refined_grid.h

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#pragma once
 
#include "cusp/transpose.h"
#include "dg/backend/memory.h"
#include "dg/blas.h"
#include "grid.h"
#include "weights.h"
#include "interpolation.h"
 
#include "base_geometry.h"
 
 
namespace dg
{
 
namespace detail
{
 
template<class real_type>
thrust::host_vector<real_type> normalize_weights_and_compute_abscissas( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights)
{
    //normalize weights
    unsigned Nx_new = weights.size()/g.n();
    for( unsigned i=0;i<weights.size(); i++)
        weights[i] *= (real_type)g.N()/(real_type)Nx_new;
 
    thrust::host_vector<real_type> boundaries(Nx_new+1), abs(g.n()*Nx_new);
    boundaries[0] = g.x0();
    for( unsigned i=0; i<Nx_new; i++)
    {
        boundaries[i+1] = boundaries[i] + g.lx()/(real_type)Nx_new/weights[g.n()*i];
        for( unsigned j=0; j<g.n(); j++)
        {
            abs[i*g.n()+j] =  (boundaries[i+1]+boundaries[i])/2. +
                (boundaries[i+1]-boundaries[i])/2.*g.dlt().abscissas()[j];
        }
    }
    return abs;
}
 
}//namespace detail
 
 
template<class real_type>
struct aRealRefinement1d
{
    void generate( const RealGrid1d<real_type>& g_old, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const
    {
        weights.resize( N_new(g_old.N(), g_old.bcx()));
        abscissas.resize( N_new(g_old.N(), g_old.bcx()));
        do_generate(g_old,weights,abscissas);
    }
    unsigned N_new( unsigned N_old, bc bcx) const
    {
        return do_N_new(N_old, bcx);
    }
    virtual aRealRefinement1d* clone()const=0;
    virtual ~aRealRefinement1d() = default;
    protected:
    aRealRefinement1d() = default;
    aRealRefinement1d(const aRealRefinement1d& src) = default;
    aRealRefinement1d& operator=(const aRealRefinement1d& src) = default;
    private:
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const =0;
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const =0;
};
 
template<class real_type>
struct RealIdentityRefinement : public aRealRefinement1d<real_type>
{
    virtual RealIdentityRefinement* clone()const{return new RealIdentityRefinement();}
    private:
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const override final{
        weights=dg::create::weights(g);
        abscissas=dg::create::abscissas(g);
    }
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const override final{
        return N_old;
    }
};
 
template<class real_type>
struct RealLinearRefinement : public aRealRefinement1d<real_type>
{
    RealLinearRefinement( unsigned multiple): m_(multiple){
        assert( multiple>= 1);
    }
    virtual RealLinearRefinement* clone()const{return new RealLinearRefinement(*this);}
    private:
    unsigned m_;
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const override final
    {
        thrust::host_vector< real_type> left( g.n()*g.N()*m_, 1);
        for( unsigned k=0; k<left.size(); k++)
            left[k] = (real_type)m_;
        weights = left;
        abscissas = dg::detail::normalize_weights_and_compute_abscissas( g, weights);
    }
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const override final{
        return N_old*m_;
    }
};
 
