music-panphasia/fd_schemes.hh

/*
 
 fd_schemes.hh - This file is part of MUSIC -
 a code to generate multi-scale initial conditions 
 for cosmological simulations 
 
 Copyright (C) 2010  Oliver Hahn
 
*/

#ifndef __FD_SCHEMES_HH
#define __FD_SCHEMES_HH

#include <vector>
#include <stdexcept>


//! abstract implementation of the Poisson/Force scheme
template< class L, class G, typename real_t=double >
class scheme
{
public:
	typedef L laplacian;
	typedef G gradient;
	
	laplacian m_laplacian;
	gradient m_gradient;
	
	//! gradient along x-direction
	template< class C >
	inline real_t grad_x( const C&c, const int i, const int j, const int k )
	{ return m_gradient.apply_x( c,i,j,k ); }

	//! gradient along y-direction
	template< class C >
	inline real_t grad_y( const C&c, const int i, const int j, const int k )
	{ return m_gradient.apply_y( c,i,j,k ); }
	
	//! gradient along z-direction	
	template< class C >
	inline real_t grad_z( const C&c, const int i, const int j, const int k )
	{ return m_gradient.apply_z( c,i,j,k ); }
	
	//! apply Laplace operator
	template< class C >
	inline real_t L_apply( const C&c, const int i, const int j, const int k ) 
	{ return m_laplacian.apply( c,i,j,k ); }
	
	//! compute an explicit solution for the central component of the discrete Poisson's equation
	template< class C >
	inline real_t L_rhs( const C&c, const int i, const int j, const int k ) 
	{ return m_laplacian.rhs( c,i,j,k ); }
	
	inline real_t ccoeff( void )
	{ return m_laplacian.ccoeff(); }
	
};

//! base class for finite difference gradients
template< int nextent, typename T >
class gradient
{
	typedef T real_t;
	std::vector<real_t> m_stencil;
	const unsigned nl;
public:
	
	gradient()
	: nl( 2*nextent+1 )
	{ 
		m_stencil.assign(nl*nl*nl,(real_t)0.0);
	}
	
	real_t& operator()(int i)
	{ return m_stencil[i+nextent]; }
	
	const real_t& operator()(int i) const
	{ return m_stencil[i+nextent]; }
	
	template< class C >
	inline void apply( const C& c, C& f, int dir )
	{
		f = c;
		
		int nx=c.size(0), ny=c.size(1), nz=c.size(2);		
		double hx = 1.0/(nx+1.0), hy = 1.0/(ny+1.0), hz = 1.0/(nz+1.0);
		
		f.zero();
		
		if( dir == 0 )
			for( int i=0; i<nx; ++i )
				for( int j=0; j<ny; ++j )
					for( int k=0; k<nz; ++k )
						for( int ii = -nextent; ii<=nextent; ++ii )
							f(i,j,k) += (*this)(ii) * c(i+ii,j,k)/hx;
		else if( dir == 1 )
			for( int i=0; i<nx; ++i )
				for( int j=0; j<ny; ++j )
					for( int k=0; k<nz; ++k )
						for( int jj = -nextent; jj<=nextent; ++jj )
							f(i,j,k) += (*this)(jj) * c(i,j+jj,k)/hy;
		else if( dir == 2 )
			for( int i=0; i<nx; ++i )
				for( int j=0; j<ny; ++j )
					for( int k=0; k<nz; ++k )
						for( int kk = -nextent; kk<=nextent; ++kk )
							f(i,j,k) += (*this)(kk) * c(i,j,k+kk)/hz;
		
	}
};

//! base class for finite difference stencils
template< int nextent, typename real_t >
class base_stencil
{
protected:
	std::vector<real_t> m_stencil;
	const unsigned nl;
public:
	bool m_modsource;
	
public:
	base_stencil( bool amodsource = false )
	: nl( 2*nextent+1 ), m_modsource( amodsource )
	{
		m_stencil.assign(nl*nl*nl,(real_t)0.0);
	}
	
	real_t& operator()(int i, int j, int k)
	{ return m_stencil[((i+nextent)*nl+(j+nextent))*nl+(k+nextent)]; }
	
	const real_t& operator()(unsigned i, unsigned j, unsigned k) const
	{ return m_stencil[((i+nextent)*nl+(j+nextent))*nl+(k+nextent)]; }
	
