Derivative.hpp

/*
 * Derivative.hpp
 *
 *  Created on: Oct 5, 2015
 *      Author: Pietro Incardona
 */

#ifndef OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_
#define OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_

#define CENTRAL 0
#define CENTRAL_B_ONE_SIDE 1
#define FORWARD 2
#define BACKWARD 3

#include "util/mathutil.hpp"
#include "Vector/map_vector.hpp"
#include "Grid/comb.hpp"
#include "FiniteDifference/util/common.hpp"
#include "util/util_num.hpp"
#include <unordered_map>

/*! \brief Derivative second order on h (spacing)
 *
 * \tparam d on which dimension derive
 * \tparam Field which field derive
 * \tparam impl which implementation
 *
 */
template<unsigned int d, typename Field, typename Sys_eqs, unsigned int impl=CENTRAL>
class D
{
	/*! \brief Calculate which colums of the Matrix are non zero
	 *
	 * \param pos position where the derivative is calculated
	 * \param gs Grid info
	 * \param cols non-zero colums calculated by the function
	 * \param coeff coefficent (constant in front of the derivative)
	 *
	 * ### Example
	 *
	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
	 *
	 */
	inline static void value(const grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
	{
		std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
	}

	/*! \brief Calculate the position where the derivative is calculated
	 *
	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
	 *  it calculate how the operator shift the calculation in the cell
	 *
	 * \param pos position where we are calculating the derivative
	 * \param gs Grid info
	 * \param s_pos staggered position of the properties
	 *
	 * \return where (in which cell) the derivative is calculated
	 *
	 */
	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
			                                          const grid_sm<Sys_eqs::dims,void> & gs,
													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
	{
		std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";

		return pos;
	}
};

/*! \brief Second order central Derivative scheme on direction i
 *
 * \verbatim
 *
 *  -1        +1
 *   *---+---*
 *
 * \endverbatim
 *
 */
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,CENTRAL>
{
	public:

	/*! \brief Calculate which colums of the Matrix are non zero
	 *
	 * \param g_map mapping grid
	 * \param kmap position where the derivative is calculated
	 * \param gs Grid info
	 * \param spacing grid spacing
	 * \param cols non-zero colums calculated by the function
	 * \param coeff coefficent (constant in front of the derivative)
	 *
	 * ### Example
	 *
	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
	 *
	 */
	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
							 const grid_sm<Sys_eqs::dims,void> & gs,
							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
							 typename Sys_eqs::stype coeff)
	{
		// if the system is staggered the CENTRAL derivative is equivalent to a forward derivative
		if (is_grid_staggered<Sys_eqs>::value())
		{
			D<d,arg,Sys_eqs,BACKWARD>::value(g_map,kmap,gs,spacing,cols,coeff);
			return;
		}

		long int old_val = kmap.getKeyRef().get(d);
		kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
		arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]/2.0 );
		kmap.getKeyRef().set_d(d,old_val);


		old_val = kmap.getKeyRef().get(d);
		kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
		arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]/2.0 );
		kmap.getKeyRef().set_d(d,old_val);
	}


	/*! \brief Calculate the position where the derivative is calculated
	 *
	 * In case on non staggered case this function just return a null grid_key, in case of staggered,
	 *  it calculate how the operator shift in the cell
	 *
 	 	 \verbatim

		+--$--+
		|     |
		#  *  #
		|     |
		0--$--+

	  # = velocity(y)
	  $ = velocity(x)
	  * = pressure

		\endverbatim
	 *
	 * Consider this 2D staggered cell and a second order central derivative scheme, this lead to
	 *
	 * \f$ \frac{\partial v_y}{\partial x} \f$ is calculated on position (*), so the function return the grid_key {0,0}
	 *
	 * \f$ \frac{\partial v_y}{\partial y} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
	 *
	 * \f$ \frac{\partial v_x}{\partial x} \f$ is calculated on position (0), so the function return the grid_key {-1,-1}
	 *
	 * \f$ \frac{\partial v_x}{\partial y} \f$ is calculated on position (*), so the function return the grid_key {0,0}
	 *
	 * \param pos position where we are calculating the derivative
	 * \param gs Grid info
	 * \param s_pos staggered position of the properties
	 *
	 * \return where (in which cell grid) the derivative is calculated
	 *
	 */
	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
			                                          const grid_sm<Sys_eqs::dims,void> & gs,
													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
	{
		auto arg_pos = arg::position(pos,gs,s_pos);
		if (is_grid_staggered<Sys_eqs>::value())
		{
			if (arg_pos.get(d) == -1)
			{
				arg_pos.set_d(d,0);
				return arg_pos;
			}
			else
			{
				arg_pos.set_d(d,-1);
				return arg_pos;
			}
		}

		return arg_pos;
	}
};


/*! \brief Second order one sided Derivative scheme on direction i
 *
 * \verbatim
 *
 *  -1.5    2.0   -0.5
 *    +------*------*
 *
 * or
 *
 *  -0.5    2.0   -1.5
 *    *------*------+
 *
 *  in the bulk
 *
 *  -1        +1
 *   *---+---*
 *
 * \endverbatim
 *
 */
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,CENTRAL_B_ONE_SIDE>
{
public:

	/*! \brief Calculate which colums of the Matrix are non zero
	 *
	 * \param g_map mapping grid points
	 * \param kmap position where the derivative is calculated
	 * \param gs Grid info
	 * \param spacing of the grid
	 * \param cols non-zero colums calculated by the function
	 * \param coeff coefficent (constant in front of the derivative)
	 *
	 * ### Example
	 *
	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
	 *
	 */
	static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
			          grid_dist_key_dx<Sys_eqs::dims> & kmap,
					  const grid_sm<Sys_eqs::dims,void> & gs,
					  typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
					  std::unordered_map<long int,typename Sys_eqs::stype > & cols,
					  typename Sys_eqs::stype coeff)
	{
#ifdef SE_CLASS1
		if (Sys_eqs::boundary[d] == PERIODIC)
			std::cerr << __FILE__ << ":" << __LINE__ << " error, it make no sense use one sided derivation with periodic boundary, please use CENTRAL\n";
#endif

		grid_key_dx<Sys_eqs::dims> pos = g_map.getGKey(kmap);

		if (pos.get(d) == (long int)gs.size(d)-1 )
		{
			arg::value(g_map,kmap,gs,spacing,cols,1.5*coeff/spacing[d]);

			long int old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
			arg::value(g_map,kmap,gs,spacing,cols,-2.0*coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);

			old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 2);
			arg::value(g_map,kmap,gs,spacing,cols,0.5*coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);
		}
		else if (pos.get(d) == 0)
		{
			arg::value(g_map,kmap,gs,spacing,cols,-1.5*coeff/spacing[d]);

			long int old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
			arg::value(g_map,kmap,gs,spacing,cols,2.0*coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);

			old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 2);
			arg::value(g_map,kmap,gs,spacing,cols,-0.5*coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);
		}
		else
		{
			long int old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
			arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);

			old_val = kmap.getKeyRef().get(d);
			kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
			arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
			kmap.getKeyRef().set_d(d,old_val);
		}
	}

	/*! \brief Calculate the position where the derivative is calculated
	 *
	 * In case on non staggered case this function just return a null grid_key, in case of staggered,
	 *  it calculate how the operator shift in the cell
	 *
 	 	 \verbatim

		+--$--+
		|     |
		#  *  #
		|     |
		0--$--+

	  # = velocity(y)
	  $ = velocity(x)
	  * = pressure

		\endverbatim
	 *
	 * In the one side stencil the cell position depend if you are or not at the boundary.
	 * outside the boundary is simply the central scheme, at the boundary it is simply the
	 * staggered position of the property
	 *
	 * \param pos position where we are calculating the derivative
	 * \param gs Grid info
	 * \param s_pos staggered position of the properties
	 *
	 * \return where (in which cell grid) the derivative is calculated
	 *
	 */
	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
	{
		return arg::position(pos,gs,s_pos);
	}
};


/*! \brief First order FORWARD derivative on direction i
 *
 * \verbatim
 *
 *  -1.0    1.0
 *    +------*
 *
 * \endverbatim
 *
 */
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,FORWARD>
{
	public:

	/*! \brief Calculate which colums of the Matrix are non zero
	 *
	 * \param g_map mapping grid
	 * \param kmap position where the derivative is calculated
	 * \param gs Grid info
	 * \param spacing grid spacing
	 * \param cols non-zero colums calculated by the function
	 * \param coeff coefficent (constant in front of the derivative)
	 *
	 * ### Example
	 *
	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
	 *
	 */
	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
							 const grid_sm<Sys_eqs::dims,void> & gs,
							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
							 typename Sys_eqs::stype coeff)
	{

		long int old_val = kmap.getKeyRef().get(d);
		kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) + 1);
		arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
		kmap.getKeyRef().set_d(d,old_val);

		// backward
		arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
	}


	/*! \brief Calculate the position where the derivative is calculated
	 *
	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
	 * the FORWARD scheme return the position of the staggered property
	 *
	 * \param pos position where we are calculating the derivative
	 * \param gs Grid info
	 * \param s_pos staggered position of the properties
	 *
	 * \return where (in which cell grid) the derivative is calculated
	 *
	 */
	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
			                                          const grid_sm<Sys_eqs::dims,void> & gs,
													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
	{
		return arg::position(pos,gs,s_pos);
	}
};

/*! \brief First order BACKWARD derivative on direction i
 *
 * \verbatim
 *
 *  -1.0    1.0
 *    *------+
 *
 * \endverbatim
 *
 */
template<unsigned int d, typename arg, typename Sys_eqs>
class D<d,arg,Sys_eqs,BACKWARD>
{
	public:

	/*! \brief Calculate which colums of the Matrix are non zero
	 *
	 * \param g_map mapping grid
	 * \param kmap position where the derivative is calculated
	 * \param gs Grid info
	 * \param spacing of the grid
	 * \param cols non-zero colums calculated by the function
	 * \param coeff coefficent (constant in front of the derivative)
	 *
	 * ### Example
	 *
	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
	 *
	 */
	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
							 const grid_sm<Sys_eqs::dims,void> & gs,
							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
							 typename Sys_eqs::stype coeff)
	{

		long int old_val = kmap.getKeyRef().get(d);
		kmap.getKeyRef().set_d(d, kmap.getKeyRef().get(d) - 1);
		arg::value(g_map,kmap,gs,spacing,cols,-coeff/spacing[d]);
		kmap.getKeyRef().set_d(d,old_val);

		// forward
		arg::value(g_map,kmap,gs,spacing,cols,coeff/spacing[d]);
	}


	/*! \brief Calculate the position where the derivative is calculated
	 *
	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
	 * the BACKWARD scheme return the position of the staggered property
	 *
	 * \param pos position where we are calculating the derivative
	 * \param gs Grid info
	 * \param s_pos staggered position of the properties
	 *
	 * \return where (in which cell grid) the derivative is calculated
	 *
	 */
	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
	{
		return arg::position(pos,gs,s_pos);
	}
};

#endif /* OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_DERIVATIVE_HPP_ */