mirror of
https://github.com/cosmo-sims/MUSIC.git
synced 2024-09-19 17:03:46 +02:00
679 lines
17 KiB
C++
679 lines
17 KiB
C++
/*
|
|
|
|
mg_solver.hh - This file is part of MUSIC -
|
|
a code to generate multi-scale initial conditions
|
|
for cosmological simulations
|
|
|
|
Copyright (C) 2010 Oliver Hahn
|
|
|
|
*/
|
|
|
|
#ifndef __MG_SOLVER_HH
|
|
#define __MG_SOLVER_HH
|
|
|
|
#include <cmath>
|
|
#include <iostream>
|
|
|
|
#include "mg_operators.hh"
|
|
#include "mg_interp.hh"
|
|
|
|
#include "mesh.hh"
|
|
|
|
#define BEGIN_MULTIGRID_NAMESPACE namespace multigrid {
|
|
#define END_MULTIGRID_NAMESPACE }
|
|
|
|
BEGIN_MULTIGRID_NAMESPACE
|
|
|
|
//! options for multigrid smoothing operation
|
|
namespace opt {
|
|
enum smtype { sm_jacobi, sm_gauss_seidel, sm_sor };
|
|
}
|
|
|
|
|
|
//! actual implementation of FAS adaptive multigrid solver
|
|
template< class S, class I, class O, typename T=double >
|
|
class solver
|
|
{
|
|
public:
|
|
typedef S scheme;
|
|
typedef O mgop;
|
|
typedef I interp;
|
|
|
|
protected:
|
|
scheme m_scheme; //!< finite difference scheme
|
|
mgop m_gridop; //!< grid prolongation and restriction operator
|
|
unsigned m_npresmooth, //!< number of pre sweeps
|
|
m_npostsmooth; //!< number of post sweeps
|
|
opt::smtype m_smoother; //!< smoothing method to be applied
|
|
unsigned m_ilevelmin; //!< index of the top grid level
|
|
|
|
const static bool m_bperiodic = true; //!< flag whether top grid is periodic
|
|
|
|
std::vector<double> m_residu_ini; //!< vector of initial residuals for each level
|
|
bool m_is_ini; //!< bool that is true for first iteration
|
|
|
|
GridHierarchy<T> *m_pu, //!< pointer to GridHierarchy for solution u
|
|
*m_pf, //!< pointer to GridHierarchy for right-hand-side
|
|
*m_pfsave; //!< pointer to saved state of right-hand-side (unused)
|
|
|
|
const MeshvarBnd<T> *m_pubnd;
|
|
|
|
//! compute residual for a level
|
|
double compute_error( const MeshvarBnd<T>& u, const MeshvarBnd<T>& unew, int ilevel );
|
|
|
|
//! compute residuals for entire grid hierarchy
|
|
double compute_error( const GridHierarchy<T>& uh, const GridHierarchy<T>& uhnew, bool verbose );
|
|
|
|
//! compute residuals for entire grid hierarchy
|
|
double compute_RMS_resid( const GridHierarchy<T>& uh, const GridHierarchy<T>& fh, bool verbose );
|
|
|
|
protected:
|
|
|
|
//! Jacobi smoothing
|
|
void Jacobi( T h, MeshvarBnd<T>* u, const MeshvarBnd<T>* f );
|
|
|
|
//! Gauss-Seidel smoothing
|
|
void GaussSeidel( T h, MeshvarBnd<T>* u, const MeshvarBnd<T>* f );
