ds.h

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#pragma once
 
#include "dg/algorithm.h"
#include "fieldaligned.h"
#ifdef MPI_VERSION
#include "mpi_fieldaligned.h"
#endif //MPI_VERSION
#include "magnetic_field.h"
 
namespace dg{
namespace geo{
 
namespace detail
{
struct DSCentered
{
    DSCentered( double alpha, double beta) : m_alpha(alpha), m_beta(beta){}
    DG_DEVICE
    void operator()( double& dsf, double fm, double fo, double fp, double hm,
            double hp)
    {
        dsf = m_alpha*(
            fm*( 1./(hp+hm) - 1./hm) +
            fo*( 1./hm - 1./hp) +
            fp*( 1./hp - 1./(hp+hm))
            ) + m_beta*dsf;
    };
 
    private:
    double m_alpha, m_beta;
};
struct DSSCentered
{
    DSSCentered( double alpha, double beta, double delta) : m_alpha(alpha), m_beta(beta), m_delta(delta){}
    DG_DEVICE
    void operator()( double& dssf, double fm, double fo, double fp, double hm,
            double hp)
    {
        dssf = m_alpha*(
                    2.*fm/(hp+hm)/hm - 2.*fo/hp/hm + 2.*fp/(hp+hm)/hp
               ) + m_beta*dssf;
    };
 
    DG_DEVICE
    void operator()( double& dssf, double fm, double fo, double fp,
        double bPm, double bP0, double bPp)
    {
        double bP2 = (bPp+bP0)/2.;
        double bM2 = (bPm+bP0)/2.;
        double fm2 = (fo-fm)/m_delta;
        double fp2 = (fp-fo)/m_delta;
 
        dssf = m_alpha*bP0*( bP2*fp2 - bM2*fm2)/m_delta + m_beta*dssf;
    }
 
    private:
    double m_alpha, m_beta, m_delta;
};
struct DSSDCentered
{
    DSSDCentered( double alpha, double beta, double delta) :
        m_alpha( alpha), m_beta(beta), m_delta(delta){}
    DG_DEVICE
    void operator()( double& dssdf, double fm, double fo, double fp, double Gm,
        double Go, double Gp, double bPm, double bP0, double bPp)
    {
        // various combinations of bP do not seem to matter
        double bP2 = (bPp+bP0)/2.;
        double bM2 = (bPm+bP0)/2.;
        double fm2 = (fo-fm)/m_delta;
        double fp2 = (fp-fo)/m_delta;
        double gp2 = (Gp + Go)/Go/2.;
        double gm2 = (Gm + Go)/Go/2.;
 
        dssdf = m_alpha*( gp2*fp2*bP2*bP2 - bM2*bM2*gm2*fm2)/m_delta + m_beta*dssdf;
 
        // does not seem to conserve nicely
        //dssdf = m_alpha*( fp*gp2*bP2*bP2 - 2*bP0*bP0*fo + bM2*bM2*gm2*fm)/(hp)/(hm) + m_beta*dssdf;
        //dssdf = m_alpha*( fp*Gp/Go*bPp*bPp - 2*bP0*bP0*fo + bPm*bPm*Gm/Go*fm)/(hp)/(hm) + m_beta*dssdf;
    };
 
    private:
    double m_alpha, m_beta, m_delta;
};
 
