#include <elementMaps3D.hh>

Inheritance diagram for concepts::MapHexahedron3d:

Public Member Functions
	MapHexahedron3d (char *map, Real scX, Real scY, Real scZ)

	MapHexahedron3d (const Real3d &vtx0, const Real3d &vtx1, const Real3d &vtx2, const Real3d &vtx3, const Real3d &vtx4, const Real3d &vtx5, const Real3d &vtx6, const Real3d &vtx7)

	MapHexahedron3d (const MapHexahedron3d &map)
	Copy constructor.

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

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

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

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

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

MapHexahedron3d *	clone () const
	Returns a copy of the map.

MappingQuad3d *	face (uint face) const

MapHexahedron3d *	part (const Real3d x0, const Real3d z0) const

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

Detailed Description

A 3D element map for a hexahedron. The reference element is the unit cube.

There are two ways to fix the map of the hexahedron: give the mapping explicitly or give the eight corners and the map is computed internally.

When giving the eight corners of the hexahedron, they must be given in the correct order, ie. first the corners of the floor (in right screwed orientation pointing into the hexahedron) and then the corners of the ceiling (in right screwed orientation pointing out of the hexahedron).

The application operator maps a point from the unit square onto the physical domain taking into account the parameter domain given in the constructor.

Examples: meshes.cc.

Definition at line 366 of file elementMaps3D.hh.

Constructor & Destructor Documentation

◆ MapHexahedron3d() [1/2]

concepts::MapHexahedron3d::MapHexahedron3d	(	char *	map,
		Real	scX,
		Real	scY,
		Real	scZ
	)

Constructor. The values of scX, scY and scZ are only for the map, they are not needed by the user for mapping a point from the reference element onto the Real element.

Parameters

map	The element map for this hexahedron as a string, x, y and z are the allowed variables, the component are separated by a comma.
scX	The range of x is [0, scX].
scY	The range of y is [0, scY].
scZ	The range of z is [0, scZ].

◆ MapHexahedron3d() [2/2]

concepts::MapHexahedron3d::MapHexahedron3d	(	const Real3d &	vtx0,
		const Real3d &	vtx1,
		const Real3d &	vtx2,
		const Real3d &	vtx3,
		const Real3d &	vtx4,
		const Real3d &	vtx5,
		const Real3d &	vtx6,
		const Real3d &	vtx7
	)

Constructor. Takes the eight physical corners of the hexahedron and computes the element map: $F_K : S \rightarrow K$ with $\vec x = F_K(\xi) = B \cdot \vec \xi + \vec b$ , where $\vec b = \mbox{vtx0}$ and $B = [ (\mbox{vtx1} - \vec b) (\mbox{vtx2} - \vec b) (\mbox{vtx3} - \vec b) ]$ .