template<class real_type>
struct RealFemRefinement : public aRealRefinement1d<real_type>
{
    RealFemRefinement( unsigned multiple): m_M(multiple){
        assert( multiple>= 1);
    }
    virtual RealFemRefinement* clone()const{return new RealFemRefinement(*this);}
    private:
    unsigned m_M;
    std::vector<real_type> simpsons_weights( unsigned N, double h) const
    {
        // Create weights for Simpson's integration on an equidistant subgrid with N cells (including end points)
        // N >= 2
        std::vector<real_type> simpson( N, h);
        if( N == 2)
        {
            simpson[0] = simpson[1] = h/2.;
            return simpson;
        }
        simpson[0]=1./3. * h;
        for( unsigned i=0; i<(N-3)/2; i++)
        {
            simpson[2*i+1] = 4./3. * h;
            simpson[2*i+2] = 2./3. * h;
        }
        if( N%2 != 0)
        {
            simpson[N-2] = 4./3. * h;
            simpson[N-1] = 1./3. * h;
        }
        else
        {
            simpson[N-4] = N==4 ? 3./8.*h : (1./3.+3./8.)*h;
            simpson[N-3] = (9./8.)*h;
            simpson[N-2] = (9./8.)*h;
            simpson[N-1] = (3./8.)*h;
        }
        return simpson;
    }
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const override final
    {
        thrust::host_vector<real_type> old = dg::create::abscissas(g);
        if( m_M == 1)
        {
            abscissas = old;
            weights = dg::evaluate( dg::one, g);
            return;
        }
        abscissas.resize( g.size()*m_M);
        weights.resize( g.size()*m_M);
        dg::blas1::copy( 0., weights);
        unsigned NLeft = m_M/2;
        double hxleft = (old[0] - g.x0())/(double)(NLeft+1);
        abscissas[0] = g.x0()+hxleft;
        weights[0] = hxleft;
        unsigned idx = 0;
        std::vector<real_type> sim = simpsons_weights( NLeft+1, hxleft);
        weights[idx] += sim[0];
        for( unsigned k=1; k<=NLeft; k++)
        {
            idx++;
            abscissas[idx] = abscissas[idx-1]+hxleft;
            weights[idx] += sim[k];
        }
        // now abs is at old[0]
        unsigned NMiddle = m_M;
        for( unsigned i=0; i<old.size()-1; i++)
        {
            double hxmiddle = (old[i+1] - old[i])/(double)NMiddle;
            sim = simpsons_weights( NMiddle+1, hxmiddle);
            weights[idx] += sim[0];
            for( unsigned k=1; k<=NMiddle; k++)
            {
                idx++;
                abscissas[idx] = abscissas[idx-1]+hxmiddle;
                weights[idx] += sim[k];
            }
        }
        unsigned NRight = m_M - 1 - m_M/2;
        double hxright = (g.x1() - old[g.size()-1] )/(double)(NRight+1);
        if( NRight > 0)
        {
            sim = simpsons_weights( NRight+1, hxright);
            weights[idx] += sim[0];
            for( unsigned k=1; k<=NRight; k++)
            {
                idx++;
                abscissas[idx] = abscissas[idx-1]+hxright;
                weights[idx] += sim[k];
            }
        }
        weights[idx] += hxright;
        RealGrid1d<real_type> nGrid( g.x0(), g.x1(), g.n(), g.N()*m_M);
        thrust::host_vector<real_type> wrong_weights = dg::create::weights(nGrid);
        dg::blas1::pointwiseDivide( wrong_weights, weights, weights);
    }
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const override final{
        return N_old*m_M;
    }
};
 
template<class real_type>
struct RealEquidistRefinement : public aRealRefinement1d<real_type>
{
    RealEquidistRefinement( unsigned add_x, unsigned node, unsigned howmany=1): add_x_(add_x), node_(node), howm_(howmany){ }
    virtual RealEquidistRefinement* clone()const{return new RealEquidistRefinement(*this);}
    private:
    unsigned add_x_, node_, howm_;
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const override final
    {
        if( add_x_ == 0 || howm_ == 0)
        {
            thrust::host_vector<real_type> w_( g.size(), 1);
            abscissas = dg::create::abscissas(g);
            weights = w_;
            return;
        }
        weights = equidist_ref( add_x_, node_, g.n(), g.N(), g.bcx(), howm_);
        abscissas = detail::normalize_weights_and_compute_abscissas( g, weights);
    }
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const override final
    {
        if( bcx == dg::PER) return N_old + 2*add_x_*howm_;
        return N_old + add_x_*howm_;
    }
    thrust::host_vector<real_type> equidist_ref( unsigned add_x, unsigned node, unsigned n, unsigned N, dg::bc bcx, unsigned howmany) const
    {
        assert( howm_ <= N);
        assert( node_ <= N);
        if( node_ != 0 && node_ != N)
            assert( howm_ <= node_ && howm_ <= N-node_);
        if( add_x_ == 0 || howm_ == 0)
        {
            thrust::host_vector<real_type> w_( n*N, 1);
            return w_;
        }
        //there are add_x+1 finer cells per refined cell ...
        thrust::host_vector< real_type> left( n*N+n*add_x_*howm_, 1), right(left);
        for( unsigned i=0; i<(add_x_+1)*howm_; i++)//the original cell and the additional ones
            for( unsigned k=0; k<n; k++)
                left[i*n+k] = add_x_ + 1;
        //mirror left into right
        for( unsigned i=0; i<right.size(); i++)
            right[i] = left[ (left.size()-1)-i];
        thrust::host_vector< real_type> both( n*N+2*n*add_x_*howm_, 1);
        for( unsigned i=0; i<left.size(); i++)
            both[i] *= left[i];
        for( unsigned i=0; i<right.size(); i++)
            both[i+n*add_x_*howm_] *= right[i];
        if(      node_ == 0     && bcx != dg::PER) { return left; }
        else if( node_ == N && bcx != dg::PER) { return right; }
        else if((node_ == N || node_ == 0) && bcx == dg::PER) { return both; }
        else
        {
            thrust::host_vector<real_type> w_ = both;
            //now shift indices so that refinement is around node_s
            for( unsigned i=0; i<both.size(); i++)
                w_[((howm_*add_x_+node_)*n+i)%both.size()] = both[i];
            return w_;
        }
    }
 
