMDAApplyBoundaryConditions(dm_stokes,A,f);
1142:   DMDAApplyBoundaryConditions(dm_stokes,B,NULL);

1144:   KSPCreate(PETSC_COMM_WORLD,&ksp);
1145:   KSPSetOptionsPrefix(ksp,"stokes_");
1146:   KSPSetDM(ksp,dm_stokes);
1147:   KSPSetDMActive(ksp,PETSC_FALSE);
1148:   KSPSetOperators(ksp,A,B);
1149:   KSPSetFromOptions(ksp);
1150:   KSPGetPC(ksp,&pc);
1151:   PetscObjectTypeCompare((PetscObject)pc,PCBDDC,&isbddc);
1152:   if (isbddc) {
1153:     KSPSetOperators(ksp,A,A);
1154:   }

1156:   /* Define u-v-p indices for fieldsplit */
1157:   {
1158:     PC             pc;
1159:     const PetscInt ufields[] = {0,1},pfields[1] = {2};

1161:     KSPGetPC(ksp,&pc);
1162:     PCFieldSplitSetBlockSize(pc,3);
1163:     PCFieldSplitSetFields(pc,"u",2,ufields,ufields);
1164:     PCFieldSplitSetFields(pc,"p",1,pfields,pfields);
1165:   }

1167:   /* If using a fieldsplit preconditioner, attach a DMDA to the velocity split so that geometric multigrid can be used */
1168:   {
1169:     PC        pc,pc_u;
1170:     KSP       *sub_ksp,ksp_u;
1171:     PetscInt  nsplits;
1172:     DM        dm_u;
1173:     PetscBool is_pcfs;

1175:     KSPGetPC(ksp,&pc);

1177:     is_pcfs = PETSC_FALSE;
1178:     PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&is_pcfs);

1180:     if (is_pcfs) {
1181:       KSPSetUp(ksp);
1182:       KSPGetPC(ksp,&pc);
1183:       PCFieldSplitGetSubKSP(pc,&nsplits,&sub_ksp);
1184:       ksp_u = sub_ksp[0];
1185:       PetscFree(sub_ksp);

1187:       if (nsplits == 2) {
1188:         DMDACreateCompatibleDMDA(dm_stokes,2,&dm_u);

1190:         KSPSetDM(ksp_u,dm_u);
1191:         KSPSetDMActive(ksp_u,PETSC_FALSE);
1192:         DMDestroy(&dm_u);

1194:         /* enforce galerkin coarse grids be used */
1195:         KSPGetPC(ksp_u,&pc_u);
1196:         PCMGSetGalerkin(pc_u,PC_MG_GALERKIN_PMAT);
1197:       }
1198:     }
1199:   }

1201:   dump_freq = 10;
1202:   PetscOptionsGetInt(NULL,NULL,"-dump_freq",&dump_freq,NULL);
1203:   nt = 10;
1204:   PetscOptionsGetInt(NULL,NULL,"-nt",&nt,NULL);
1205:   time = 0.0;
1206:   for (tk=1; tk<=nt; tk++) {

1208:     PetscPrintf(PETSC_COMM_WORLD,".... assemble\n");
1209:     AssembleStokes_A(A,dm_stokes,dms_quadrature);
1210:     AssembleStokes_PC(B,dm_stokes,dms_quadrature);
1211:     AssembleStokes_RHS(f,dm_stokes,dms_quadrature);

1213:     PetscPrintf(PETSC_COMM_WORLD,".... bc imposition\n");
1214:     DMDAApplyBoundaryConditions(dm_stokes,A,f);
1215:     DMDAApplyBoundaryConditions(dm_stokes,B,NULL);

1217:     PetscPrintf(PETSC_COMM_WORLD,".... solve\n");
1218:     KSPSetOperators(ksp,A, isbddc ? A : B);
1219:     KSPSolve(ksp,f,X);

1221:     VecStrideMax(X,0,NULL,&vx[1]);
1222:     VecStrideMax(X,1,NULL,&vy[1]);
1223:     VecStrideMin(X,0,NULL,&vx[0]);
1224:     VecStrideMin(X,1,NULL,&vy[0]);

1226:     max_v_step = PetscMax(vx[0],vx[1]);
1227:     max_v_step = PetscMax(max_v_step,vy[0]);
1228:     max_v_step = PetscMax(max_v_step,vy[1]);
1229:     max_v = PetscMax(max_v,max_v_step);

