A 3D hexahedral element map for interpolation between arbitrary curved boundary quadrilateral elements according to the Linear Blending Function Method (Gordon and Hall, 1971). More...

#include <elementMaps3D.hh>

Inheritance diagram for concepts::BlendingHexahedron3d:

Public Member Functions
	BlendingHexahedron3d (const BlendingHexahedron3d &v)

	BlendingHexahedron3d (const MappingQuad3d quadmap0, const MappingQuad3d quadmap1, const MappingQuad3d quadmap2, const MappingQuad3d quadmap3, const MappingQuad3d quadmap4, const MappingQuad3d quadmap5, const Hexahedron &hex)

	BlendingHexahedron3d (const Sequence< const MappingQuad3d * > quadmap, const Hexahedron &hex)
	Constructor. More...

BlendingHexahedron3d *	clone () const override
	Returns a copy of the map. More...

MappingEdge3d *	edge (const uint edge) const

MappingQuad3d *	face (const uint face) const override
	Returns the mapping of the given face. More...

MapReal3d	hessian (uint i, const Real x, const Real y, const Real z) const override
	Returns the Hessian, the integer indicates which 3x3 submap of the 3x3xi (i=1..3) tensor is required. More...

MapReal3d	jacobian (const Real x, const Real y, const Real z) const override
	Returns the jacobian of the element map. More...

virtual Real	jacobianDeterminant (const Real x, const Real y, const Real z) const
	Returns the determinant of the Jacobian. More...

virtual MapReal3d	jacobianInverse (const Real x, const Real y, const Real z) const
	Computes the inverse of the jacobian: More...

Real3d	operator() (Real x, Real y, Real z) const override
	Returns a point in 3D mapped from the unit cube [0,1]³ onto the element in physical 3d space. More...

MappingHexahedron3d *	part (const Real3d xi0, const Real3d xi1) const override

	~BlendingHexahedron3d () override

Protected Member Functions
std::ostream &	info (std::ostream &os) const override
	Returns information in an output stream. More...

Private Member Functions
void	construct_ (const std::array< const MappingQuad3d *, 6 > &quadmap, const Hexahedron &hex)

Private Attributes
std::array< std::unique_ptr< MappingEdge3d >, 12 >	edgemap_

std::array< std::unique_ptr< MappingQuad3d >, 6 >	quadmap_

std::array< Real3d, 8 >	vtx_

Detailed Description

A 3D hexahedral element map for interpolation between arbitrary curved boundary quadrilateral elements according to the Linear Blending Function Method (Gordon and Hall, 1971).

Element parametrization:

$F_K (s,t,u) = \Pi_0 \oplus \Pi_1 \oplus \Pi_2 [F_K] (s,t,u),$

where $\Pi_0 \oplus \Pi_1 \oplus \Pi_2$ denotes a boolean operator sum of coordinate interpolation operators, e.g.

$\Pi_1 [f](s,t,u) = (1-t) f(s,0,u) + t f(s,1,u),$

See also: BlendingQuad3d for a detailed explanation

Author: , Lukas Drescher, 2014

Todo:

move invertOrientation documentation to MappingQuad3d

homogenize construction with MappingQuad3d-iterators template <typename MappingQuad3dIterator> BlendingHexahedron3d( MappingQuad3dIterator begin, MappingQuad3dIterator end, const Hexahedron& hex);

Definition at line 242 of file elementMaps3D.hh.

Constructor & Destructor Documentation

◆ BlendingHexahedron3d() [1/3]

concepts::BlendingHexahedron3d::BlendingHexahedron3d	(	const Sequence< const MappingQuad3d * >	quadmap,
		const Hexahedron &	hex
	)

Constructor.

Every element of a given sequence of boundary quadrilateral mappings is cloned and reoriented from the quadrilateral orientations in the topological hexahedron to those induced by the coordinate directions in the hexahedral reference domain. IMPORTANT: The orientation of the quadrilateral element mappings in the input sequence must be aligned with the corresponding topological quadrilaterals. That is: The topological complex must be consistent with the geometric complex.

Parameters

quadmap	boundary element mappings forming the images of $( [0,1] \times [0,1] \times \{ 0 \}, \quad [0,1] \times \{ 0 \} \times [0,1], \quad \{ 1 \} \times [0,1] \times [0,1], \quad [0,1] \times \{ 1 \} \times [0,1], \quad \{ 0 \} \times [0,1] \times [0,1], \quad [0,1] \times [0,1] \times \{ 1 \} )$ of the element mapping to be constructed consistent with the orientation flags in the parameter hex
hex	topological object corresponding to the element mapping to be constructed. Orientations in topological cell complex must be consistent with passed boundary element mappings in quadmap