};
 
template<class real_type>
struct RealExponentialRefinement : public aRealRefinement1d<real_type>
{
    RealExponentialRefinement( unsigned add_x, unsigned node): add_x_(add_x), node_(node) {}
    virtual RealExponentialRefinement* clone()const{return new RealExponentialRefinement(*this);}
    private:
    unsigned add_x_, node_;
    virtual void do_generate( const RealGrid1d<real_type>& g, thrust::host_vector<real_type>& weights, thrust::host_vector<real_type>& abscissas) const override final
    {
        if( add_x_ == 0)
        {
            thrust::host_vector<real_type> w_( g.size(), 1);
            abscissas= dg::create::abscissas(g);
            weights = w_;
            return;
        }
        weights = exponential_ref( add_x_, node_, g.n(), g.N(), g.bcx());
        abscissas = detail::normalize_weights_and_compute_abscissas( g, weights);
    }
    virtual unsigned do_N_new( unsigned N_old, bc bcx) const override final
    {
        if( bcx == dg::PER) return N_old + 2*add_x_;
        return N_old + add_x_;
    }
    thrust::host_vector<real_type> exponential_ref( unsigned add_x, unsigned node, unsigned n, unsigned N, dg::bc bcx) const
    {
        if( add_x_ == 0)
        {
            thrust::host_vector<real_type> w_( n*N, 1);
            return w_;
        }
        assert( node_ <= N);
        //there are add_x_+1 finer cells per refined cell ...
        thrust::host_vector< real_type> left( n*N+n*add_x_, 1), right(left);
        for( unsigned k=0; k<n; k++)//the original cell and the additional ones
            left[k] = pow( 2, add_x_);
        for( unsigned i=0; i<add_x_; i++)
            for( unsigned k=0; k<n; k++)
                left[(i+1)*n+k] = pow( 2, add_x_-i);
        //mirror left into right
        for( unsigned i=0; i<right.size(); i++)
            right[i] = left[ (left.size()-1)-i];
        thrust::host_vector< real_type> both( n*N+2*n*add_x_, 1);
        for( unsigned i=0; i<left.size(); i++)
            both[i] *= left[i];
        for( unsigned i=0; i<right.size(); i++)
            both[i+n*add_x_] *= right[i];
        if(      node_ == 0     && bcx != dg::PER) { return left; }
        else if( node_ == N && bcx != dg::PER) { return right; }
        else if((node_ == N || node_ == 0) && bcx == dg::PER) { return both; }
        else
        {
            thrust::host_vector<real_type> w_ = both;
            //now shift indices so that refinement is around node_s
            for( unsigned i=0; i<both.size(); i++)
                w_[((add_x_+node_)*n+i)%both.size()] = both[i];
            return w_;
        }
    }
};
 