	template< class C >
	inline real_t rhs( const C& c, const int i, const int j, const int k )
	{
		real_t sum = this->apply( c, i, j, k );
		sum -= (*this)(0,0,0) * c(i,j,k);
		return sum;
	}
	
	inline real_t ccoeff( void )
	{
		return (*this)(0,0,0);
	}
	
	
	template< class C >
	inline real_t apply( const C& c, const int i, const int j, const int k )
	{
		real_t sum = 0.0;
		
		for( int ii=-nextent; ii<=nextent; ++ii )
			for( int jj=-nextent; jj<=nextent; ++jj )
				for( int kk=-nextent; kk<=nextent; ++kk )
					sum += (*this)(ii,jj,kk) * c(i+ii,j+jj,k+kk);
		
		return sum;
	}
	
	template< class C >
	inline real_t modsource( const C& c, const int i, const int j, const int k )
	{
		return 0.0;
	}
	
};


/***************************************************************************************/
/***************************************************************************************/
/***************************************************************************************/


//... Implementation of the Gradient schemes............................................


template< typename real_t >
class deriv_2P : public gradient<1,real_t>
{
	
public:
	deriv_2P( void )
	{
		(*this)( 0 ) =  0.0;
		(*this)(-1 ) = -0.5;
		(*this)(+1 ) = +0.5;		
	}
	
	
};

//... Implementation of the Laplacian schemes..........................................

//! 7-point, 2nd order finite difference Laplacian
template< typename real_t >
class stencil_7P : public base_stencil<1,real_t>
{
	
public:
	stencil_7P( void )
	{
		(*this)( 0, 0, 0) = -6.0;
		(*this)(-1, 0, 0) = +1.0;
		(*this)(+1, 0, 0) = +1.0;
		(*this)( 0,-1, 0) = +1.0;
		(*this)( 0,+1, 0) = +1.0;
		(*this)( 0, 0,-1) = +1.0;
		(*this)( 0, 0,+1) = +1.0;
	}
	
	template< class C >
	inline real_t apply( const C& c, const int i, const int j, const int k ) const
	{
		//return c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1)-6.0*c(i,j,k);
		return (double)c(i-1,j,k)+(double)c(i+1,j,k)+(double)c(i,j-1,k)+(double)c(i,j+1,k)+(double)c(i,j,k-1)+(double)c(i,j,k+1)-6.0*(double)c(i,j,k);
	}
	
	template< class C >
	inline real_t rhs( const C& c, const int i, const int j, const int k ) const
	{
		return c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1);
	}
	
	inline real_t ccoeff( void )
	{
		return -6.0;
	}
};

//! 13-point, 4th order finite difference Laplacian
template< typename real_t >
class stencil_13P : public base_stencil<2,real_t>
{
	
public:
	stencil_13P( void )
	{
		(*this)( 0, 0, 0) = -90.0/12.;
		
		(*this)(-1, 0, 0) = 
		(*this)(+1, 0, 0) = 
		(*this)( 0,-1, 0) = 
		(*this)( 0,+1, 0) = 
		(*this)( 0, 0,-1) = 
		(*this)( 0, 0,+1) = 16./12.;
		
		(*this)(-2, 0, 0) = 
		(*this)(+2, 0, 0) = 
		(*this)( 0,-2, 0) = 
		(*this)( 0,+2, 0) = 
		(*this)( 0, 0,-2) = 
		(*this)( 0, 0,+2) = -1./12.;
	}
	
	template< class C >
	inline real_t apply( const C& c, const int i, const int j, const int k )
	{
		return 
			(-1.0*(c(i-2,j,k)+c(i+2,j,k)+c(i,j-2,k)+c(i,j+2,k)+c(i,j,k-2)+c(i,j,k+2))
			 +16.0*(c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1))
			 -90.0*c(i,j,k))/12.0;
	}
	
	template< class C >
	inline real_t rhs( const C& c, const int i, const int j, const int k )
	{
		return 
			(-1.0*(c(i-2,j,k)+c(i+2,j,k)+c(i,j-2,k)+c(i,j+2,k)+c(i,j,k-2)+c(i,j,k+2))
			 +16.0*(c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1)))/12.0;
	}
	
	inline real_t ccoeff( void )
	{
		return -90.0/12.0;
	}
};


//! 19-point, 6th order finite difference Laplacian
template< typename real_t >
class stencil_19P : public base_stencil<3,real_t>
{
	
public:
	stencil_19P( void )
	{
		(*this)( 0, 0, 0) = -1470./180.;
		
