int main(int argc,char **argv)
{
PetscMPIInt rank;
PetscInt M=8,dof=1,stencil_width=1,i,start,end,P=5,N = 6,m=PETSC_DECIDE,n=PETSC_DECIDE,p=PETSC_DECIDE,pt = 0,st = 0;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE,flg2,flg3;
DMBoundaryType periodic;
DMDAStencilType stencil_type;
DM da;
Vec local,global,local_copy;
PetscScalar value;
PetscReal norm,work;
PetscViewer viewer;
char filename[64];
FILE *file;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-dof",&dof,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-stencil_width",&stencil_width,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-periodic",&pt,NULL);CHKERRQ(ierr);
periodic = (DMBoundaryType) pt;
ierr = PetscOptionsGetInt(NULL,NULL,"-stencil_type",&st,NULL);CHKERRQ(ierr);
stencil_type = (DMDAStencilType) st;
ierr = PetscOptionsHasName(NULL,NULL,"-grid2d",&flg2);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-grid3d",&flg3);CHKERRQ(ierr);
if (flg2) {
ierr = DMDACreate2d(PETSC_COMM_WORLD,periodic,periodic,stencil_type,M,N,m,n,dof,stencil_width,NULL,NULL,&da);CHKERRQ(ierr);
} else if (flg3) {
ierr = DMDACreate3d(PETSC_COMM_WORLD,periodic,periodic,periodic,stencil_type,M,N,P,m,n,p,dof,stencil_width,NULL,NULL,NULL,&da);CHKERRQ(ierr);
} else {
ierr = DMDACreate1d(PETSC_COMM_WORLD,periodic,M,dof,stencil_width,NULL,&da);CHKERRQ(ierr);
}
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&global);CHKERRQ(ierr);
ierr = DMCreateLocalVector(da,&local);CHKERRQ(ierr);
ierr = VecDuplicate(local,&local_copy);CHKERRQ(ierr);
/* zero out vectors so that ghostpoints are zero */
value = 0;
ierr = VecSet(local,value);CHKERRQ(ierr);
ierr = VecSet(local_copy,value);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(global,&start,&end);CHKERRQ(ierr);
for (i=start; i<end; i++) {
value = i + 1;
ierr = VecSetValues(global,1,&i,&value,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(global);CHKERRQ(ierr);
ierr = VecAssemblyEnd(global);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMLocalToLocalBegin(da,local,INSERT_VALUES,local_copy);CHKERRQ(ierr);
ierr = DMLocalToLocalEnd(da,local,INSERT_VALUES,local_copy);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-save",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
sprintf(filename,"local.%d",rank);
ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetPointer(viewer,&file);CHKERRQ(ierr);
ierr = VecView(local,viewer);CHKERRQ(ierr);
fprintf(file,"Vector with correct ghost points\n");
ierr = VecView(local_copy,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = VecAXPY(local_copy,-1.0,local);CHKERRQ(ierr);
ierr = VecNorm(local_copy,NORM_MAX,&work);CHKERRQ(ierr);
ierr = MPI_Allreduce(&work,&norm,1,MPIU_REAL,MPIU_MAX,PETSC_COMM_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of difference %g should be zero\n",(double)norm);CHKERRQ(ierr);
ierr = VecDestroy(&local_copy);CHKERRQ(ierr);
ierr = VecDestroy(&local);CHKERRQ(ierr);
ierr = VecDestroy(&global);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscInitialize(&argc,&argv,(char*)0,help);
const int d = 2; // d = DOF
Mat A, Aminus;
// these are dense d x d sequential matrices, unrelated to the grid
// (each processor owns whole matrix)
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,d,d,d,NULL,&A); CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"A_"); CHKERRQ(ierr);
ierr = MatSetFromOptions(A); CHKERRQ(ierr);
// fill A
double val[d][d], c = 3.0;
val[0][0] = 0.0; val[0][1] = c;
val[1][0] = c; val[1][1] = 0.0;
ierr = fillsmallmat(2,val,A); CHKERRQ(ierr);
// fill Aminus; see getAminus.m for computation of Aminus from A
ierr = MatDuplicate(A,MAT_SHARE_NONZERO_PATTERN,&Aminus); CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(Aminus,"Aminus_"); CHKERRQ(ierr);
val[0][0] = -1.5; val[0][1] = 1.5;
val[1][0] = 1.5; val[1][1] = -1.5;