1231:     dt_max = 2.0;
1232:     dt = 0.5 * (dh / max_v_step);
1233:     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);
1234:     dt = PetscMin(dt_max,dt);

1236:     /* advect */
1237:     PetscPrintf(PETSC_COMM_WORLD,".... advect\n");
1238:     MaterialPoint_AdvectRK1(dm_stokes,X,dt,dms_mpoint);

1240:     /* migrate */
1241:     PetscPrintf(PETSC_COMM_WORLD,".... migrate\n");
1242:     DMSwarmMigrate(dms_mpoint,PETSC_TRUE);

1244:     /* update cell population */
1245:     PetscPrintf(PETSC_COMM_WORLD,".... populate cells\n");
1246:     MaterialPoint_PopulateCell(dm_stokes,dms_mpoint);

1248:     /* update coefficients on quadrature points */
1249:     PetscPrintf(PETSC_COMM_WORLD,".... project\n");
1250:     DMSwarmProjectFields(dms_mpoint,2,fieldnames,&pfields,PETSC_TRUE);
1251:     eta_v = pfields[0];
1252:     rho_v = pfields[1];
1253:     PetscPrintf(PETSC_COMM_WORLD,".... interp\n");
1254:     MaterialPoint_Interpolate(dm_coeff,eta_v,rho_v,dms_quadrature);

1256:     if (tk%dump_freq == 0) {
1257:       PetscViewer viewer;

1259:       PetscPrintf(PETSC_COMM_WORLD,".... write XDMF, VTS\n");
1260:       PetscSNPrintf(filename,PETSC_MAX_PATH_LEN-1,"step%.4D_coeff_dms.xmf",tk);
1261:       DMSwarmViewXDMF(dms_mpoint,filename);

1263:       PetscSNPrintf(filename,PETSC_MAX_PATH_LEN-1,"step%.4D_vp_dm.vts",tk);
1264:       PetscViewerCreate(PETSC_COMM_WORLD,&viewer);
1265:       PetscViewerSetType(viewer,PETSCVIEWERVTK);
1266:       PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1267:       PetscViewerFileSetName(viewer,filename);
1268:       VecView(X,viewer);
1269:       PetscViewerDestroy(&viewer);
1270:     }
1271:     time += dt;
1272:     PetscPrintf(PETSC_COMM_WORLD,"step %D : time %1.2e \n",tk,(double)time);
1273:   }

1275:   KSPDestroy(&ksp);
1276:   VecDestroy(&X);
1277:   VecDestroy(&f);
1278:   MatDestroy(&A);
1279:   MatDestroy(&B);
1280:   VecDestroy(&eta_v);
1281:   VecDestroy(&rho_v);
1282:   PetscFree(pfields);

1284:   DMDestroy(&dms_mpoint);
1285:   DMDestroy(&dms_quadrature);
1286:   DMDestroy(&dm_coeff);
1287:   DMDestroy(&dm_stokes);
1288:   return(0);
1289: }

1291: /*
1292:  <sequential run>
1293:  ./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
1294: */
1295: int main(int argc,char **args)
1296: {
1298:   PetscInt       mx,my;
1299:   PetscBool      set = PETSC_FALSE;

1301:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
1302:   mx = my = 10;
1303:   PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
1304:   PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
1305:   PetscOptionsGetInt(NULL,NULL,"-mxy",&mx,&set);
1306:   if (set) {
1307:     my = mx;
1308:   }
1309:   SolveTimeDepStokes(mx,my);
1310:   PetscFinalize();
1311:   return ierr;
1312: }

1314: /* -------------------------- helpers for boundary conditions -------------------------------- */
1315: static PetscErrorCode BCApplyZero_EAST(DM da,PetscInt d_idx,Mat A,Vec b)
1316: {
1317:   DM                     cda;
1318:   Vec                    coords;
1319:   PetscInt               si,sj,nx,ny,i,j;
1320:   PetscInt               M,N;
1321:   DMDACoor2d             **_coords;
1322:   const PetscInt         *g_idx;
1323:   PetscInt               *bc_global_ids;
1324:   PetscScalar            *bc_vals;
1325:   PetscInt               nbcs;
1326:   PetscInt               n_dofs;
1327:   PetscErrorCode         ierr;
1328:   ISLocalToGlobalMapping ltogm;

1331:   DMGetLocalToGlobalMapping(da,&ltogm);
1332:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1334:   DMGetCoordinateDM(da,&cda);
1335:   DMGetCoordinatesLocal(da,&coords);
1336:   DMDAVecGetArray(cda,coords,&_coords);
1337:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1338:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1340:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1341:   PetscMalloc1(ny*n_dofs,&bc_vals);

