ippl::HexahedralElement< T > Class Template Reference

Inheritance diagram for ippl::HexahedralElement< T >:

Collaboration diagram for ippl::HexahedralElement< T >:

Public Types
typedef Element3D< T, NumVertices >::point_t	point_t
typedef Element3D< T, NumVertices >::vertex_points_t	vertex_points_t
Public Types inherited from ippl::Element< T, Dim, NumVertices >
typedef Vector< T, Dim >	point_t
typedef Vector< point_t, NumVertices >	vertex_points_t

Public Member Functions
KOKKOS_FUNCTION vertex_points_t	getLocalVertices () const
	Returns the coordinates of the vertices of the reference element.
KOKKOS_FUNCTION point_t	getTransformationJacobian (const vertex_points_t &global_vertices) const
	Returns the Jacobian of the transformation matrix.
KOKKOS_FUNCTION point_t	getInverseTransformationJacobian (const vertex_points_t &global_vertices) const
	Returns the inverse of the Jacobian of the transformation matrix.
KOKKOS_FUNCTION point_t	globalToLocal (const vertex_points_t &global_vertices, const point_t &point) const
	Transforms a point from global to local coordinates.
KOKKOS_FUNCTION point_t	localToGlobal (const vertex_points_t &global_vertices, const point_t &point) const
	Transforms a point from local to global coordinates.
KOKKOS_FUNCTION T	getDeterminantOfTransformationJacobian (const vertex_points_t &global_vertices) const
	Returns the determinant of the transformation Jacobian.
KOKKOS_FUNCTION point_t	getInverseTransposeTransformationJacobian (const vertex_points_t &global_vertices) const
	Returns the inverse of the transpose of the transformation Jacobian.
KOKKOS_FUNCTION bool	isPointInRefElement (const Vector< T, 3 > &point) const
	Returns whether a point in local coordinates ([0, 1]^3) is inside the reference element.

Static Public Attributes
static constexpr unsigned	NumVertices = 8
Static Public Attributes inherited from ippl::Element< T, Dim, NumVertices >
static constexpr unsigned	dim = Dim
static constexpr unsigned	numVertices = NumVertices

Member Function Documentation

getDeterminantOfTransformationJacobian()

template<typename T >

KOKKOS_FUNCTION T ippl::HexahedralElement< T >::getDeterminantOfTransformationJacobian

(

const vertex_points_t &

global_vertices

)

const

Returns the determinant of the transformation Jacobian.

Parameters

global_vertices

A vector of the vertex coordinates of the global element to transform to.

Returns

T - The determinant of the transformation Jacobian

getInverseTransformationJacobian()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::point_t ippl::HexahedralElement< T >::getInverseTransformationJacobian

(

const vertex_points_t &

global_vertices

)

const

Returns the inverse of the Jacobian of the transformation matrix.

Parameters

global_vertices

A vector of the vertex coordinates of the global element to transform to.

Returns

point_t (Vector<T, 3>) - A vector representing the diagonal elements of the inverse Jacobian matrix

getInverseTransposeTransformationJacobian()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::point_t ippl::HexahedralElement< T >::getInverseTransposeTransformationJacobian

(

const vertex_points_t &

global_vertices

)

const

Returns the inverse of the transpose of the transformation Jacobian.

Parameters

global_vertices

A vector of the vertex coordinates of the global element to transform to.

Returns

point_t (Vector<T, 3>) - A vector representing the diagonal elements of the inverse transpose Jacobian matrix

getLocalVertices()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::vertex_points_t ippl::HexahedralElement< T >::getLocalVertices

(

)

const

Returns the coordinates of the vertices of the reference element.

Returns

vertex_points_t (Vector<Vector<T, 3>, 8>)

getTransformationJacobian()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::point_t ippl::HexahedralElement< T >::getTransformationJacobian

(

const vertex_points_t &

global_vertices

)

const

Returns the Jacobian of the transformation matrix.

Parameters

global_vertices

A vector of the vertex coordinates of the global element to transform to.

Returns

point_t (Vector<T, 3>) - A vector representing the diagonal elements of the Jacobian matrix

globalToLocal()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::point_t ippl::HexahedralElement< T >::globalToLocal	(	const vertex_points_t &	global_vertices,
		const point_t &	point
	)		const

Transforms a point from global to local coordinates.

Parameters

global_vertices	A vector of the vertex indices of the global element to transform to in the mesh.
point	A point in global coordinates with respect to the global element.

Returns

point_t

isPointInRefElement()

template<typename T >

KOKKOS_FUNCTION bool ippl::HexahedralElement< T >::isPointInRefElement

(

const Vector< T, 3 > &

point

)

const

Returns whether a point in local coordinates ([0, 1]^3) is inside the reference element.

Parameters

point

A point in local coordinates with respect to the reference element.

Returns

boolean - Returns true when the point is inside the reference element or on the boundary. Returns false else

localToGlobal()

template<typename T >

KOKKOS_FUNCTION HexahedralElement< T >::point_t ippl::HexahedralElement< T >::localToGlobal	(	const vertex_points_t &	global_vertices,
		const point_t &	point
	)		const

Transforms a point from local to global coordinates.

Parameters

global_vertices	A vector of the vertex indices of the global element to transform to in the mesh.
point	A point in local coordinates with respect to the reference element.

Equivalent to transforming a local point \(\hat{\boldsymbol{x}}\) on the local element \(\hat{K}\) to a point in the global coordinate system \(\boldsymbol{x}\) on \(K\) by applying the transformation \(\mathbf{\Phi}_K\)

\[\boldsymbol{x} = \mathbf{\Phi}_K(\hat{\boldsymbol{x}})\]

Returns

point_t

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

• ippl-src/src/FEM/Elements/HexahedralElement.h
• ippl-src/src/FEM/Elements/HexahedralElement.hpp