A class for describing the Czarny 2D mapping. More...

Public Types
using	cartesian_tag_x = X
	Indicate the first physical coordinate.

using	cartesian_tag_y = Y
	Indicate the second physical coordinate.

using	curvilinear_tag_r = R
	Indicate the first logical coordinate.

using	curvilinear_tag_theta = Theta
	Indicate the second logical coordinate.

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

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

Public Member Functions
	CzarnyToCartesian (double epsilon, double e)
	Instantiate a CzarnyToCartesian from parameters.

KOKKOS_FUNCTION	CzarnyToCartesian (CzarnyToCartesian const &other)
	Instantiate a CzarnyToCartesian from another CzarnyToCartesian (lvalue).

	CzarnyToCartesian (CzarnyToCartesian &&x)=default
	Instantiate a CzarnyToCartesian from another temporary CzarnyToCartesian (rvalue).

CzarnyToCartesian &	operator= (CzarnyToCartesian const &x)=default
	Assign a CzarnyToCartesian from another CzarnyToCartesian (lvalue).

CzarnyToCartesian &	operator= (CzarnyToCartesian &&x)=default
	Assign a CzarnyToCartesian from another temporary CzarnyToCartesian (rvalue).

KOKKOS_FUNCTION double	epsilon () const
	Return the \( \epsilon \) parameter.

KOKKOS_FUNCTION double	e () const
	Return the \( e \) parameter.

KOKKOS_FUNCTION ddc::Coordinate< X, Y >	operator() (ddc::Coordinate< R, Theta > const &coord) const
	Convert the \( (r, \theta) \) coordinate to the equivalent (x,y) coordinate.

KOKKOS_FUNCTION double	jacobian (ddc::Coordinate< R, Theta > const &coord) const
	Compute the Jacobian, the determinant of the Jacobian matrix of the mapping.

KOKKOS_FUNCTION void	jacobian_matrix (ddc::Coordinate< R, Theta > const &coord, Matrix_2x2 &matrix) const
	Compute full Jacobian matrix.

KOKKOS_FUNCTION double	jacobian_11 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (1,1) coefficient of the Jacobian matrix.

KOKKOS_FUNCTION double	jacobian_12 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (1,2) coefficient of the Jacobian matrix.

KOKKOS_FUNCTION double	jacobian_21 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (2,1) coefficient of the Jacobian matrix.

KOKKOS_FUNCTION double	jacobian_22 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (2,2) coefficient of the Jacobian matrix.

KOKKOS_FUNCTION void	inv_jacobian_matrix (ddc::Coordinate< R, Theta > const &coord, Matrix_2x2 &matrix) const
	Compute full inverse Jacobian matrix.

KOKKOS_FUNCTION double	inv_jacobian_11 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (1,1) coefficient of the inverse Jacobian matrix.

KOKKOS_FUNCTION double	inv_jacobian_12 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (1,2) coefficient of the inverse Jacobian matrix.

KOKKOS_FUNCTION double	inv_jacobian_21 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (2,1) coefficient of the inverse Jacobian matrix.

KOKKOS_FUNCTION double	inv_jacobian_22 (ddc::Coordinate< R, Theta > const &coord) const
	Compute the (2,2) coefficient of the inverse Jacobian matrix.

CartesianToCzarny< X, Y, R, Theta >	get_inverse_mapping () const
	Get the inverse mapping.

Detailed Description

template<class R, class Theta, class X, class Y>
class CzarnyToCartesian< R, Theta, X, Y >

A class for describing the Czarny 2D mapping.

The mapping \( (r,\theta)\mapsto (x,y) \) is defined by

\( x(r,\theta) = \frac{1}{\epsilon} \left( 1 - \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} \right),\)

\( y(r,\theta) = \frac{e\xi r \sin(\theta)}{2 -\sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} },\)

with \( \xi = 1/\sqrt{1 - \epsilon^2 /4} \) and \( e \) and \( \epsilon \) given as parameters. It and its Jacobian matrix are invertible everywhere except for \( r = 0 \).