1343:   /* init the entries to -1 so VecSetValues will ignore them */
1344:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1346:   i = nx-1;
1347:   for (j = 0; j < ny; j++) {
1348:     PetscInt local_id;

1350:     local_id = i+j*nx;

1352:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1354:     bc_vals[j] =  0.0;
1355:   }
1356:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1357:   nbcs = 0;
1358:   if ((si+nx) == (M)) nbcs = ny;

1360:   if (b) {
1361:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1362:     VecAssemblyBegin(b);
1363:     VecAssemblyEnd(b);
1364:   }
1365:   if (A) {
1366:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1367:   }

1369:   PetscFree(bc_vals);
1370:   PetscFree(bc_global_ids);

1372:   DMDAVecRestoreArray(cda,coords,&_coords);
1373:   return(0);
1374: }

1376: static PetscErrorCode BCApplyZero_WEST(DM da,PetscInt d_idx,Mat A,Vec b)
1377: {
1378:   DM                     cda;
1379:   Vec                    coords;
1380:   PetscInt               si,sj,nx,ny,i,j;
1381:   PetscInt               M,N;
1382:   DMDACoor2d             **_coords;
1383:   const PetscInt         *g_idx;
1384:   PetscInt               *bc_global_ids;
1385:   PetscScalar            *bc_vals;
1386:   PetscInt               nbcs;
1387:   PetscInt               n_dofs;
1388:   PetscErrorCode         ierr;
1389:   ISLocalToGlobalMapping ltogm;

1392:   DMGetLocalToGlobalMapping(da,&ltogm);
1393:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1395:   DMGetCoordinateDM(da,&cda);
1396:   DMGetCoordinatesLocal(da,&coords);
1397:   DMDAVecGetArray(cda,coords,&_coords);
1398:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1399:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1401:   PetscMalloc1(ny*n_dofs,&bc_global_ids);
1402:   PetscMalloc1(ny*n_dofs,&bc_vals);

1404:   /* init the entries to -1 so VecSetValues will ignore them */
1405:   for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;

1407:   i = 0;
1408:   for (j = 0; j < ny; j++) {
1409:     PetscInt local_id;

1411:     local_id = i+j*nx;

1413:     bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];

1415:     bc_vals[j] =  0.0;
1416:   }
1417:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1418:   nbcs = 0;
1419:   if (si == 0) nbcs = ny;

1421:   if (b) {
1422:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1423:     VecAssemblyBegin(b);
1424:     VecAssemblyEnd(b);
1425:   }

1427:   if (A) {
1428:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1429:   }

1431:   PetscFree(bc_vals);
1432:   PetscFree(bc_global_ids);

1434:   DMDAVecRestoreArray(cda,coords,&_coords);
1435:   return(0);
1436: }

1438: static PetscErrorCode BCApplyZero_NORTH(DM da,PetscInt d_idx,Mat A,Vec b)
1439: {
1440:   DM                     cda;
1441:   Vec                    coords;
1442:   PetscInt               si,sj,nx,ny,i,j;
1443:   PetscInt               M,N;
1444:   DMDACoor2d             **_coords;
1445:   const PetscInt         *g_idx;
1446:   PetscInt               *bc_global_ids;
1447:   PetscScalar            *bc_vals;
1448:   PetscInt               nbcs;
1449:   PetscInt               n_dofs;
1450:   PetscErrorCode         ierr;
1451:   ISLocalToGlobalMapping ltogm;

1454:   DMGetLocalToGlobalMapping(da,&ltogm);
1455:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1457:   DMGetCoordinateDM(da,&cda);
1458:   DMGetCoordinatesLocal(da,&coords);
1459:   DMDAVecGetArray(cda,coords,&_coords);
1460:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1461:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1463:   PetscMalloc1(nx,&bc_global_ids);
1464:   PetscMalloc1(nx,&bc_vals);

1466:   /* init the entries to -1 so VecSetValues will ignore them */
1467:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

1469:   j = ny-1;
1470:   for (i = 0; i < nx; i++) {
1471:     PetscInt local_id;

1473:     local_id = i+j*nx;

1475:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

1477:     bc_vals[i] =  0.0;
1478:   }
1479:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1480:   nbcs = 0;
1481:   if ((sj+ny) == (N)) nbcs = nx;