|
|
|
|
//! Successive-Overrelaxation smoothing
|
|
void SOR( T h, MeshvarBnd<T>* u, const MeshvarBnd<T>* f );
|
|
|
|
//! main two-grid (V-cycle) for multi-grid iterations
|
|
void twoGrid( unsigned ilevel );
|
|
|
|
//! apply boundary conditions
|
|
void setBC( unsigned ilevel );
|
|
|
|
//! make top grid periodic boundary conditions
|
|
void make_periodic( MeshvarBnd<T> *u );
|
|
|
|
//void interp_coarse_fine_cubic( unsigned ilevel, MeshvarBnd<T>& coarse, MeshvarBnd<T>& fine );
|
|
|
|
public:
|
|
|
|
//! constructor
|
|
solver( GridHierarchy<T>& f, opt::smtype smoother, unsigned npresmooth, unsigned npostsmooth );
|
|
|
|
//! destructor
|
|
~solver()
|
|
{ }
|
|
|
|
//! solve Poisson's equation
|
|
double solve( GridHierarchy<T>& u, double accuracy, double h=-1.0, bool verbose=false );
|
|
|
|
//! solve Poisson's equation
|
|
double solve( GridHierarchy<T>& u, double accuracy, bool verbose=false )
|
|
{
|
|
return this->solve ( u, accuracy, -1.0, verbose );
|
|
}
|
|
|
|
|
|
|
|
};
|
|
|
|
|
|
template< class S, class I, class O, typename T >
|
|
solver<S,I,O,T>::solver( GridHierarchy<T>& f, opt::smtype smoother, unsigned npresmooth, unsigned npostsmooth )
|
|
: m_scheme(), m_gridop(), m_npresmooth( npresmooth ), m_npostsmooth( npostsmooth ),
|
|
m_smoother( smoother ), m_ilevelmin( f.levelmin() ), m_is_ini( true ), m_pf( &f )
|
|
{
|
|
m_is_ini = true;
|
|
}
|
|
|
|
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::Jacobi( T h, MeshvarBnd<T> *u, const MeshvarBnd<T>* f )
|
|
{
|
|
int
|
|
nx = u->size(0),
|
|
ny = u->size(1),
|
|
nz = u->size(2);
|
|
|
|
double
|
|
c0 = -1.0/m_scheme.ccoeff(),
|
|
h2 = h*h;
|
|
|
|
MeshvarBnd<T> uold(*u);
|
|
|
|
double alpha = 0.95, ialpha = 1.0-alpha;
|
|
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
(*u)(ix,iy,iz) = ialpha * uold(ix,iy,iz) + alpha * (m_scheme.rhs( uold, ix, iy, iz ) + h2 * (*f)(ix,iy,iz))*c0;
|
|
|
|
}
|
|
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::SOR( T h, MeshvarBnd<T> *u, const MeshvarBnd<T>* f )
|
|
{
|
|
int
|
|
nx = u->size(0),
|
|
ny = u->size(1),
|
|
nz = u->size(2);
|
|
|
|
double
|
|
c0 = -1.0/m_scheme.ccoeff(),
|
|
h2 = h*h;
|
|
|
|
MeshvarBnd<T> uold(*u);
|
|
|
|
double
|
|
alpha = 1.2,
|
|
//alpha = 2 / (1 + 4 * atan(1.0) / double(u->size(0)))-1.0, //.. ideal alpha
|
|
ialpha = 1.0-alpha;
|
|
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
if( (ix+iy+iz)%2==0 )
|
|
(*u)(ix,iy,iz) = ialpha * uold(ix,iy,iz) + alpha * (m_scheme.rhs( uold, ix, iy, iz ) + h2 * (*f)(ix,iy,iz))*c0;
