curvilinear.h

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#pragma once
 
#include "dg/algorithm.h"
#include "generator.h"
 
namespace dg
{
namespace geo
{
 
 
struct Topology1d
{
    unsigned n;
    unsigned N;
    bc b = dg::PER;
};
 
 
template<class real_type>
struct RealCurvilinearProductGrid3d;
namespace detail
{
template<class host_vector>
dg::SparseTensor<host_vector> square( const dg::SparseTensor<host_vector >& jac, const host_vector& R, bool orthogonal)
{
    std::vector<host_vector> values( 5, R);
    {
        dg::blas1::scal( values[0], 0); //0
        dg::blas1::pointwiseDot( 1., jac.value(0,0), jac.value(0,0), 1., jac.value(0,1), jac.value(0,1), 0., values[1]); //xx
        dg::blas1::pointwiseDot( 1., jac.value(1,0), jac.value(1,0), 1., jac.value(1,1), jac.value(1,1), 0., values[2]); //yy
        dg::blas1::pointwiseDot( values[3], values[3], values[3]);
        dg::blas1::pointwiseDivide( 1., values[3], values[3]); //pp == 1/R^2
 
        dg::blas1::pointwiseDot( 1., jac.value(0,0), jac.value(1,0), 1., jac.value(0,1), jac.value(1,1), 0., values[4]); //xy
    }
    SparseTensor<host_vector> metric(values[0]); //unit tensor
    metric.values().pop_back(); //remove the one
    metric.idx(0,0) = 1; metric.values().push_back( values[1]);
    metric.idx(1,1) = 2; metric.values().push_back( values[2]);
    metric.idx(2,2) = 3; metric.values().push_back( values[3]);
    if( !orthogonal)
    {
        metric.idx(1,0) = metric.idx(0,1) = 4;
        metric.values().push_back( values[4]);
    }
    return metric;
}
}//namespace detail
 
//when we make a 3d grid with eta and phi swapped the metric structure and the transformation changes
//In practise it can only be orthogonal due to the projection tensor in the elliptic operator
 
template<class real_type>
struct RealCurvilinearGrid2d : public dg::aRealGeometry2d<real_type>
{
    RealCurvilinearGrid2d( const aRealGenerator2d<real_type>& generator, unsigned n, unsigned Nx, unsigned Ny, dg::bc bcx=dg::DIR, bc bcy=dg::PER):
        RealCurvilinearGrid2d( generator, {n,Nx,bcx}, {n,Ny,bcy}){}
    RealCurvilinearGrid2d( const aRealGenerator2d<real_type>& generator, Topology1d tx, Topology1d ty) :
        dg::aRealGeometry2d<real_type>( {0, generator.width(), tx.n, tx.N, tx.b}, {0., generator.height(), ty.n, ty.N, ty.b}), m_handle(generator)
    {
        construct( tx.n, tx.N, ty.n, ty.N);
    }
 
    explicit RealCurvilinearGrid2d( RealCurvilinearProductGrid3d<real_type> g);
 
    const aRealGenerator2d<real_type>& generator() const{return *m_handle;}
    virtual RealCurvilinearGrid2d* clone()const override final{return new RealCurvilinearGrid2d(*this);}
    private:
    virtual void do_set(unsigned nx, unsigned Nx, unsigned ny, unsigned Ny) override final
    {
        dg::aRealTopology2d<real_type>::do_set( nx, Nx, ny,Ny);
        construct( nx, Nx, ny, Ny);
    }
    void construct( unsigned nx, unsigned Nx, unsigned ny, unsigned Ny);
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_jacobian( ) const override final{
        return m_jac;
    }
    virtual SparseTensor<thrust::host_vector<real_type>> do_compute_metric( ) const override final{
        return m_metric;
    }
    virtual std::vector<thrust::host_vector<real_type>> do_compute_map()const override final{return m_map;}
    dg::SparseTensor<thrust::host_vector<real_type>> m_jac, m_metric;
    std::vector<thrust::host_vector<real_type>> m_map;
    dg::ClonePtr<aRealGenerator2d<real_type>> m_handle;
};
 
 
template<class real_type>
struct RealCurvilinearProductGrid3d : public dg::aRealProductGeometry3d<real_type>
{
    using perpendicular_grid = RealCurvilinearGrid2d<real_type>;
 
    RealCurvilinearProductGrid3d( const aRealGenerator2d<real_type>& generator, unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, bc bcx=dg::DIR, bc bcy=dg::PER, bc bcz=dg::PER):
        RealCurvilinearProductGrid3d( generator, {n,Nx,bcx}, {n,Ny,bcy}, {0., 2.*M_PI, 1,Nz,bcz}){}
 