using aRefinement1d         = dg::aRealRefinement1d<double>;
using IdentityRefinement    = dg::RealIdentityRefinement<double>;
using FemRefinement         = dg::RealFemRefinement<double>;
using LinearRefinement      = dg::RealLinearRefinement<double>;
using EquidistRefinement    = dg::RealEquidistRefinement<double>;
using ExponentialRefinement = dg::RealExponentialRefinement<double>;
 
 
template<class real_type>
struct RealCartesianRefinedGrid2d : public dg::aRealGeometry2d<real_type>
{
    RealCartesianRefinedGrid2d( const aRealRefinement1d<real_type>& refX, const aRealRefinement1d<real_type>& refY, real_type x0, real_type x1, real_type y0, real_type y1,
            unsigned n, unsigned Nx, unsigned Ny, bc bcx = dg::PER, bc bcy = dg::PER) : dg::aGeometry2d( {x0, x1, n, refX.N_new(Nx,bcx), bcx}, {y0, y1, n, refY.N_new(Ny,bcy),bcy}), refX_(refX), refY_(refY), w_(2), a_(2)
    {
        construct_weights_and_abscissas(n,Nx,n,Ny);
    }
 
    virtual RealCartesianRefinedGrid2d* clone()const{return new RealCartesianRefinedGrid2d(*this);}
    private:
    ClonePtr<aRealRefinement1d<real_type>> refX_, refY_;
    std::vector<thrust::host_vector<real_type> > w_, a_;
    void construct_weights_and_abscissas(unsigned nx, unsigned Nx, unsigned ny, unsigned Ny)
    {
        RealGrid1d<real_type> gx( this->x0(), this->x1(), nx, Nx, this->bcx());
        RealGrid1d<real_type> gy( this->y0(), this->y1(), ny, Ny, this->bcy());
        thrust::host_vector<real_type> wx, ax, wy, ay;
        refX_->generate( gx, wx, ax);
        refY_->generate( gy, wy, ay);
        w_[0].resize(this->size()), w_[1].resize(this->size());
        a_[0].resize(this->size()), a_[1].resize(this->size());
        //now make product space
        for( unsigned i=0; i<wy.size(); i++)
            for( unsigned j=0; j<wx.size(); j++)
            {
                w_[0][i*wx.size()+j] = wx[j];
                w_[1][i*wx.size()+j] = wy[i];
                a_[0][i*wx.size()+j] = ax[j];
                a_[1][i*wx.size()+j] = ay[i];
            }
    }
    virtual void do_set(unsigned nx, unsigned Nx, unsigned ny, unsigned Ny)override final{
        aRealTopology2d<real_type>::do_set(nx,refX_->N_new(Nx,this->bcx()),ny,refY_->N_new(Ny, this->bcy()));
        construct_weights_and_abscissas(nx,Nx,ny,Ny);
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_metric()const override final{
        SparseTensor<thrust::host_vector<real_type> > t(*this);
        t.values().push_back( w_[0]);
        t.values().push_back( w_[1]);
        dg::blas1::pointwiseDot( w_[0], w_[0], t.values()[2]);
        dg::blas1::pointwiseDot( w_[1], w_[1], t.values()[3]);
        t.idx(0,0)=2, t.idx(1,1)=3;
        return t;
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_jacobian()const override final{
        SparseTensor<thrust::host_vector<real_type> > t(*this);
        t.values().push_back( w_[0]);
        t.values().push_back( w_[1]);
        t.idx(0,0)=2, t.idx(1,1)=3;
        return t;
    }
    virtual std::vector<thrust::host_vector<real_type> > do_compute_map()const override final{
        return a_;
    }
};
 
template< class real_type>
struct RealCartesianRefinedGrid3d : public dg::aRealGeometry3d<real_type>
{
    RealCartesianRefinedGrid3d( const aRealRefinement1d<real_type>& refX, const aRealRefinement1d<real_type>& refY, aRealRefinement1d<real_type>& refZ, real_type x0, real_type x1, real_type y0, real_type y1, real_type z0, real_type z1,
            unsigned n, unsigned Nx, unsigned Ny, unsigned Nz, bc bcx = dg::PER, bc bcy = dg::PER, bc bcz=dg::PER) :
        dg::aGeometry3d( {x0, x1, n, refX.N_new(Nx,bcx), bcx}, { y0, y1, refY.N_new(Ny,bcy), bcy}, {z0,z1, 1, refZ.N_new(Nz,bcz), bcz}), refX_(refX), refY_(refY), refZ_(refZ), w_(3), a_(3)
    {
        construct_weights_and_abscissas(n, Nx, n, Ny,1, Nz);
    }
 