|
|
|
|
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
if( (ix+iy+iz)%2!=0 )
|
|
(*u)(ix,iy,iz) = ialpha * uold(ix,iy,iz) + alpha * (m_scheme.rhs( *u, ix, iy, iz ) + h2 * (*f)(ix,iy,iz))*c0;
|
|
|
|
|
|
|
|
}
|
|
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::GaussSeidel( T h, MeshvarBnd<T>* u, const MeshvarBnd<T>* f )
|
|
{
|
|
int
|
|
nx = u->size(0),
|
|
ny = u->size(1),
|
|
nz = u->size(2);
|
|
|
|
T
|
|
c0 = -1.0/m_scheme.ccoeff(),
|
|
h2 = h*h;
|
|
|
|
for( int color=0; color < 2; ++color )
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
if( (ix+iy+iz)%2 == color )
|
|
(*u)(ix,iy,iz) = (m_scheme.rhs( *u, ix, iy, iz ) + h2 * (*f)(ix,iy,iz))*c0;
|
|
|
|
}
|
|
|
|
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::twoGrid( unsigned ilevel )
|
|
{
|
|
MeshvarBnd<T> *uf, *uc, *ff, *fc;
|
|
|
|
|
|
double
|
|
h = 1.0/(1<<ilevel),
|
|
c0 = -1.0/m_scheme.ccoeff(),
|
|
h2 = h*h;
|
|
|
|
uf = m_pu->get_grid(ilevel);
|
|
ff = m_pf->get_grid(ilevel);
|
|
|
|
uc = m_pu->get_grid(ilevel-1);
|
|
fc = m_pf->get_grid(ilevel-1);
|
|
|
|
|
|
int
|
|
nx = uf->size(0),
|
|
ny = uf->size(1),
|
|
nz = uf->size(2);
|
|
|
|
if( m_bperiodic && ilevel <= m_ilevelmin)
|
|
make_periodic( uf );
|
|
else if(!m_bperiodic)
|
|
setBC( ilevel );
|
|
|
|
//... do smoothing sweeps with specified solver
|
|
for( unsigned i=0; i<m_npresmooth; ++i ){
|
|
|
|
if( ilevel > m_ilevelmin )
|
|
interp().interp_coarse_fine(ilevel,*uc,*uf);
|
|
|
|
if( m_smoother == opt::sm_gauss_seidel )
|
|
GaussSeidel( h, uf, ff );
|
|
|
|
else if( m_smoother == opt::sm_jacobi )
|
|
Jacobi( h, uf, ff);
|
|
|
|
else if( m_smoother == opt::sm_sor )
|
|
SOR( h, uf, ff );
|
|
|
|
if( m_bperiodic && ilevel <= m_ilevelmin )
|
|
make_periodic( uf );
|
|
}
|
|
|
|
|
|
m_gridop.restrict( *uf, *uc );
|
|
|
|
//... essential!!
|
|
if( m_bperiodic && ilevel <= m_ilevelmin )
|
|
make_periodic( uc );
|
|
else if( ilevel > m_ilevelmin )
|
|
interp().interp_coarse_fine(ilevel,*uc,*uf);
|
|
|
|
|
|
//....................................................................
|
|
//... we now use hard-coded restriction+operatore app, see below
|
|
/*meshvar_bnd Lu(*uf,false);
|
|
Lu.zero();
|
|
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
Lu(ix,iy,iz) = m_scheme.apply( (*uf), ix, iy, iz )/h2;
|
|
|
|
meshvar_bnd tLu(*uc,false);
|
|
|
|
|
|
//... restrict Lu
|
|
m_gridop.restrict( Lu, tLu );
|
|
Lu.deallocate();*/
|
|
//....................................................................