◆ BlendingHexahedron3d() [2/3]

concepts::BlendingHexahedron3d::BlendingHexahedron3d	(	const MappingQuad3d *	quadmap0,
		const MappingQuad3d *	quadmap1,
		const MappingQuad3d *	quadmap2,
		const MappingQuad3d *	quadmap3,
		const MappingQuad3d *	quadmap4,
		const MappingQuad3d *	quadmap5,
		const Hexahedron &	hex
	)

◆ BlendingHexahedron3d() [3/3]

concepts::BlendingHexahedron3d::BlendingHexahedron3d ( const BlendingHexahedron3d & v )

◆ ~BlendingHexahedron3d()

concepts::BlendingHexahedron3d::~BlendingHexahedron3d ( )

override

Member Function Documentation

◆ clone()

BlendingHexahedron3d* concepts::BlendingHexahedron3d::clone ( ) const

inlineoverridevirtual

Returns a copy of the map.

Implements concepts::MappingHexahedron3d.

Definition at line 276 of file elementMaps3D.hh.

◆ construct_()

void concepts::BlendingHexahedron3d::construct_	(	const std::array< const MappingQuad3d *, 6 > &	quadmap,
		const Hexahedron &	hex
	)

private

◆ edge()

MappingEdge3d* concepts::BlendingHexahedron3d::edge ( const uint edge ) const

◆ face()

MappingQuad3d* concepts::BlendingHexahedron3d::face ( const uint face ) const

overridevirtual

Returns the mapping of the given face.

Implements concepts::MappingHexahedron3d.

◆ hessian()

MapReal3d concepts::BlendingHexahedron3d::hessian	(	uint	i,
		const Real	x,
		const Real	y,
		const Real	z
	)		const

overridevirtual

Returns the Hessian, the integer indicates which 3x3 submap of the 3x3xi (i=1..3) tensor is required.

Implements concepts::MappingHexahedron3d.

◆ info()

std::ostream& concepts::BlendingHexahedron3d::info ( std::ostream & os ) const

overrideprotectedvirtual

Returns information in an output stream.

Implements concepts::MappingHexahedron3d.

◆ jacobian()

MapReal3d concepts::BlendingHexahedron3d::jacobian	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

overridevirtual

Returns the jacobian of the element map.

$\left(\frac{\partial F_K}{\partial\vec\xi}\right) = \left\{\frac{\partial x^i}{\partial \xi_j}\right\}_{i,j=1}^3$

Implements concepts::MappingHexahedron3d.

◆ jacobianDeterminant()

virtual Real concepts::MappingHexahedron3d::jacobianDeterminant	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inlinevirtualinherited

Returns the determinant of the Jacobian.

Reimplemented in concepts::MapHexahedron3d.

Definition at line 200 of file elementMaps3D.hh.

◆ jacobianInverse()

virtual MapReal3d concepts::MappingHexahedron3d::jacobianInverse	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inlinevirtualinherited

Computes the inverse of the jacobian:

$\left(\frac{\partial F_K}{\partial\vec\xi}\right)^{-1} = \left\{\frac{\partial \xi_i}{\partial x^j}\right\}_{i,j=1}^3$

Reimplemented in concepts::MapHexahedron3d.

Definition at line 196 of file elementMaps3D.hh.

◆ operator()()

Real3d concepts::BlendingHexahedron3d::operator()	(	Real	x,
		Real	y,
		Real	z
	)		const

overridevirtual

Returns a point in 3D mapped from the unit cube [0,1]³ onto the element in physical 3d space.

Returns

Implements concepts::MappingHexahedron3d.

◆ part()

MappingHexahedron3d* concepts::BlendingHexahedron3d::part	(	const Real3d	xi0,
		const Real3d	xi1
	)		const

overridevirtual

Todo:: part supposed to be implemented for parent class

Implements concepts::MappingHexahedron3d.

Member Data Documentation

◆ edgemap_

std::array<std::unique_ptr<MappingEdge3d>,12> concepts::BlendingHexahedron3d::edgemap_

private

Definition at line 291 of file elementMaps3D.hh.

◆ quadmap_

std::array<std::unique_ptr<MappingQuad3d>,6> concepts::BlendingHexahedron3d::quadmap_

private

Definition at line 289 of file elementMaps3D.hh.

◆ vtx_

std::array<Real3d,8> concepts::BlendingHexahedron3d::vtx_

private

Definition at line 293 of file elementMaps3D.hh.

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

geometry/elementMaps3D.hh

concepts::BlendingHexahedron3d Class Reference

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BlendingHexahedron3d() [1/3]

◆ BlendingHexahedron3d() [2/3]

◆ BlendingHexahedron3d() [3/3]

◆ ~BlendingHexahedron3d()

Member Function Documentation

◆ clone()

◆ construct_()

◆ edge()

◆ face()

◆ hessian()

◆ info()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ operator()()

◆ part()

Member Data Documentation

◆ edgemap_

◆ quadmap_

◆ vtx_