A 3D element map for a hexahedron. More...

#include <elementMaps3D.hh>

Inheritance diagram for concepts::MapHexahedron3d:

Public Member Functions
MapHexahedron3d *	clone () const
	Returns a copy of the map. More...

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

MapReal3d	hessian (uint i, const Real x, const Real y, const Real z) const
	Returns the hessian of the element map. More...

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

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

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

	MapHexahedron3d (char *map, Real scX, Real scY, Real scZ)
	Constructor. More...

	MapHexahedron3d (const MapHexahedron3d &map)
	Copy constructor. More...

	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. More...

Real3d	operator() (Real x, Real y, Real z) const
	Returns a point in 3D mapped from the unit cube onto the element in the original mesh. More...

MapHexahedron3d *	part (const Real3d x0, const Real3d z0) const
	Returns a part of the mapping. More...

	~MapHexahedron3d ()

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

Private Member Functions
void	operator= (const MapHexahedron3d &)
	Private assignement operator. More...

Private Attributes
Real3d *	comp_
	Computed map. More...

uchar *	map_
	Parsed formula for the map. More...

Real	scx_
	Right border of the x parameter domain. More...

Real	scy_
	Right border of the y parameter domain. More...

Real	scz_
	Right border of the z parameter domain. More...

uint	sz_
	Length of the parsed formula. More...

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() [1/3]

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() [2/3]

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 $B = [ (\mbox{vtx1} - \vec b) (\mbox{vtx2} - \vec b) (\mbox{vtx3} - \vec b) ]$ .

◆ MapHexahedron3d() [3/3]

concepts::MapHexahedron3d::MapHexahedron3d ( const MapHexahedron3d & map )

Copy constructor.

◆ ~MapHexahedron3d()

concepts::MapHexahedron3d::~MapHexahedron3d ( )

inline

Definition at line 416 of file elementMaps3D.hh.

Member Function Documentation

◆ clone()

MapHexahedron3d* concepts::MapHexahedron3d::clone ( ) const

inlinevirtual

Returns a copy of the map.

Implements concepts::MappingHexahedron3d.

Definition at line 472 of file elementMaps3D.hh.

◆ face()

MappingQuad3d* concepts::MapHexahedron3d::face ( uint face ) const

virtual

Returns the mapping of the given face.

Implements concepts::MappingHexahedron3d.

◆ hessian()

MapReal3d concepts::MapHexahedron3d::hessian	(	uint	i,
		const Real	x,
		const Real	y,
		const Real	z
	)		const

virtual

Returns the hessian of the element map.

Implements concepts::MappingHexahedron3d.

◆ info()

virtual std::ostream& concepts::MapHexahedron3d::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Implements concepts::MappingHexahedron3d.

◆ jacobian()

MapReal3d concepts::MapHexahedron3d::jacobian	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

virtual

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()

Real concepts::MapHexahedron3d::jacobianDeterminant	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inlinevirtual

Returns the determinant of the Jacobian.

Reimplemented from concepts::MappingHexahedron3d.

Definition at line 467 of file elementMaps3D.hh.

◆ jacobianInverse()

MapReal3d concepts::MapHexahedron3d::jacobianInverse	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inlinevirtual

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 from concepts::MappingHexahedron3d.

Definition at line 462 of file elementMaps3D.hh.

◆ operator()()

Real3d concepts::MapHexahedron3d::operator()	(	Real	x,
		Real	y,
		Real	z
	)		const

inlinevirtual

Returns a point in 3D mapped from the unit cube onto the element in the original mesh.

Returns

Parameters

x	$\in [0, 1]$
y	$\in [0, 1]$
z	$\in [0, 1]$

Implements concepts::MappingHexahedron3d.

Definition at line 426 of file elementMaps3D.hh.

◆ operator=()

void concepts::MapHexahedron3d::operator= ( const MapHexahedron3d & )

private

Private assignement operator.

◆ part()

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

virtual

Returns a part of the mapping.

Implements concepts::MappingHexahedron3d.

Member Data Documentation

◆ comp_

Real3d* concepts::MapHexahedron3d::comp_

private

Computed map.

Definition at line 384 of file elementMaps3D.hh.

◆ map_

uchar* concepts::MapHexahedron3d::map_

private

Parsed formula for the map.

Definition at line 369 of file elementMaps3D.hh.

◆ scx_

Real concepts::MapHexahedron3d::scx_

private

Right border of the x parameter domain.

Definition at line 375 of file elementMaps3D.hh.

◆ scy_

Real concepts::MapHexahedron3d::scy_

private

Right border of the y parameter domain.

Definition at line 378 of file elementMaps3D.hh.

◆ scz_

Real concepts::MapHexahedron3d::scz_

private

Right border of the z parameter domain.

Definition at line 381 of file elementMaps3D.hh.

◆ sz_

uint concepts::MapHexahedron3d::sz_

private

Length of the parsed formula.

Definition at line 372 of file elementMaps3D.hh.

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

geometry/elementMaps3D.hh

concepts::MapHexahedron3d Class Reference

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MapHexahedron3d() [1/3]

◆ MapHexahedron3d() [2/3]

◆ MapHexahedron3d() [3/3]

◆ ~MapHexahedron3d()

Member Function Documentation

◆ clone()

◆ face()

◆ hessian()

◆ info()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ operator()()

◆ operator=()

◆ part()

Member Data Documentation

◆ comp_

◆ map_

◆ scx_

◆ scy_

◆ scz_

◆ sz_