A class describing a mapping from a Cartesian domain to a pseudo-Cartesian. More...

Public Types
using	CartesianCoordinate = ddc::Coordinate< typename MappingToCartesian::cartesian_tag_x, typename MappingToCartesian::cartesian_tag_y >
	The type of a coordinate in the Cartesian geometry.

using	cartesian_tag_x = typename MappingToCartesian::cartesian_tag_x
	The X dimension in the Cartesian geometry.

using	cartesian_tag_y = typename MappingToCartesian::cartesian_tag_y
	The Y dimension in the Cartesian geometry.

using	pseudo_cartesian_tag_x = typename MappingToPseudoCartesian::cartesian_tag_x
	The X dimension in the pseudo-Cartesian geometry.

using	pseudo_cartesian_tag_y = typename MappingToPseudoCartesian::cartesian_tag_y
	The Y dimension in the pseudo-Cartesian geometry.

using	CoordArg = ddc::Coordinate< cartesian_tag_x, cartesian_tag_y >
	The type of the argument of the function described by this mapping.

using	CoordResult = ddc::Coordinate< pseudo_cartesian_tag_x, pseudo_cartesian_tag_y >
	The type of the result of the function described by this mapping.

Public Member Functions
	CartesianToPseudoCartesian (MappingToPseudoCartesian mapping_to_pseudo_cartesian, MappingToCartesian mapping_to_cartesian, double epsilon)
	Construct an instance of the class. More...

KOKKOS_FUNCTION void	jacobian_matrix (CoordRTheta const &coord_rtheta, Matrix_2x2 &J) const
	Compute the full Jacobian matrix. More...

KOKKOS_FUNCTION double	jacobian (CoordRTheta const &coord_rtheta) const
	Compute the determinant of the Jacobian matrix. More...

KOKKOS_FUNCTION double	jacobian_11 (CoordRTheta const &coord_rtheta) const
	Compute the (1,1) coefficient of the Jacobian matrix. More...

KOKKOS_FUNCTION double	jacobian_12 (CoordRTheta const &coord_rtheta) const
	Compute the (1,2) coefficient of the Jacobian matrix. More...

KOKKOS_FUNCTION double	jacobian_21 (CoordRTheta const &coord_rtheta) const
	Compute the (2,1) coefficient of the Jacobian matrix. More...

KOKKOS_FUNCTION double	jacobian_22 (CoordRTheta const &coord_rtheta) const
	Compute the (2,2) coefficient of the Jacobian matrix. More...

KOKKOS_FUNCTION void	inv_jacobian_matrix (CoordRTheta const &coord_rtheta, Matrix_2x2 &J) const
	Compute the full inverse of the Jacobian matrix. More...

KOKKOS_FUNCTION double	inv_jacobian_11 (CoordRTheta const &coord_rtheta) const
	Compute the (1,1) coefficient of the inverse of the Jacobian matrix. More...

KOKKOS_FUNCTION double	inv_jacobian_12 (CoordRTheta const &coord_rtheta) const
	Compute the (1,2) coefficient of the inverse of the Jacobian matrix. More...

KOKKOS_FUNCTION double	inv_jacobian_21 (CoordRTheta const &coord_rtheta) const
	Compute the (2,1) coefficient of the inverse of the Jacobian matrix. More...

KOKKOS_FUNCTION double	inv_jacobian_22 (CoordRTheta const &coord_rtheta) const
	Compute the (2,2) coefficient of the inverse of the Jacobian matrix. More...

Detailed Description

template<class MappingToCartesian, class MappingToPseudoCartesian>
class CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >

A class describing a mapping from a Cartesian domain to a pseudo-Cartesian.

This operation is carried out using 2 curvilinear to Cartesian mappings. The Cartesian to pseudo-Cartesian mapping is obtained by combining these 2 mappings.

Constructor & Destructor Documentation

◆ CartesianToPseudoCartesian()

template<class MappingToCartesian , class MappingToPseudoCartesian >

CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::CartesianToPseudoCartesian	(	MappingToPseudoCartesian	mapping_to_pseudo_cartesian,
		MappingToCartesian	mapping_to_cartesian,
		double	epsilon
	)

inline

Construct an instance of the class.

Parameters

[in]	mapping_to_cartesian	A curvilinear to Cartesian mapping.
[in]	mapping_to_pseudo_cartesian	A curvilinear to Cartesian mapping where the role of the Cartesian geometry is fulfilled by the pseudo-Cartesian geometry.
[in]	epsilon	The parameter \( \varepsilon \) which determines when a point is close enough to the central O-point for linearization to be required when calculating the Jacobian.

Member Function Documentation

◆ jacobian_matrix()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION void CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian_matrix	(	CoordRTheta const &	coord_rtheta,
		Matrix_2x2 &	J
	)		const

inline

Compute the full Jacobian matrix.

This is calculated by combining the Jacobian matrices of the 2 curvilinear mappings. If a point is within \( \varepsilon \) of the O-point then a linearisation is carried out between the Jacobian matrix at \( \varepsilon \) and the matrix at the O-point.