}//namespace detail
 
template<class FieldAligned, class container>
void assign_bc_along_field_2nd( const FieldAligned& fa, const container& fm,
        const container& f, const container& fp, container& fmg, container& fpg,
        dg::bc bound, std::array<double,2> boundary_value = {0,0})
{
    double delta = fa.deltaPhi();
    if( bound == dg::NEU)
    {
        double dbm = boundary_value[0], dbp = boundary_value[1];
        dg::blas1::subroutine( [dbm, dbp, delta]DG_DEVICE( double fm, double fo,
                    double fp, double& fmg, double& fpg,
                    double hbm, double hbp, double bbm, double bbo, double bbp
                    ){
            //formula derived for non-equidistant grid
            double hm = delta, hp = delta;
            double plus=0, minus=0, bothP=0, bothM = 0;
            plus = dbp*hp*(hm+hp)/(2.*hbp+hm) +
                fo*(2.*hbp+hm-hp)*(hm+hp)/hm/(2.*hbp+hm) + fm*hp*(-2.*hbp +
                    hp)/hm/(2.*hbp + hm);
            minus = fp*hm*(-2.*hbm+hm)/hp/(2.*hbm+hp) -
                dbm*hm*(hm+hp)/(2.*hbm+hp) +
                fo*(2.*hbm-hm+hp)*(hm+hp)/hp/(2.*hbm+hp);
            bothM = fo + dbp*hm*(-2.*hbm + hm)/2./(hbm+hbp) -
                dbm*hm*(2.*hbp+hm)/2./(hbm+hbp);
            bothP = fo + dbp*hp*(2.*hbm + hp)/2./(hbm+hbp) +
                dbm*hp*(2.*hbp-hp)/2./(hbm+hbp);
            fmg = (1.-bbo-bbm)*fm + bbm*minus + bbo*bothM;
            fpg = (1.-bbo-bbp)*fp + bbp*plus  + bbo*bothP;
        }, fm, f, fp, fmg, fpg, fa.hbm(), fa.hbp(), fa.bbm(),
                fa.bbo(), fa.bbp() );
    }
    else// if( bound == dg:DIR)
    {
        double fbm = boundary_value[0], fbp = boundary_value[1];
        dg::blas1::subroutine( [fbm, fbp, delta]DG_DEVICE( double fm, double fo,
                    double fp, double& fmg, double& fpg,
                    double hbm, double hbp, double bbm, double bbo, double bbp
                    ){
            //formula derived for non-equidistant grid
            double hm = delta, hp = delta;
            double plus=0, minus=0, bothP=0, bothM = 0;
            plus  = fm*hp*(-hbp + hp)/hm/(hbp+hm) + fo*(hbp-hp)*(hm+hp)/hbp/hm
                +fbp*hp*(hm+hp)/hbp/(hbp+hm);
            minus = +fo*(hbm-hm)*(hm+hp)/hbm/hp + fbm*hm*(hm+hp)/hbm/(hbm+hp)
                + fp*hm*(-hbm+hm)/hp/(hbm+hp);
            bothM = fbp*hm*(-hbm+hm)/hbp/(hbm+hbp) +
                fo*(hbm-hm)*(hbp+hm)/hbm/hbp + fbm*hm*(hbp+hm)/hbm/(hbm+hbp);
            bothP = fo*(hbp-hp)*(hbm+hp)/hbm/hbp +
                fbp*hp*(hbm+hp)/hbp/(hbm+hbp) + fbm*hp*(-hbp+hp)/hbm/(hbm+hbp);
            fmg = (1.-bbo-bbm)*fm + bbm*minus + bbo*bothM;
            fpg = (1.-bbo-bbp)*fp + bbp*plus  + bbo*bothP;
        }, fm, f, fp, fmg, fpg, fa.hbm(), fa.hbp(), fa.bbm(),
                fa.bbo(), fa.bbp());
    }
 