1483:   if (b) {
1484:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1485:     VecAssemblyBegin(b);
1486:     VecAssemblyEnd(b);
1487:   }
1488:   if (A) {
1489:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1490:   }

1492:   PetscFree(bc_vals);
1493:   PetscFree(bc_global_ids);

1495:   DMDAVecRestoreArray(cda,coords,&_coords);
1496:   return(0);
1497: }

1499: static PetscErrorCode BCApplyZero_SOUTH(DM da,PetscInt d_idx,Mat A,Vec b)
1500: {
1501:   DM                     cda;
1502:   Vec                    coords;
1503:   PetscInt               si,sj,nx,ny,i,j;
1504:   PetscInt               M,N;
1505:   DMDACoor2d             **_coords;
1506:   const PetscInt         *g_idx;
1507:   PetscInt               *bc_global_ids;
1508:   PetscScalar            *bc_vals;
1509:   PetscInt               nbcs;
1510:   PetscInt               n_dofs;
1511:   PetscErrorCode         ierr;
1512:   ISLocalToGlobalMapping ltogm;

1515:   DMGetLocalToGlobalMapping(da,&ltogm);
1516:   ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);

1518:   DMGetCoordinateDM(da,&cda);
1519:   DMGetCoordinatesLocal(da,&coords);
1520:   DMDAVecGetArray(cda,coords,&_coords);
1521:   DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1522:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);

1524:   PetscMalloc1(nx,&bc_global_ids);
1525:   PetscMalloc1(nx,&bc_vals);

1527:   /* init the entries to -1 so VecSetValues will ignore them */
1528:   for (i = 0; i < nx; i++) bc_global_ids[i] = -1;

1530:   j = 0;
1531:   for (i = 0; i < nx; i++) {
1532:     PetscInt local_id;

1534:     local_id = i+j*nx;

1536:     bc_global_ids[i] = g_idx[n_dofs*local_id+d_idx];

1538:     bc_vals[i] =  0.0;
1539:   }
1540:   ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1541:   nbcs = 0;
1542:   if (sj == 0) nbcs = nx;

1544:   if (b) {
1545:     VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1546:     VecAssemblyBegin(b);
1547:     VecAssemblyEnd(b);
1548:   }
1549:   if (A) {
1550:     MatZeroRowsColumns(A,nbcs,bc_global_ids,1.0,0,0);
1551:   }

1553:   PetscFree(bc_vals);
1554:   PetscFree(bc_global_ids);

1556:   DMDAVecRestoreArray(cda,coords,&_coords);
1557:   return(0);
1558: }

1560: /*
1561:  Impose free slip boundary conditions on the left/right faces: u_i n_i = 0, tau_{ij} t_j = 0
1562:  Impose no slip boundray conditions on the top/bottom faces:   u_i n_i = 0, u_i t_i = 0
1563: */
1564: static PetscErrorCode DMDAApplyBoundaryConditions(DM dm_stokes,Mat A,Vec f)
1565: {

1569:   BCApplyZero_NORTH(dm_stokes,0,A,f);
1570:   BCApplyZero_NORTH(dm_stokes,1,A,f);
1571:   BCApplyZero_EAST(dm_stokes,0,A,f);
1572:   BCApplyZero_SOUTH(dm_stokes,0,A,f);
1573:   BCApplyZero_SOUTH(dm_stokes,1,A,f);
1574:   BCApplyZero_WEST(dm_stokes,0,A,f);
1575:   return(0);
1576: }

1578: /*TEST

1580:    test:
1581:      suffix: 1
1582:      args: -no_view
1583:      requires: !complex double
1584:      filter: grep -v atomic
1585:      filter_output: grep -v atomic
1586:    test:
1587:      suffix: 1_matis
1588:      requires: !complex double
1589:      args: -no_view -dm_mat_type is
1590:      filter: grep -v atomic
1591:      filter_output: grep -v atomic
1592:    testset:
1593:      nsize: 4
1594:      requires: !complex double
1595:      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
1596:      filter: grep -v atomic
1597:      filter_output: grep -v atomic
1598:      test:
1599:        suffix: fetidp
1600:        args: -stokes_fetidp_bddc_pc_bddc_coarse_redundant_pc_type svd
1601:      test:
1602:        suffix: fetidp_lumped
1603:        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
1604:      test:
1605:        suffix: fetidp_saddlepoint
1606:        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
1607:      test:
1608:        suffix: fetidp_saddlepoint_lumped
1609:        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
1610: TEST*/