    virtual RealCartesianRefinedGrid3d* clone()const{return new RealCartesianRefinedGrid3d(*this);}
    private:
    ClonePtr<aRealRefinement1d<real_type>> refX_, refY_, refZ_;
    std::vector<thrust::host_vector<real_type> > w_, a_;
    void construct_weights_and_abscissas(unsigned nx, unsigned Nx, unsigned ny, unsigned Ny, unsigned nz, unsigned Nz)
    {
        RealGrid1d<real_type> gx( this->x0(), this->x1(), nx, Nx, this->bcx());
        RealGrid1d<real_type> gy( this->y0(), this->y1(), ny, Ny, this->bcy());
        RealGrid1d<real_type> gz( this->y0(), this->y1(), nz, Nz, this->bcz());
        thrust::host_vector<real_type> w[3], a[3];
        refX_->generate( gx, w[0], a[0]);
        refY_->generate( gy, w[1], a[1]);
        refZ_->generate( gz, w[2], a[2]);
        w_[0].resize(this->size()), w_[1].resize(this->size()), w_[2].resize(this->size());
        a_[0].resize(this->size()), a_[1].resize(this->size()), a_[2].resize(this->size());
        //now make product space
    for( unsigned s=0; s<w[2].size(); s++)
        for( unsigned i=0; i<w[1].size(); i++)
            for( unsigned j=0; j<w[0].size(); j++)
            {
                w_[0][(s*w[1].size()+i)*w[0].size()+j] = w[0][j];
                w_[1][(s*w[1].size()+i)*w[0].size()+j] = w[1][i];
                w_[2][(s*w[1].size()+i)*w[0].size()+j] = w[2][s];
                a_[0][(s*w[1].size()+i)*w[0].size()+j] = a[0][j];
                a_[1][(s*w[1].size()+i)*w[0].size()+j] = a[1][i];
                a_[2][(s*w[1].size()+i)*w[0].size()+j] = a[1][s];
            }
    }
    virtual void do_set(unsigned nx, unsigned Nx, unsigned ny, unsigned Ny, unsigned nz, unsigned Nz) override final{
        aRealTopology3d<real_type>::do_set(nx,refX_->N_new(Nx, this->bcx()),ny,refY_->N_new(Ny,this->bcy()), nz, refZ_->N_new(Nz,this->bcz()));
        construct_weights_and_abscissas(nx, Nx, ny, Ny, nz, Nz);
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_metric()const override final {
        SparseTensor<thrust::host_vector<real_type> > t(*this);
        t.values().resize( 4, t.values()[0]);
        dg::blas1::pointwiseDot( w_[0], w_[0], t.values()[1]);
        dg::blas1::pointwiseDot( w_[1], w_[1], t.values()[2]);
        dg::blas1::pointwiseDot( w_[2], w_[2], t.values()[3]);
        t.idx(0,0)=1, t.idx(1,1)=2, t.idx(2,2)=3;
        return t;
    }
    virtual SparseTensor<thrust::host_vector<real_type> > do_compute_jacobian()const override final{
        SparseTensor<thrust::host_vector<real_type> > t(*this);
        t.values().push_back( w_[0]);
        t.values().push_back( w_[1]);
        t.values().push_back( w_[2]);
        t.idx(0,0)=2, t.idx(1,1)=3, t.idx(2,2)=4;
        return t;
    }
    virtual std::vector<thrust::host_vector<real_type> > do_compute_map()const override final {
        return a_;
    }
};
 
using CartesianRefinedGrid2d = dg::RealCartesianRefinedGrid2d<double>;
using CartesianRefinedGrid3d = dg::RealCartesianRefinedGrid3d<double>;
 
}//namespace dg