|
|
|
|
int
|
|
oxp = uf->offset(0),
|
|
oyp = uf->offset(1),
|
|
ozp = uf->offset(2);
|
|
|
|
meshvar_bnd tLu(*uc,false);
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<nx/2; ++ix )
|
|
{
|
|
int iix=2*ix;
|
|
for( int iy=0,iiy=0; iy<ny/2; ++iy,iiy+=2 )
|
|
|
|
|
|
for( int iz=0,iiz=0; iz<nz/2; ++iz,iiz+=2 )
|
|
tLu(ix+oxp,iy+oyp,iz+ozp) = 0.125 * (
|
|
m_scheme.apply( (*uf), iix, iiy, iiz )
|
|
+m_scheme.apply( (*uf), iix, iiy, iiz+1 )
|
|
+m_scheme.apply( (*uf), iix, iiy+1, iiz )
|
|
+m_scheme.apply( (*uf), iix, iiy+1, iiz+1 )
|
|
+m_scheme.apply( (*uf), iix+1, iiy, iiz )
|
|
+m_scheme.apply( (*uf), iix+1, iiy, iiz+1 )
|
|
+m_scheme.apply( (*uf), iix+1, iiy+1, iiz )
|
|
+m_scheme.apply( (*uf), iix+1, iiy+1, iiz+1 )
|
|
)/h2;
|
|
}
|
|
|
|
//... restrict source term
|
|
m_gridop.restrict( *ff, *fc );
|
|
|
|
int oi, oj, ok;
|
|
oi = ff->offset(0);
|
|
oj = ff->offset(1);
|
|
ok = ff->offset(2);
|
|
|
|
#pragma omp parallel for
|
|
for( int ix=oi; ix<oi+(int)ff->size(0)/2; ++ix )
|
|
for( int iy=oj; iy<oj+(int)ff->size(1)/2; ++iy )
|
|
for( int iz=ok; iz<ok+(int)ff->size(2)/2; ++iz )
|
|
(*fc)(ix,iy,iz) += ((tLu( ix, iy, iz ) - (m_scheme.apply( *uc, ix, iy, iz )/(4.0*h2))));
|
|
|
|
tLu.deallocate();
|
|
|
|
meshvar_bnd ucsave(*uc,true);
|
|
|
|
//... have we reached the end of the recursion or do we need to go up one level?
|
|
if( ilevel == 1 )
|
|
if( m_bperiodic )
|
|
(*uc)(0,0,0) = 0.0;
|
|
else
|
|
(*uc)(0,0,0) = (m_scheme.rhs( (*uc), 0, 0, 0 ) + 4.0 * h2 * (*fc)(0,0,0))*c0;
|
|
else
|
|
twoGrid( ilevel-1 );
|
|
|
|
meshvar_bnd cc(*uc,false);
|
|
|
|
|
|
//... compute correction on coarse grid
|
|
#pragma omp parallel for
|
|
for( int ix=0; ix<(int)cc.size(0); ++ix )
|
|
for( int iy=0; iy<(int)cc.size(1); ++iy )
|
|
for( int iz=0; iz<(int)cc.size(2); ++iz )
|
|
cc(ix,iy,iz) = (*uc)(ix,iy,iz) - ucsave(ix,iy,iz);
|
|
|
|
ucsave.deallocate();
|
|
|
|
if( m_bperiodic && ilevel <= m_ilevelmin )
|
|
make_periodic( &cc );
|
|
|
|
m_gridop.prolong_add( cc, *uf );
|
|
|
|
//... interpolate and apply coarse-fine boundary conditions on fine level
|
|
if( m_bperiodic && ilevel <= m_ilevelmin )
|
|
make_periodic( uf );
|
|
else if(!m_bperiodic)
|
|
setBC( ilevel );
|
|
|
|
//... do smoothing sweeps with specified solver
|
|
for( unsigned i=0; i<m_npostsmooth; ++i ){
|
|
|
|
if( ilevel > m_ilevelmin )
|
|
interp().interp_coarse_fine(ilevel,*uc,*uf);
|
|
|
|
if( m_smoother == opt::sm_gauss_seidel )
|
|
GaussSeidel( h, uf, ff );
|
|
|
|
else if( m_smoother == opt::sm_jacobi )
|
|
Jacobi( h, uf, ff);
|
|
|
|
else if( m_smoother == opt::sm_sor )
