CartesianToCircular< X, Y, R, Theta > Class Template Reference

A class for describing the circular 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< X, Y >
	The type of the argument of the function described by this mapping.
using	CoordResult = ddc::Coordinate< R, Theta >
	The type of the result of the function described by this mapping.

Public Member Functions
KOKKOS_FUNCTION	CartesianToCircular (CartesianToCircular const &other)
	Instantiate a CartesianToCircular from another CartesianToCircular (lvalue).
	CartesianToCircular (CartesianToCircular &&x)=default
	Instantiate a Curvilinear2DToCartesian from another temporary CartesianToCircular (rvalue).
CartesianToCircular &	operator= (CartesianToCircular const &x)=default
	Assign a CartesianToCircular from another CartesianToCircular (lvalue).
CartesianToCircular &	operator= (CartesianToCircular &&x)=default
	Assign a CartesianToCircular from another temporary CartesianToCircular (rvalue).
KOKKOS_FUNCTION ddc::Coordinate< R, Theta >	operator() (ddc::Coordinate< X, Y > const &coord) const
	Convert the coordinate (x,y) to the equivalent \( (r, \theta) \) coordinate.
KOKKOS_FUNCTION double	jacobian (ddc::Coordinate< X, Y > const &coord)
	Compute the Jacobian, the determinant of the Jacobian matrix of the mapping.
KOKKOS_FUNCTION void	jacobian_matrix (ddc::Coordinate< X, Y > const &coord, Matrix_2x2 &matrix)
	Compute full Jacobian matrix.
KOKKOS_FUNCTION double	jacobian_11 (ddc::Coordinate< X, Y > const &coord)
	Compute the (1,1) coefficient of the Jacobian matrix.
KOKKOS_FUNCTION double	jacobian_12 (ddc::Coordinate< X, Y > const &coord)
	Compute the (1,2) coefficient of the Jacobian matrix.
KOKKOS_FUNCTION double	jacobian_21 (ddc::Coordinate< X, Y > const &coord)
	Compute the (2,1) coefficient of the Jacobian matrix.
KOKKOS_FUNCTION double	jacobian_22 (ddc::Coordinate< X, Y > const &coord)
	Compute the (2,2) coefficient of the Jacobian matrix.
CircularToCartesian< R, Theta, X, Y >	get_inverse_mapping () const
	Get the inverse mapping.

Detailed Description

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

A class for describing the circular 2D mapping.

The mapping \( (x,y)\mapsto (r,\theta) \) is defined as follow :

\( r(x,y) = \sqrt x^2+y^2 ,\)

\( \theta(x,y) = atan2(\frac{y}{x}) .\)

It and its Jacobian matrix are invertible everywhere except for \( r = 0 \).

The Jacobian matrix coefficients are defined as follow

\( J_{11}(r,\theta) =\frac{2x}{\sqrt{x^2+y^2}} \)

\( J_{12}(r,\theta) =\frac{2y}{\sqrt{x^2+y^2}} \)

\( J_{21}(r,\theta) =\frac{-y}{(x^2+y^2)^2} \)

\( J_{22}(r,\theta) =\frac{x}{(x^2+y^2)^2} \)

and the matrix determinant: \( det(J) = r \).

Constructor & Destructor Documentation

CartesianToCircular() [1/2]

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

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

inline

Instantiate a CartesianToCircular from another CartesianToCircular (lvalue).

Parameters

[in]

other

CartesianToCircular mapping used to instantiate the new one.

CartesianToCircular() [2/2]

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

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

default

Instantiate a Curvilinear2DToCartesian from another temporary CartesianToCircular (rvalue).

Parameters

[in]

x

Curvilinear2DToCartesian mapping used to instantiate the new one.

Member Function Documentation

operator=() [1/2]

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

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

default

Assign a CartesianToCircular from another CartesianToCircular (lvalue).

Parameters

[in]

x

CartesianToCircular mapping used to assign.

Returns

The CartesianToCircular assigned.

operator=() [2/2]

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

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

default

Assign a CartesianToCircular from another temporary CartesianToCircular (rvalue).

Parameters

[in]

x

CartesianToCircular mapping used to assign.

Returns

The CartesianToCircular assigned.

operator()()

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

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

inline

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

Parameters

[in]

coord

The coordinate to be converted.

Returns

The equivalent coordinate.

jacobian()

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

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

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 X , class Y , class R , class Theta >

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

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 X , class Y , class R , class Theta >

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

inline

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

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

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 X , class Y , class R , class Theta >

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

inline

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

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

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 X , class Y , class R , class Theta >

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

inline

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

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

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 X , class Y , class R , class Theta >

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

inline

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

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

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.

get_inverse_mapping()

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

CircularToCartesian< R, Theta, X, Y > CartesianToCircular< X, Y, R, Theta >::get_inverse_mapping ( ) const

inline

Get the inverse mapping.

Returns

The inverse mapping.

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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_circular.hpp