\( J_{(x,y)->(x_pC, y_pC)} = J_{(r, \theta)->(x_pC,y_pC)}J_{(x, y)->(r, \theta)} \) \( = J_{(r, \theta)->(x_pC,y_pC)} [J_{(r, \theta)->(x, y)}]^{-1} \)

Parameters

[in]	coord_rtheta	The coordinate where we evaluate the Jacobian matrix.
[out]	J	The Jacobian matrix returned.

◆ jacobian()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian ( CoordRTheta const & coord_rtheta ) const

inline

Compute the determinant of the Jacobian matrix.

See also: jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the Jacobian matrix.

Returns: The determinant of the Jacobian matrix.

◆ jacobian_11()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian_11 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (1,1) coefficient of the Jacobian matrix.

See also: jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the Jacobian matrix.

Returns: The (1,1) coefficient of the Jacobian matrix.

◆ jacobian_12()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian_12 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (1,2) coefficient of the Jacobian matrix.

See also: jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the Jacobian matrix.

Returns: The (1,2) coefficient of the Jacobian matrix.

◆ jacobian_21()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian_21 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (2,1) coefficient of the Jacobian matrix.

See also: jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the Jacobian matrix.

Returns: The (2,1) coefficient of the Jacobian matrix.

◆ jacobian_22()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::jacobian_22 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (2,2) coefficient of the Jacobian matrix.

See also: jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the Jacobian matrix.

Returns: The (2,2) coefficient of the Jacobian matrix.

◆ inv_jacobian_matrix()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION void CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::inv_jacobian_matrix	(	CoordRTheta const &	coord_rtheta,
		Matrix_2x2 &	J
	)		const

inline

Compute the full inverse of the Jacobian matrix.

This is calculated by combining the Jacobian matrices of the 2 curvilinear mappings. If a point is within \( \varepsilon \) of the O-point then a linearisation is carried out between the Jacobian matrix at \( \varepsilon \) and the matrix at the O-point.

\( [J_{(x,y)->(x_pC, y_pC)}]^{-1} = [J_{(r, \theta)->(x_pC, y_pC)} J_{(x, y)->(r, \theta)}]^{-1} \) \( = [J_{(r, \theta)->(x_pC, y_pC)} [J_{(x, y)->(r, \theta)}]^{-1}]^{-1} \) \( = J_{(x, y)->(r, \theta)} [J_{(r, \theta)->(x_pC, y_pC)}]^{-1} \)

Parameters

[in]	coord_rtheta	The coordinate where we evaluate the Jacobian matrix.
[out]	J	The Jacobian matrix returned.

◆ inv_jacobian_11()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::inv_jacobian_11 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (1,1) coefficient of the inverse of the Jacobian matrix.

See also: inv_jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the inverse of the Jacobian matrix.

Returns: The (1,1) coefficient of the inverse of the Jacobian matrix.

◆ inv_jacobian_12()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::inv_jacobian_12 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (1,2) coefficient of the inverse of the Jacobian matrix.

See also: inv_jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the inverse of the Jacobian matrix.

Returns: The (1,2) coefficient of the inverse of the Jacobian matrix.

◆ inv_jacobian_21()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::inv_jacobian_21 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (2,1) coefficient of the inverse of the Jacobian matrix.

See also: inv_jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the inverse of the Jacobian matrix.

Returns: The (2,1) coefficient of the inverse of the Jacobian matrix.

◆ inv_jacobian_22()

template<class MappingToCartesian , class MappingToPseudoCartesian >

KOKKOS_FUNCTION double CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >::inv_jacobian_22 ( CoordRTheta const & coord_rtheta ) const

inline

Compute the (2,2) coefficient of the inverse of the Jacobian matrix.

See also: inv_jacobian_matrix

Parameters

[in] coord_rtheta The coordinate where we evaluate the inverse of the Jacobian matrix.

Returns: The (2,2) coefficient of the inverse of the Jacobian matrix.

The documentation for this class was generated from the following file:

/home/runner/work/gyselalibxx/gyselalibxx/code_branch/vendor/sll/include/sll/mapping/cartesian_to_pseudo_cartesian.hpp

Public Types

Public Member Functions

Detailed Description

template<class MappingToCartesian, class MappingToPseudoCartesian> class CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >

Constructor & Destructor Documentation

◆ CartesianToPseudoCartesian()

Member Function Documentation

◆ jacobian_matrix()

◆ jacobian()

◆ jacobian_11()

◆ jacobian_12()

◆ jacobian_21()

◆ jacobian_22()

◆ inv_jacobian_matrix()

◆ inv_jacobian_11()

◆ inv_jacobian_12()

◆ inv_jacobian_21()

◆ inv_jacobian_22()

template<class MappingToCartesian, class MappingToPseudoCartesian>
class CartesianToPseudoCartesian< MappingToCartesian, MappingToPseudoCartesian >