|
|
SOR( h, uf, ff );
|
|
|
|
if( m_bperiodic && ilevel <= m_ilevelmin )
|
|
make_periodic( uf );
|
|
|
|
}
|
|
|
|
}
|
|
|
|
template< class S, class I, class O, typename T >
|
|
double solver<S,I,O,T>::compute_error( const MeshvarBnd<T>& u, const MeshvarBnd<T>& f, int ilevel )
|
|
{
|
|
int
|
|
nx = u.size(0),
|
|
ny = u.size(1),
|
|
nz = u.size(2);
|
|
|
|
double err = 0.0, err2 = 0.0;
|
|
size_t count = 0;
|
|
|
|
double h = 1.0/(1ul<<ilevel), h2=h*h;
|
|
|
|
#pragma omp parallel for reduction(+:err,count)
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
if( true )//fabs(unew(ix,iy,iz)) > 0.0 )//&& u(ix,iy,iz) != unew(ix,iy,iz) )
|
|
{
|
|
//err += fabs(1.0 - (double)u(ix,iy,iz)/(double)unew(ix,iy,iz));
|
|
/*err += fabs(((double)m_scheme.apply( u, ix, iy, iz )/h2 + (double)(f(ix,iy,iz)) ));
|
|
err2 += fabs((double)f(ix,iy,iz));*/
|
|
|
|
err += fabs( (double)m_scheme.apply( u, ix, iy, iz )/h2/(double)(f(ix,iy,iz)) + 1.0 );
|
|
++count;
|
|
}
|
|
|
|
if( count != 0 )
|
|
err /= count;
|
|
|
|
return err;
|
|
}
|
|
|
|
template< class S, class I, class O, typename T >
|
|
double solver<S,I,O,T>::compute_error( const GridHierarchy<T>& uh, const GridHierarchy<T>& fh, bool verbose )
|
|
{
|
|
double maxerr = 0.0;
|
|
|
|
for( unsigned ilevel=uh.levelmin(); ilevel <= uh.levelmax(); ++ilevel )
|
|
{
|
|
int
|
|
nx = uh.get_grid(ilevel)->size(0),
|
|
ny = uh.get_grid(ilevel)->size(1),
|
|
nz = uh.get_grid(ilevel)->size(2);
|
|
|
|
double err = 0.0, mean_res = 0.0;
|
|
size_t count = 0;
|
|
|
|
double h = 1.0/(1ul<<ilevel), h2=h*h;
|
|
|
|
#pragma omp parallel for reduction(+:err,count)
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
{
|
|
double res = (double)m_scheme.apply( *uh.get_grid(ilevel), ix, iy, iz ) + h2 * (double)((*fh.get_grid(ilevel))(ix,iy,iz));
|
|
double val = (*uh.get_grid(ilevel))( ix, iy, iz );
|
|
|
|
if( fabs(val) > 0.0 )
|
|
{
|
|
err += fabs( res/val );
|
|
mean_res += fabs(res);
|
|
++count;
|
|
}
|
|
}
|
|
|
|
if( count != 0 )
|
|
{
|
|
err /= count;
|
|
mean_res /= count;
|
|
}
|
|
if( verbose )
|
|
std::cout << " Level " << std::setw(6) << ilevel << ", Error = " << err << std::endl;
|
|
|
|
LOGDEBUG("[mg] level %3d, residual %g, rel. error %g",ilevel, mean_res, err);
|
|
|
|
maxerr = std::max(maxerr,err);
|
|
|
|
}
|
|
return maxerr;
|
|
}
|
|
|
|
template< class S, class I, class O, typename T >
|
|
double solver<S,I,O,T>::compute_RMS_resid( const GridHierarchy<T>& uh, const GridHierarchy<T>& fh, bool verbose )
|
|
{
|
|
if( m_is_ini )
|
|
m_residu_ini.assign( uh.levelmax()+1, 0.0 );
|
|
|
|