}
template<class FieldAligned, class container>
void assign_bc_along_field_1st( const FieldAligned& fa, const container& fm,
        const container& fp, container& fmg, container& fpg,
        dg::bc bound, std::array<double,2> boundary_value = {0,0})
{
    double delta = fa.deltaPhi();
    if( bound == dg::NEU)
    {
        double dbm = boundary_value[0], dbp = boundary_value[1];
        dg::blas1::subroutine( [dbm, dbp, delta]DG_DEVICE( double fm, double fp,
                    double& fmg, double& fpg, double bbm, double bbp
                    ){
            double hm = delta, hp = delta;
            double plus=0, minus=0;
            plus = fm + dbp*(hp+hm);
            minus = fp - dbm*(hp+hm);
            fmg = (1.-bbm)*fm + bbm*minus;
            fpg = (1.-bbp)*fp + bbp*plus;
        }, fm, fp, fmg, fpg, fa.bbm(), fa.bbp() );
    }
    else// if( bound == dg:DIR)
    {
        double fbm = boundary_value[0], fbp = boundary_value[1];
        dg::blas1::subroutine( [fbm, fbp, delta]DG_DEVICE( double fm, double fp,
                    double& fmg, double& fpg, double hbm,
                    double hbp, double bbm, double bbo, double bbp
                    ){
            double hm = delta, hp = delta;
            double plus=0, minus=0, bothP=0, bothM = 0;
            plus  = fm + (fbp-fm)/(hbp+hm)*(hp+hm) ;
            minus = fp - (hp+hm)*(fp-fbm)/(hp+hbm);
            bothM = fbp + (fbp-fbm)/(hbp+hbm)*(hp+hbm);
            bothP = fbp - (fbp-fbm)/(hbp+hbm)*(hbp+hm);
            fmg = (1.-bbo-bbm)*fm + bbm*minus + bbo*bothM;
            fpg = (1.-bbo-bbp)*fp + bbp*plus  + bbo*bothP;
        }, fm, fp, fmg, fpg, fa.hbm(), fa.hbp(), fa.bbm(),
                fa.bbo(), fa.bbp());
    }
}
 
template<class FieldAligned, class container>
void swap_bc_perp( const FieldAligned& fa, const container& fm,
        const container& fp, container& fmg, container& fpg)
{
    dg::blas1::subroutine( []DG_DEVICE( double fm, double fp,
                double& fmg, double& fpg,
                double bbm, double bbo, double bbp
                ){
        fmg = (1.-bbo-bbm)*fm + (bbm+bbo)*(-fm);
        fpg = (1.-bbo-bbp)*fp + (bbp+bbo)*(-fp);
    }, fm, fp, fmg, fpg, fa.bbm(), fa.bbo(), fa.bbp() );
 
}
 
template< class ProductGeometry, class IMatrix, class container >
struct DS
{
    typedef dg::geo::Fieldaligned<ProductGeometry, IMatrix, container> FA; 
    DS(){}
 
    template <class Limiter>
    DS(const dg::geo::TokamakMagneticField& vec, const ProductGeometry& grid,
        dg::bc bcx = dg::NEU,
        dg::bc bcy = dg::NEU,
        Limiter limit = FullLimiter(),
        double eps = 1e-5,
        unsigned mx=10, unsigned my=10,
        double deltaPhi=-1, std::string interpolation_method = "dg",
        bool benchmark=true):
        DS( FA( vec, grid, bcx, bcy, limit, eps, mx, my, deltaPhi,
                    interpolation_method, benchmark) )
    {
    }
    template<class Limiter>
    DS(const dg::geo::CylindricalVectorLvl1& vec, const ProductGeometry& grid,
        dg::bc bcx = dg::NEU,
        dg::bc bcy = dg::NEU,
        Limiter limit = FullLimiter(),
        double eps = 1e-5,
        unsigned mx=10, unsigned my=10,
        double deltaPhi=-1, std::string interpolation_method = "dg",
        bool benchmark=true):
        DS( FA( vec, grid, bcx, bcy, limit, eps, mx, my, deltaPhi,
                    interpolation_method, benchmark))
    {
    }
    DS( FA fieldaligned);
    template<class ...Params>
    void construct( Params&& ...ps)
    {
        //construct and swap
        *this = DS( std::forward<Params>( ps)...);
    }
 
    void set_boundaries( dg::bc bcz, double left, double right){
        m_fa.set_boundaries( bcz, left, right);
    }
    void set_boundaries( dg::bc bcz, const container& left, const container& right){
        m_fa.set_boundaries( bcz, left, right);
    }
    void set_boundaries( dg::bc bcz, const container& global, double scal_left, double scal_right){
        m_fa.set_boundaries( bcz, global, scal_left, scal_right);
    }
 