    RealCurvilinearProductGrid3d( const aRealGenerator2d<real_type>& generator, Topology1d tx, Topology1d ty, RealGrid1d<real_type> gz):
        dg::aRealProductGeometry3d<real_type>( {0, generator.width(), tx.n, tx.N, tx.b}, {0., generator.height(), ty.n, ty.N, ty.b},gz), m_handle(generator)
    {
        m_map.resize(3);
        constructPerp( this->nx(), this->Nx(), this->ny(), this->Ny());
        constructParallel(this->nz(), this->Nz());
    }
 
 
    const aRealGenerator2d<real_type> & generator() const{return *m_handle;}
    virtual RealCurvilinearProductGrid3d* clone()const override final{return new RealCurvilinearProductGrid3d(*this);}
    private:
    virtual RealCurvilinearGrid2d<real_type>* do_perp_grid() const override final;
    virtual void do_set( unsigned nx, unsigned Nx, unsigned ny, unsigned Ny,unsigned nz,unsigned Nz) override final{
        dg::aRealTopology3d<real_type>::do_set( nx, Nx, ny, Ny, nz, Nz);
        if( !( nx == this->nx() && Nx == this->Nx() && ny == this->ny() && Ny == this->Ny() ) )
            constructPerp( nx, Nx, ny,Ny);
        constructParallel(nz,Nz);
    }
    //construct phi and lift rest to 3d
    void constructParallel(unsigned nz,unsigned Nz)
    {
        m_map[2]=dg::evaluate(dg::cooZ3d, *this);
        unsigned size = this->size();
        unsigned size2d = this->nx()*this->ny()*this->Nx()*this->Ny();
        //resize for 3d values
        for( unsigned r=0; r<6;r++)
            m_jac.values()[r].resize(size);
        m_map[0].resize(size);
        m_map[1].resize(size);
        //lift to 3D grid
        for( unsigned k=1; k<nz*Nz; k++)
            for( unsigned i=0; i<size2d; i++)
            {
                for(unsigned r=0; r<6; r++)
                    m_jac.values()[r][k*size2d+i] = m_jac.values()[r][(k-1)*size2d+i];
                m_map[0][k*size2d+i] = m_map[0][(k-1)*size2d+i];
                m_map[1][k*size2d+i] = m_map[1][(k-1)*size2d+i];
            }
    }
    //construct 2d plane
    void constructPerp( unsigned nx, unsigned Nx, unsigned ny, unsigned Ny)
    {
        dg::Grid1d gX1d( this->x0(), this->x1(), nx, Nx);
        dg::Grid1d gY1d( this->y0(), this->y1(), ny, Ny);
        thrust::host_vector<real_type> x_vec = dg::evaluate( dg::cooX1d, gX1d);
        thrust::host_vector<real_type> y_vec = dg::evaluate( dg::cooX1d, gY1d);
        m_jac = SparseTensor< thrust::host_vector<real_type>>( x_vec);//unit tensor
        m_jac.values().resize( 6);
        m_handle->generate( x_vec, y_vec, m_map[0], m_map[1], m_jac.values()[2], m_jac.values()[3], m_jac.values()[4], m_jac.values()[5]);
        m_jac.idx(0,0) = 2, m_jac.idx(0,1) = 3, m_jac.idx(1,0)=4, m_jac.idx(1,1) = 5;
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_jacobian( ) const override final{
        return m_jac;
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_metric( ) const override final
    {
        return detail::square( m_jac, m_map[0], m_handle->isOrthogonal());
    }
    virtual std::vector<thrust::host_vector<real_type> > do_compute_map()const override final{return m_map;}
    std::vector<thrust::host_vector<real_type> > m_map;
    SparseTensor<thrust::host_vector<real_type> > m_jac;
    dg::ClonePtr<aRealGenerator2d<real_type>> m_handle;
};
 
using CurvilinearGrid2d         = dg::geo::RealCurvilinearGrid2d<double>;
using CurvilinearProductGrid3d  = dg::geo::RealCurvilinearProductGrid3d<double>;
#ifndef MPI_VERSION
namespace x{
using CurvilinearGrid2d         = CurvilinearGrid2d        ;
using CurvilinearProductGrid3d  = CurvilinearProductGrid3d ;
}
#endif
 
template<class real_type>
RealCurvilinearGrid2d<real_type>::RealCurvilinearGrid2d( RealCurvilinearProductGrid3d<real_type> g):
    dg::aRealGeometry2d<real_type>( g.gx(), g.gy() ), m_handle(g.generator())
{
    g.set( this->nx(), this->Nx(), this->ny(), this->Ny(), 1, 1); //shouldn't trigger 2d grid generator
    m_map=g.map();
    m_jac=g.jacobian();
    m_metric=g.metric();
    // we rely on the fact that the 3d grid uses square to compute its metric
    // so the (2,2) entry is value 3 that we need to set to 1 (for the
    // create::volume function to work properly)
    dg::blas1::copy( 1., m_metric.values()[3]);
    m_map.pop_back();
}
template<class real_type>
void RealCurvilinearGrid2d<real_type>::construct( unsigned nx, unsigned Nx, unsigned ny, unsigned Ny)
{
    RealCurvilinearProductGrid3d<real_type> g( *m_handle, {nx,Nx,this->bcx()}, {ny,Ny,this->bcy()}, {0., 2.*M_PI, 1,1});
    *this = RealCurvilinearGrid2d<real_type>(g);
}
template<class real_type>
typename RealCurvilinearProductGrid3d<real_type>::perpendicular_grid* RealCurvilinearProductGrid3d<real_type>::do_perp_grid() const { return new typename RealCurvilinearProductGrid3d<real_type>::perpendicular_grid(*this);}
 
}//namespace geo
}//namespace dg