double maxerr=0.0;
|
|
|
|
for( unsigned ilevel=uh.levelmin(); ilevel <= uh.levelmax(); ++ilevel )
|
|
{
|
|
int
|
|
nx = uh.get_grid(ilevel)->size(0),
|
|
ny = uh.get_grid(ilevel)->size(1),
|
|
nz = uh.get_grid(ilevel)->size(2);
|
|
|
|
double h = 1.0/(1<<ilevel), h2=h*h;
|
|
double sum = 0.0, sumd2 = 0.0;
|
|
size_t count = 0;
|
|
|
|
#pragma omp parallel for reduction(+:sum,sumd2,count)
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
{
|
|
double d = (double)(*fh.get_grid(ilevel))(ix,iy,iz);
|
|
sumd2 += d*d;
|
|
|
|
double r = ((double)m_scheme.apply( *uh.get_grid(ilevel), ix, iy, iz )/h2 + (double)(*fh.get_grid(ilevel))(ix,iy,iz));
|
|
sum += r*r;
|
|
|
|
++count;
|
|
}
|
|
|
|
if( m_is_ini )
|
|
m_residu_ini[ilevel] = sqrt(sum)/count;
|
|
|
|
double err_abs = sqrt(sum/count);
|
|
double err_rel = err_abs / sqrt(sumd2/count);
|
|
|
|
if( verbose && !m_is_ini )
|
|
std::cout << " Level " << std::setw(6) << ilevel << ", Error = " << err_rel << std::endl;
|
|
|
|
LOGDEBUG("[mg] level %3d, rms residual %g, rel. error %g",ilevel, err_abs, err_rel);
|
|
|
|
if( err_rel > maxerr )
|
|
maxerr = err_rel;
|
|
|
|
}
|
|
|
|
if( m_is_ini )
|
|
m_is_ini = false;
|
|
|
|
return maxerr;
|
|
}
|
|
|
|
|
|
template< class S, class I, class O, typename T >
|
|
double solver<S,I,O,T>::solve( GridHierarchy<T>& uh, double acc, double h, bool verbose )
|
|
{
|
|
|
|
double err, maxerr = 1e30;
|
|
unsigned niter = 0;
|
|
|
|
bool fullverbose = false;
|
|
|
|
m_pu = &uh;
|
|
|
|
//err = compute_RMS_resid( *m_pu, *m_pf, fullverbose );
|
|
|
|
//... iterate ...//
|
|
while (true)
|
|
{
|
|
|
|
LOGUSER("Performing multi-grid V-cycle...");
|
|
twoGrid( uh.levelmax() );
|
|
|
|
//err = compute_RMS_resid( *m_pu, *m_pf, fullverbose );
|
|
err = compute_error( *m_pu, *m_pf, fullverbose );
|
|
++niter;
|
|
|
|
if( fullverbose ){
|
|
LOGUSER(" multigrid iteration %3d, maximum RMS residual = %g", niter, err );
|
|
std::cout << " - Step No. " << std::setw(3) << niter << ", Max Err = " << err << std::endl;
|
|
std::cout << " ---------------------------------------------------\n";
|
|
}
|
|
|
|
if( err < maxerr )
|
|
maxerr = err;
|
|
|
|
if( (niter > 1) && ((err < acc) || (niter > 20)) )
|
|
break;
|
|
}
|
|
|
|
if( err > acc )
|
|
{
|
|
std::cout << "Error : no convergence in Poisson solver" << std::endl;
|
|
LOGERR("No convergence in Poisson solver, final error: %g.",err);
|
|
}
|
|
else if( verbose )
|
|
{
|
|
std::cout << " - Converged in " << niter << " steps to " << maxerr << std::endl;
|
|
LOGUSER("Poisson solver converged to max. error of %g in %d steps.",err,niter);