    void forward( double alpha, const container& f, double beta, container& g){
        m_fa(zeroForw, f, m_tempO);
        m_fa(einsPlus, f, m_tempP);
        ds_forward( m_fa, alpha, m_tempO, m_tempP, beta, g);
    }
    void forward2( double alpha, const container& f, double beta, container& g){
        m_fa(zeroForw, f, m_tempO);
        m_fa(einsPlus, f, m_tempP);
        m_fa(einsPlus, m_tempP, m_tempM);
        ds_forward2( m_fa, alpha, m_tempO, m_tempP, m_tempM, beta, g);
    }
    void backward( double alpha, const container& f, double beta, container& g){
        m_fa(einsMinus, f, m_tempM);
        m_fa(zeroForw, f, m_tempO);
        ds_backward( m_fa, alpha, m_tempM, m_tempO, beta, g);
    }
    void backward2( double alpha, const container& f, double beta, container& g){
        m_fa(einsMinus, f, m_tempM);
        m_fa(einsMinus, m_tempM, m_tempP);
        m_fa(zeroForw, f, m_tempO);
        ds_backward2( m_fa, alpha, m_tempP, m_tempM, m_tempO, beta, g);
    }
    void centered( double alpha, const container& f, double beta, container& g){
        m_fa(einsPlus,  f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        ds_centered( m_fa, alpha, m_tempM, m_tempP, beta, g);
    }
    void centered_bc_along_field(
        double alpha, const container& f, double beta, container& g, dg::bc bound,
        std::array<double,2> boundary_value = {0,0}){
        m_fa(einsPlus,  f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        assign_bc_along_field_2nd( m_fa, m_tempM, f, m_tempP, m_tempM, m_tempP,
                bound, boundary_value);
        ds_centered( m_fa, alpha, m_tempM, m_tempP, beta, g);
 
    }
    void backward( const container& f, container& g){
        backward(1., f,0.,g);
    }
    void forward( const container& f, container& g){
        forward(1.,f, 0.,g);
    }
    void centered( const container& f, container& g){
        centered(1.,f,0.,g);
    }
 
    void divForward( double alpha, const container& f, double beta, container& g){
        m_fa(einsPlus,  f, m_tempP);
        m_fa(zeroForw,  f, m_tempO);
        ds_divForward( m_fa, alpha, m_tempO, m_tempP, beta, g);
    }
    void divBackward( double alpha, const container& f, double beta, container& g){
        m_fa(einsMinus,  f, m_tempM);
        m_fa(zeroForw,  f, m_tempO);
        ds_divBackward( m_fa, alpha, m_tempM, m_tempO, beta, g);
    }
    void divCentered(double alpha, const container& f, double beta, container& g){
        m_fa(einsPlus,  f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        ds_divCentered( m_fa, alpha, m_tempM, m_tempP, beta, g);
    }
    void divForward(const container& f, container& g){
        divForward( 1.,f,0.,g);
    }
    void divBackward(const container& f, container& g){
        divBackward( 1.,f,0.,g);
    }
    void divCentered(const container& f, container& g){
        divCentered( 1.,f,0.,g);
    }
 
    void ds(dg::direction dir,  const container& f, container& g){
        ds(dir, 1., f, 0., g);
    }
    void ds(dg::direction dir, double alpha, const container& f, double beta, container& g);
    void div(dg::direction dir,  const container& f, container& g){
        div(dir, 1., f, 0., g);
    }
    void div(dg::direction dir, double alpha, const container& f, double beta, container& g);
 
    void symv( const container& f, container& g){ symv( 1., f, 0., g);}
    void symv( double alpha, const container& f, double beta, container& g);
    void dss( const container& f, container& g){
        dss( 1., f, 0., g);}
    void dss( double alpha, const container& f, double beta, container& g){
        m_fa(einsPlus, f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        m_fa(zeroForw,  f, m_tempO);
        dss_centered( m_fa, alpha, m_tempM, m_tempO, m_tempP, beta, g);
    }
    void dss_bc_along_field(
        double alpha, const container& f, double beta, container& g, dg::bc bound,
        std::array<double,2> boundary_value = {0,0}){
        m_fa(einsPlus, f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        m_fa(zeroForw,  f, m_tempO);
        assign_bc_along_field_2nd( m_fa, m_tempM, m_tempO, m_tempP, m_tempM, m_tempP,
                bound, boundary_value);
        dss_centered( m_fa, alpha, m_tempM, m_tempO, m_tempP, beta, g);
    }
    void dssd( double alpha, const container& f, double
            beta, container& g){
        m_fa(einsPlus, f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        m_fa(zeroForw,  f, m_tempO);
        dssd_centered( m_fa, alpha, m_tempM, m_tempO, m_tempP, beta, g);
    }
    void dssd_bc_along_field( double alpha, const
            container& f, double beta, container& g, dg::bc bound,
            std::array<double,2> boundary_value = {0,0}){
        m_fa(einsPlus, f, m_tempP);
        m_fa(einsMinus, f, m_tempM);
        m_fa(zeroForw,  f, m_tempO);
        assign_bc_along_field_2nd( m_fa, m_tempM, m_tempO, m_tempP, m_tempM, m_tempP,
                bound, boundary_value);
        dssd_centered( m_fa, alpha, m_tempM, f, m_tempP, beta, g);
    }
 