Its Jacobian coefficients are defined as follow

\( J_{11}(r,\theta) = - \cos(\theta)\frac{1}{ \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} } \)

\( J_{12}(r,\theta) = r\sin(\theta)\frac{1}{ \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} } \)

\( J_{21}(r,\theta) = \cos(\theta)\frac{e\epsilon \xi r\sin(\theta)}{ \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} \left( 2 - \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} \right)^2 } + \sin(\theta)\frac{e\xi }{ 2- \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} }\)

\( J_{22}(r,\theta) = r \sin(\theta)\frac{- e\epsilon \xi r \sin(\theta)}{ \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} \left( 2 - \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} \right)^2 } + r\cos(\theta)\frac{e\xi }{ 2 -\sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))} }\).

and \( \det(J(r, \theta)) = \frac{- r}{ \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))}} \frac{e\xi}{2 - \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta))}}. \)

Constructor & Destructor Documentation

◆ CzarnyToCartesian() [1/3]

template<class R , class Theta , class X , class Y >

CzarnyToCartesian< R, Theta, X, Y >::CzarnyToCartesian	(	double	epsilon,
		double	e
	)

inline

Instantiate a CzarnyToCartesian from parameters.

Parameters

[in]	epsilon	The \( \epsilon \) parameter in the definition of the mapping CzarnyToCartesian.
[in]	e	The \( e \) parameter in the definition of the mapping CzarnyToCartesian.

See also: CzarnyToCartesian

◆ CzarnyToCartesian() [2/3]

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION CzarnyToCartesian< R, Theta, X, Y >::CzarnyToCartesian ( CzarnyToCartesian< R, Theta, X, Y > const & other )

inline

Instantiate a CzarnyToCartesian from another CzarnyToCartesian (lvalue).

Parameters

[in] other CzarnyToCartesian mapping used to instantiate the new one.

◆ CzarnyToCartesian() [3/3]

template<class R , class Theta , class X , class Y >

CzarnyToCartesian< R, Theta, X, Y >::CzarnyToCartesian ( CzarnyToCartesian< R, Theta, X, Y > && x )

default

Instantiate a CzarnyToCartesian from another temporary CzarnyToCartesian (rvalue).

Parameters

[in] x CzarnyToCartesian mapping used to instantiate the new one.

Member Function Documentation

◆ operator=() [1/2]

template<class R , class Theta , class X , class Y >

CzarnyToCartesian & CzarnyToCartesian< R, Theta, X, Y >::operator= ( CzarnyToCartesian< R, Theta, X, Y > const & x )

default

Assign a CzarnyToCartesian from another CzarnyToCartesian (lvalue).

Parameters

[in] x CzarnyToCartesian mapping used to assign.

Returns: The CzarnyToCartesian assigned.

◆ operator=() [2/2]

template<class R , class Theta , class X , class Y >

CzarnyToCartesian & CzarnyToCartesian< R, Theta, X, Y >::operator= ( CzarnyToCartesian< R, Theta, X, Y > && x )

default

Assign a CzarnyToCartesian from another temporary CzarnyToCartesian (rvalue).

Parameters

[in] x CzarnyToCartesian mapping used to assign.

Returns: The CzarnyToCartesian assigned.

◆ epsilon()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::epsilon ( ) const

inline

Return the \( \epsilon \) parameter.

Returns: The value of \( \epsilon \).

See also: CzarnyToCartesian

◆ e()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::e ( ) const

inline

Return the \( e \) parameter.

Returns: The value of \( e \).

See also: CzarnyToCartesian

◆ operator()()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION ddc::Coordinate< X, Y > CzarnyToCartesian< R, Theta, X, Y >::operator() ( ddc::Coordinate< R, Theta > const & coord ) const

inline

Convert the \( (r, \theta) \) coordinate to the equivalent (x,y) coordinate.

Parameters

[in] coord The coordinate to be converted.

Returns: The equivalent coordinate.

◆ jacobian()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::jacobian ( ddc::Coordinate< R, Theta > const & coord ) const

inline

Compute the Jacobian, the determinant of the Jacobian matrix of the mapping.

Parameters

[in] coord The coordinate where we evaluate the Jacobian.

Returns: A double with the value of the determinant of the Jacobian matrix.

◆ jacobian_matrix()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION void CzarnyToCartesian< R, Theta, X, Y >::jacobian_matrix	(	ddc::Coordinate< R, Theta > const &	coord,
		Matrix_2x2 &	matrix
	)		const

inline

Compute full Jacobian matrix.

For some computations, we need the complete Jacobian matrix or just the coefficients. The coefficients can be given independently with the functions jacobian_11, jacobian_12, jacobian_21 and jacobian_22.

