fem_weights.h

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#pragma once
#include "weights.h"
 
namespace dg {
namespace create{
namespace detail
{
template<class real_type>
std::vector<real_type> fem_weights( unsigned nn)
{
    std::vector<real_type> x = dg::DLT<real_type>::abscissas(nn);
    std::vector<real_type> w = x;
    unsigned n = x.size();
    if( n== 1)
        w[0] = 2;
    else
    {
        w[0] = 0.5*(x[1] - (x[n-1]-2));
        w[n-1] = 0.5*((x[0]+2) - x[n-2]);
        for( unsigned i=1; i<n-1; i++)
            w[i] = 0.5*(x[i+1]-x[i-1]);
    }
    return w;
}
}//namespace detail
// TODO Maybe generalize this into the BOX class?
 
 
template<class real_type>
thrust::host_vector<real_type> fem_weights( const RealGrid1d<real_type>& g)
{
    thrust::host_vector<real_type> v( g.size());
    std::vector<real_type> w = detail::fem_weights<real_type>(g.n());
    for( unsigned i=0; i<g.N(); i++)
        for( unsigned j=0; j<g.n(); j++)
            v[i*g.n() + j] = g.h()/2.*w[j];
    return v;
}
template<class real_type>
thrust::host_vector<real_type> fem_inv_weights( const RealGrid1d<real_type>& g)
{
    thrust::host_vector<real_type> v = fem_weights<real_type>( g);
    for( unsigned i=0; i<g.size(); i++)
        v[i] = 1./v[i];
    return v;
}
 
template<class real_type>
thrust::host_vector<real_type> fem_weights( const aRealTopology2d<real_type>& g)
{
    thrust::host_vector<real_type> v( g.size());
    std::vector<real_type> wx = detail::fem_weights<real_type>(g.nx());
    std::vector<real_type> wy = detail::fem_weights<real_type>(g.ny());
    for( unsigned i=0; i<g.size(); i++)
        v[i] = g.hx()*g.hy()/4.*
                wx[i%g.nx()]*
                wy[(i/(g.nx()*g.Nx()))%g.ny()];
    return v;
}
template<class real_type>
thrust::host_vector<real_type> fem_inv_weights( const aRealTopology2d<real_type>& g)
{
    thrust::host_vector<real_type> v = fem_weights<real_type>( g);
    for( unsigned i=0; i<g.size(); i++)
        v[i] = 1./v[i];
    return v;
}
 
template<class real_type>
thrust::host_vector<real_type> fem_weights( const aRealTopology3d<real_type>& g)
{
    thrust::host_vector<real_type> v( g.size());
    std::vector<real_type> wx = detail::fem_weights<real_type>(g.nx());
    std::vector<real_type> wy = detail::fem_weights<real_type>(g.ny());
    std::vector<real_type> wz = detail::fem_weights<real_type>(g.nz());
    for( unsigned i=0; i<g.size(); i++)
        v[i] = g.hx()*g.hy()*g.hz()/8.*
               wx[i%g.nx()]*
               wy[(i/(g.nx()*g.Nx()))%g.ny()]*
               wz[(i/(g.nx()*g.ny()*g.Nx()*g.Ny()))%g.nz()];
    return v;
}
 
template<class real_type>
thrust::host_vector<real_type> fem_inv_weights( const aRealTopology3d<real_type>& g)
{
    thrust::host_vector<real_type> v = fem_weights<real_type>( g);
    for( unsigned i=0; i<g.size(); i++)
        v[i] = 1./v[i];
    return v;
}
}//namespace create
}//namespace dg