    const container& weights()const {
        return m_fa.sqrtG();
    }
 
    FA& fieldaligned(){return m_fa;}
    const FA& fieldaligned()const{return m_fa;}
    private:
    Fieldaligned<ProductGeometry, IMatrix, container> m_fa;
    container m_tempP, m_tempO, m_tempM;
};
 
 
template<class Geometry, class I, class container>
DS<Geometry, I, container>::DS( Fieldaligned<Geometry, I, container> fa): m_fa(fa)
{
    m_tempP = fa.sqrtG(), m_tempM = m_tempO = m_tempP;
}
 
template<class G, class I, class container>
inline void DS<G,I,container>::ds( dg::direction dir, double alpha,
    const container& f, double beta, container& dsf) {
    switch( dir){
        case dg::centered:
        return centered( alpha, f, beta, dsf);
        case dg::forward:
        return forward( alpha, f, beta, dsf);
        case dg::backward:
        return backward( alpha, f, beta, dsf);
    }
}
template<class G, class I, class container>
inline void DS<G,I,container>::div( dg::direction dir, double alpha,
    const container& f, double beta, container& dsf) {
    switch( dir){
        case dg::centered:
        return divCentered( alpha, f, beta, dsf);
        case dg::forward:
        return divForward( alpha, f, beta, dsf);
        case dg::backward:
        return divBackward( alpha, f, beta, dsf);
    }
}
 
 
template<class G,class I, class container>
void DS<G,I,container>::symv( double alpha, const container& f, double beta, container& dsTdsf)
{
    dssd( alpha, f, beta, dsTdsf);
};
 
template<class FieldAligned, class container>
void ds_forward(const FieldAligned& fa, double alpha, const container& f,
    const container& fp, double beta, container& g)
{
    //direct
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [ alpha, beta, delta]DG_DEVICE(
            double& dsf, double fo, double fp, double bphi){
                dsf = alpha*bphi*( fp - fo)/delta + beta*dsf;
            },
            g, f, fp, fa.bphi());
}
template<class FieldAligned, class container>
void ds_forward2(const FieldAligned& fa, double alpha, const container& f,
    const container& fp, const container& fpp, double beta, container& g)
{
    //direct
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [ alpha, beta, delta]DG_DEVICE(
            double& dsf, double fo, double fp, double fpp, double bphi){
                dsf = alpha*bphi*( -3.*fo + 4.*fp - fpp)/2./delta
                     + beta*dsf;
            },
            g, f, fp, fpp, fa.bphi());
}
 
template<class FieldAligned, class container>
void ds_backward( const FieldAligned& fa, double alpha, const container& fm,
    const container& f, double beta, container& g)
{
    //direct
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [ alpha, beta, delta] DG_DEVICE(
            double& dsf, double fo, double fm, double bphi){
                dsf = alpha*bphi*( fo - fm)/delta + beta*dsf;
            },
            g, f, fm, fa.bphi());
 
}
template<class FieldAligned, class container>
void ds_backward2( const FieldAligned& fa, double alpha, const container& fmm, const container& fm, const container& f, double beta, container& g)
{
    //direct
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [ alpha, beta, delta] DG_DEVICE(
            double& dsf, double fo, double fm,  double fmm, double bphi){
                dsf = alpha*bphi*( 3.*fo - 4.*fm + fmm)/2./delta
                    + beta*dsf;
            },
            g, f, fm, fmm, fa.bphi());
 