|
|
}
|
|
|
|
|
|
//.. make sure that the RHS does not contain the FAS corrections any more
|
|
for( int i=m_pf->levelmax(); i>0; --i )
|
|
m_gridop.restrict( *m_pf->get_grid(i), *m_pf->get_grid(i-1) );
|
|
|
|
|
|
return err;
|
|
}
|
|
|
|
|
|
|
|
//TODO: this only works for 2nd order! (but actually not needed)
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::setBC( unsigned ilevel )
|
|
{
|
|
//... set only on level before additional refinement starts
|
|
if( ilevel == m_ilevelmin )
|
|
{
|
|
MeshvarBnd<T> *u = m_pu->get_grid(ilevel);
|
|
int
|
|
nx = u->size(0),
|
|
ny = u->size(1),
|
|
nz = u->size(2);
|
|
|
|
for( int iy=0; iy<ny; ++iy )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
{
|
|
(*u)(-1,iy,iz) = 2.0*(*m_pubnd)(-1,iy,iz) - (*u)(0,iy,iz);
|
|
(*u)(nx,iy,iz) = 2.0*(*m_pubnd)(nx,iy,iz) - (*u)(nx-1,iy,iz);;
|
|
}
|
|
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iz=0; iz<nz; ++iz )
|
|
{
|
|
(*u)(ix,-1,iz) = 2.0*(*m_pubnd)(ix,-1,iz) - (*u)(ix,0,iz);
|
|
(*u)(ix,ny,iz) = 2.0*(*m_pubnd)(ix,ny,iz) - (*u)(ix,ny-1,iz);
|
|
}
|
|
|
|
for( int ix=0; ix<nx; ++ix )
|
|
for( int iy=0; iy<ny; ++iy )
|
|
{
|
|
(*u)(ix,iy,-1) = 2.0*(*m_pubnd)(ix,iy,-1) - (*u)(ix,iy,0);
|
|
(*u)(ix,iy,nz) = 2.0*(*m_pubnd)(ix,iy,nz) - (*u)(ix,iy,nz-1);
|
|
}
|
|
|
|
|
|
|
|
}
|
|
}
|
|
|
|
|
|
|
|
//... enforce periodic boundary conditions
|
|
template< class S, class I, class O, typename T >
|
|
void solver<S,I,O,T>::make_periodic( MeshvarBnd<T> *u )
|
|
{
|
|
|
|
|
|
int
|
|
nx = u->size(0),
|
|
ny = u->size(1),
|
|
nz = u->size(2);
|
|
int nb = u->m_nbnd;
|
|
|
|
|
|
//if( u->offset(0) == 0 )
|
|
for( int iy=-nb; iy<ny+nb; ++iy )
|
|
for( int iz=-nb; iz<nz+nb; ++iz )
|
|
{
|
|
int iiy( (iy+ny)%ny ), iiz( (iz+nz)%nz );
|
|
|
|
for( int i=-nb; i<0; ++i )
|
|
{
|
|
(*u)(i,iy,iz) = (*u)(nx+i,iiy,iiz);
|
|
(*u)(nx-1-i,iy,iz) = (*u)(-1-i,iiy,iiz);
|
|
}
|
|
|
|
}
|
|
|
|
//if( u->offset(1) == 0 )
|
|
for( int ix=-nb; ix<nx+nb; ++ix )
|
|
for( int iz=-nb; iz<nz+nb; ++iz )
|
|
{
|
|
int iix( (ix+nx)%nx ), iiz( (iz+nz)%nz );
|
|
|
|
for( int i=-nb; i<0; ++i )
|
|
{
|
|
(*u)(ix,i,iz) = (*u)(iix,ny+i,iiz);
|
|
(*u)(ix,ny-1-i,iz) = (*u)(iix,-1-i,iiz);
|
|
}
|
|
}
|
|
|
|
//if( u->offset(2) == 0 )
|
|
for( int ix=-nb; ix<nx+nb; ++ix )
|
|
for( int iy=-nb; iy<ny+nb; ++iy )
|
|
{
|
|
int iix( (ix+nx)%nx ), iiy( (iy+ny)%ny );
|
|
|
|
for( int i=-nb; i<0; ++i )
|
|
{
|
|
(*u)(ix,iy,i) = (*u)(iix,iiy,nz+i);
|
|
(*u)(ix,iy,nz-1-i) = (*u)(iix,iiy,-1-i);
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
|
|
END_MULTIGRID_NAMESPACE
|
|
|
|
#endif
|