#include <elementMaps3D.hh>

Inheritance diagram for concepts::BlendingHexahedron3d:

Public Member Functions
	BlendingHexahedron3d (const Sequence< const MappingQuad3d * > quadmap, const Hexahedron &hex)

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

	BlendingHexahedron3d (const BlendingHexahedron3d &v)

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

Real3d	operator() (Real x, Real y, Real z) const override

MapReal3d	jacobian (const Real x, const Real y, const Real z) const override

MapReal3d	hessian (uint i, const Real x, const Real y, const Real z) const override

MappingQuad3d *	face (const uint face) const override

MappingEdge3d *	edge (const uint edge) const

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

virtual MapReal3d	jacobianInverse (const Real x, const Real y, const Real z) const

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

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

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()

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