}
 
 
template<class FieldAligned, class container>
void ds_centered( const FieldAligned& fa, double alpha, const container& fm,
        const container& fp, double beta, container& g)
{
    //direct discretisation
    double delta=fa.deltaPhi();
    dg::blas1::subroutine( [alpha,beta,delta]DG_DEVICE( double& g, double fm,
        double fp, double bphi){
            g = alpha*bphi*(fp-fm)/2./delta + beta*g;
            }, g, fm, fp, fa.bphi());
}
template<class FieldAligned, class container>
void dss_centered( const FieldAligned& fa, double alpha, const container& fm,
        const container& f, const container& fp, double beta, container& g)
{
    dg::blas1::subroutine( detail::DSSCentered( alpha, beta, fa.deltaPhi()),
        g, fm, f, fp, fa.bphiM(), fa.bphi(), fa.bphiP());
}
template<class FieldAligned, class container>
void dssd_centered( const FieldAligned& fa, double alpha, const container& fm,
    const container& f, const container& fp, double beta, container& g)
{
    dg::blas1::subroutine( detail::DSSDCentered( alpha, beta, fa.deltaPhi()),
        g, fm, f, fp, fa.sqrtGm(), fa.sqrtG(), fa.sqrtGp(),
        fa.bphiM(), fa.bphi(), fa.bphiP());
}
 
template<class FieldAligned, class container>
void ds_divBackward( const FieldAligned& fa, double alpha, const container& fm,
    const container& f, double beta, container& g)
{
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [alpha,beta,delta] DG_DEVICE( double& dsf, double f0,
            double f1, double Gm, double G0, double bPm, double bP0){
                dsf = alpha*(bP0*G0*f0 - bPm*Gm*f1)/G0/delta + beta*dsf; },
            g, f, fm, fa.sqrtGm(), fa.sqrtG(), fa.bphiM(), fa.bphi());
}
 
template<class FieldAligned, class container>
void ds_divForward( const FieldAligned& fa, double alpha, const container& f,
    const container& fp, double beta, container& g)
{
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [alpha,beta,delta] DG_DEVICE( double& dsf, double f0,
            double f1, double Gp, double G0, double bPp, double bP0){
                dsf = alpha*(bPp*Gp*f1 - bP0*G0*f0)/G0/delta + beta*dsf; },
            g, f, fp, fa.sqrtGp(), fa.sqrtG(), fa.bphiP(), fa.bphi());
}
template<class FieldAligned, class container>
void ds_divCentered( const FieldAligned& fa, double alpha, const container& fm, const container& fp,
    double beta, container& g)
{
    double delta = fa.deltaPhi();
    dg::blas1::subroutine( [alpha,beta,delta]DG_DEVICE( double& dsf, double fm,
        double fp, double Gm, double Gp, double G0,
        double bPm, double bP0, double bPp)
        {
            dsf = alpha*( fp*Gp*bPp - fm*Gm*bPm )/G0/2./delta + beta*dsf;
        }, g, fm, fp, fa.sqrtGm(),
        fa.sqrtGp(), fa.sqrtG(), fa.bphiM(), fa.bphi(), fa.bphiP());
 
}
 
template<class FieldAligned, class container>
void ds_average( const FieldAligned& fa, double alpha,
        const container& fm, const container& fp, double beta, container& g)
{
    dg::blas1::subroutine( [alpha,beta]DG_DEVICE( double& g, double fm, double fp
                ){
            g = alpha*(fp+fm)/2. + beta*g;
            }, g, fm, fp);
}
template<class FieldAligned, class container>
void ds_slope( const FieldAligned& fa, double alpha,
        const container& fm, const container& fp, double beta, container& g)
{
    ds_centered( fa, alpha, fm, fp, beta, g);
}
 
 
}//namespace geo
 
template< class G, class I, class V>
struct TensorTraits< geo::DS<G,I, V> >
{
    using value_type = double;
    using tensor_category = SelfMadeMatrixTag;
};
}//namespace dg