Parameters

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

See also: Jacobian::jacobian_11; Jacobian::jacobian_12; Jacobian::jacobian_21; Jacobian::jacobian_22

◆ jacobian_11()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::jacobian_11 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

For a mapping given by \( \mathcal{F} : (r,\theta)\mapsto (x,y) \), the (1,1) coefficient of the Jacobian matrix is given by \( \frac{\partial x}{\partial r} \).

Parameters

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

Returns: A double with the value of the (1,1) coefficient of the Jacobian matrix.

◆ jacobian_12()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::jacobian_12 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

For a mapping given by \( \mathcal{F} : (r,\theta)\mapsto (x,y) \), the (1,2) coefficient of the Jacobian matrix is given by \( \frac{\partial x}{\partial \theta} \).

Parameters

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

Returns: A double with the value of the (1,2) coefficient of the Jacobian matrix.

◆ jacobian_21()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::jacobian_21 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

For a mapping given by \( \mathcal{F} : (r,\theta)\mapsto (x,y) \), the (2,1) coefficient of the Jacobian matrix is given by \( \frac{\partial y}{\partial r} \).

Parameters

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

Returns: A double with the value of the (2,1) coefficient of the Jacobian matrix.

◆ jacobian_22()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::jacobian_22 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

For a mapping given by \( \mathcal{F} : (r,\theta)\mapsto (x,y) \), the (2,2) coefficient of the Jacobian matrix is given by \( \frac{\partial y}{\partial \theta} \).

Parameters

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

Returns: A double with the value of the (2,2) coefficient of the Jacobian matrix.

◆ inv_jacobian_matrix()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION void CzarnyToCartesian< R, Theta, X, Y >::inv_jacobian_matrix	(	ddc::Coordinate< R, Theta > const &	coord,
		Matrix_2x2 &	matrix
	)		const

inline

Compute full inverse Jacobian matrix.

For some computations, we need the complete inverse Jacobian matrix or just the coefficients. The coefficients can be given independently with the functions inv_jacobian_11, inv_jacobian_12, inv_jacobian_21 and inv_jacobian_22.

Parameters

[in]	coord	The coordinate where we evaluate the Jacobian matrix.
[out]	matrix	The inverse Jacobian matrix returned.

See also: Jacobian::inv_jacobian_11; Jacobian::inv_jacobian_12; Jacobian::inv_jacobian_21; Jacobian::inv_jacobian_22

◆ inv_jacobian_11()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::inv_jacobian_11 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

Be careful because not all mappings are invertible, especially at the center point.

Parameters

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

Returns: A double with the value of the (1,1) coefficient of the inverse Jacobian matrix.

◆ inv_jacobian_12()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::inv_jacobian_12 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

Be careful because not all mappings are invertible, especially at the center point.

Parameters

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

Returns: A double with the value of the (1,2) coefficient of the inverse Jacobian matrix.

◆ inv_jacobian_21()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::inv_jacobian_21 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

Be careful because not all mappings are invertible, especially at the center point.

Parameters

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

Returns: A double with the value of the (2,1) coefficient of the inverse Jacobian matrix.

◆ inv_jacobian_22()

template<class R , class Theta , class X , class Y >

KOKKOS_FUNCTION double CzarnyToCartesian< R, Theta, X, Y >::inv_jacobian_22 ( ddc::Coordinate< R, Theta > const & coord ) const

inline

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

Be careful because not all mappings are invertible, especially at the center point.

Parameters

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

Returns: A double with the value of the (2,2) coefficient of the inverse Jacobian matrix.

◆ get_inverse_mapping()

template<class R , class Theta , class X , class Y >

CartesianToCzarny< X, Y, R, Theta > CzarnyToCartesian< R, Theta, X, Y >::get_inverse_mapping ( ) const

inline

Get the inverse mapping.

Returns: The inverse mapping.

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

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

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ CzarnyToCartesian() [1/3]

◆ CzarnyToCartesian() [2/3]

◆ CzarnyToCartesian() [3/3]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ epsilon()

◆ e()

◆ operator()()

◆ jacobian()

◆ jacobian_matrix()

◆ jacobian_11()

◆ jacobian_12()

◆ jacobian_21()

◆ jacobian_22()

◆ inv_jacobian_matrix()

◆ inv_jacobian_11()

◆ inv_jacobian_12()

◆ inv_jacobian_21()

◆ inv_jacobian_22()

◆ get_inverse_mapping()