ierr = fillsmallmat(2,val,Aminus); CHKERRQ(ierr);
// set up the grid
DM da;
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC,
-50, // override with -da_grid_x or -da_refine
d, 1, NULL, // dof = 1 and stencil width = 1
&da); CHKERRQ(ierr);
// determine grid locations (cell-centered grid)
DMDALocalInfo info;
double L = 10.0, dx;
ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
dx = L / (double)(info.mx);
ierr = DMDASetUniformCoordinates(da,dx/2,L-dx/2,-1.0,-1.0,-1.0,-1.0);CHKERRQ(ierr);
// u = u(t_n), unew = u(t_n+1)
Vec u, unew, F;
ierr = DMCreateLocalVector(da,&u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"solution u"); CHKERRQ(ierr);
ierr = VecDuplicate(u,&F);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)F,"flux F"); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&unew);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)unew,"updated solution unew"); CHKERRQ(ierr);
ierr = VecSet(unew,0.0); CHKERRQ(ierr);
// at each cell we will need to compute Fcell = A qleft + Aminus dq
Vec dq, qleft, tmp, Fcell;
ierr = VecCreateSeq(PETSC_COMM_WORLD,d,&dq); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&qleft); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&tmp); CHKERRQ(ierr);
ierr = VecDuplicate(dq,&Fcell); CHKERRQ(ierr);
// view the solution graphically; control with -draw_pause
PetscViewer viewer;
ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,NULL,"solution u",
PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,&viewer); CHKERRQ(ierr);
/* time-stepping loop */
double t = 0.0, tf = 10.0, dt, nu;
int n, NN = 10;
dt = tf / NN;
nu = dt / dx;
for (n = 0; n < NN; ++n) {
ierr = PetscPrintf(PETSC_COMM_WORLD, " time[%3d]=%6g: \n", n, t); CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,unew,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,unew,INSERT_VALUES,u); CHKERRQ(ierr);
ierr = VecView(u,viewer); CHKERRQ(ierr);
double **au, **aunew, **aF;
int j, p;
ierr = DMDAVecGetArrayDOF(da, u, &au);CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, F, &aF);CHKERRQ(ierr);
for (j=info.xs; j<info.xs+info.xm; j++) {
double *adq, *aqleft, *aFcell;
ierr = VecGetArray(dq,&adq); CHKERRQ(ierr);
ierr = VecGetArray(qleft,&aqleft); CHKERRQ(ierr);
for (p = 0; p < d; p++) {
adq[p] = au[j+1][p] - au[j][p];
aqleft[p] = au[j][p];
}
ierr = VecRestoreArray(dq,&adq); CHKERRQ(ierr);
ierr = VecRestoreArray(qleft,&aqleft); CHKERRQ(ierr);
// tmp = A qleft
// Fcell = tmp + Aminus dq
ierr = MatMult(A,qleft,tmp); CHKERRQ(ierr);
ierr = MatMultAdd(Aminus,dq,tmp,Fcell); CHKERRQ(ierr);
ierr = VecGetArray(Fcell,&aFcell); CHKERRQ(ierr);
for (p = 0; p < d; p++)
aF[j][p] = aFcell[p];
ierr = VecRestoreArray(Fcell,&aFcell); CHKERRQ(ierr);
}
ierr = DMDAVecRestoreArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMLocalToLocalBegin(da,F,INSERT_VALUES,F); CHKERRQ(ierr);
ierr = DMLocalToLocalEnd(da,F,INSERT_VALUES,F); CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMDAVecGetArrayDOF(da, unew, &aunew);CHKERRQ(ierr);
for (j=info.xs; j<info.xs+info.xm; j++) {
for (p = 0; p < d; p++)
aunew[j][p] = au[j][p] - nu * (aF[j+1][p] - aF[j][p]);
}
ierr = DMDAVecRestoreArrayDOF(da, u, &au);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayDOF(da, F, &aF);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayDOF(da, unew, &aunew);CHKERRQ(ierr);
t += dt;
}
// clean up
ierr = VecDestroy(&u); CHKERRQ(ierr);
ierr = VecDestroy(&unew); CHKERRQ(ierr);
ierr = VecDestroy(&F); CHKERRQ(ierr);
ierr = VecDestroy(&dq); CHKERRQ(ierr);
ierr = VecDestroy(&qleft); CHKERRQ(ierr);
ierr = VecDestroy(&tmp); CHKERRQ(ierr);
ierr = VecDestroy(&Fcell); CHKERRQ(ierr);
ierr = MatDestroy(&A); CHKERRQ(ierr);
ierr = MatDestroy(&Aminus); CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
ierr = DMDestroy(&da); CHKERRQ(ierr);
ierr = PetscFinalize(); CHKERRQ(ierr);
return 0;
}