		(*this)(-1, 0, 0) = 
		(*this)(+1, 0, 0) = 
		(*this)( 0,-1, 0) = 
		(*this)( 0,+1, 0) = 
		(*this)( 0, 0,-1) = 
		(*this)( 0, 0,+1) = 270./180.;
		
		(*this)(-2, 0, 0) = 
		(*this)(+2, 0, 0) = 
		(*this)( 0,-2, 0) = 
		(*this)( 0,+2, 0) = 
		(*this)( 0, 0,-2) = 
		(*this)( 0, 0,+2) = -27./180.;
		
		(*this)(-3, 0, 0) = 
		(*this)(+3, 0, 0) = 
		(*this)( 0,-3, 0) = 
		(*this)( 0,+3, 0) = 
		(*this)( 0, 0,-3) = 
		(*this)( 0, 0,+3) = 2./180.;
		
	}
	
	template< class C >
	inline real_t apply( const C& c, const int i, const int j, const int k )
	{
		return 
		(2.0*(c(i-3,j,k)+c(i+3,j,k)+c(i,j-3,k)+c(i,j+3,k)+c(i,j,k-3)+c(i,j,k+3))
		 -27.0*(c(i-2,j,k)+c(i+2,j,k)+c(i,j-2,k)+c(i,j+2,k)+c(i,j,k-2)+c(i,j,k+2))
		 +270.0*(c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1))
		 -1470.0*c(i,j,k))/180.0;
	}
	
	template< class C >
	inline real_t rhs( const C& c, const int i, const int j, const int k )
	{
		return 
		(2.0*(c(i-3,j,k)+c(i+3,j,k)+c(i,j-3,k)+c(i,j+3,k)+c(i,j,k-3)+c(i,j,k+3))
		 -27.0*(c(i-2,j,k)+c(i+2,j,k)+c(i,j-2,k)+c(i,j+2,k)+c(i,j,k-2)+c(i,j,k+2))
		 +270.0*(c(i-1,j,k)+c(i+1,j,k)+c(i,j-1,k)+c(i,j+1,k)+c(i,j,k-1)+c(i,j,k+1)))/180.0;
	}
	
	inline real_t ccoeff( void )
	{
		return -1470.0/180.0;
	}
	
};


//! flux operator for the 4th order FD Laplacian
template< typename real_t >
class Laplace_flux_O4
{
public:
	/*! computes flux across a surface normal to x-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_x( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/12.0;
		return fac*(-c(i-2,j,k)+15.0*c(i-1,j,k)-15.0*c(i,j,k)+c(i+1,j,k));
	}
	
	/*! computes flux across a surface normal to y-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_y( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/12.0;
		return fac*(-c(i,j-2,k)+15.0*c(i,j-1,k)-15.0*c(i,j,k)+c(i,j+1,k));
	}
	
	/*! computes flux across a surface normal to z-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_z( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/12.0;
		return fac*(-c(i,j,k-2)+15.0*c(i,j,k-1)-15.0*c(i,j,k)+c(i,j,k+1));
	}
	
};


//! flux operator for the 6th order FD Laplacian
template< typename real_t >
class Laplace_flux_O6
{
public:
	
	/*! computes flux across a surface normal to x-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_x( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/180.0;
		return fac*(2.*c(i-3,j,k)-25.*c(i-2,j,k)+245.*c(i-1,j,k)-245.0*c(i,j,k)+25.*c(i+1,j,k)-2.*c(i+2,j,k));
	}
	
	/*! computes flux across a surface normal to y-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_y( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/180.0;
		return fac*(2.*c(i,j-3,k)-25.*c(i,j-2,k)+245.*c(i,j-1,k)-245.0*c(i,j,k)+25.*c(i,j+1,k)-2.*c(i,j+2,k));
	}
	
	/*! computes flux across a surface normal to z-direction
	 * @param idir idir is -1 for left boundary, +1 for right boundary
	 * @param c array on which to apply the operator
	 * @param i grid x-index
	 * @param j grid y-index
	 * @param k grid z-index
	 * @returns flux value
	 */
	template< class C >
	inline double apply_z( int idir, const C& c, const int i, const int j, const int k )
	{
		double fac = -((double)idir)/180.0;
		return fac*(2.*c(i,j,k-3)-25.*c(i,j,k-2)+245.*c(i,j,k-1)-245.0*c(i,j,k)+25.*c(i,j,k+1)-2.*c(i,j,k+2));
	}
	
};



#endif