linDG2D::TriangleP1 Class Referenceabstract

Triangular element with orthogonal linear shape functions in 2D. More...

#include <triangle.hh>

Inheritance diagram for linDG2D::TriangleP1:

Public Types
typedef Real	type

Public Member Functions
virtual const concepts::Triangle2d &	cell () const
	Returns the underlying geometrical triangle. More...
virtual const Cell &	cell () const=0
	Returns the cell on which the element is built. More...
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
virtual const concepts::ElementGraphics< Real > *	graphics () const
	Returns the element graphics object. More...
virtual Real	shapeFct (const uint i, const Real xi1, const Real xi2) const
	Computes the value of the ith shape function in the point (xi1, xi2). More...
concepts::Real2d	shapeFctGradient (const uint i) const
	Returns the gradient of the ith shape function, transformed to real world coordinates. More...
virtual Real	solution (const concepts::Vector< Real > &coeffs, const Real xi1, const Real xi2) const
	Returns the value of a mesh function within this element. More...
virtual const concepts::Triangle &	support () const
	Returns the topological triangle supporting the element. More...
virtual const concepts::TMatrixBase< Real > &	T () const
	Returns the T matrix of this element. More...
virtual const TMatrixBase< Real > &	T () const=0
	Returns the T matrix of the element. More...
	TriangleP1 (const concepts::Triangle2d &cell, uint idx[])
	Constructor. More...

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

Protected Attributes
std::unique_ptr< concepts::TMatrixBase< Real > >	T_
	T matrix of this element. More...

Private Attributes
const concepts::Triangle2d &	cell_
	Cell under this element. More...

Static Private Attributes
static std::unique_ptr< TriangleGraphics >	graphics_
	Graphics object of this element. More...

Detailed Description

Triangular element with orthogonal linear shape functions in 2D.

Author

Christoph Winkelmann, 2003

Definition at line 77 of file triangle.hh.

Member Typedef Documentation

type

typedef Real concepts::ElementWithCell< Real >::type

inherited

Definition at line 81 of file element.hh.

Constructor & Destructor Documentation

TriangleP1()

linDG2D::TriangleP1::TriangleP1 ( const concepts::Triangle2d &  cell, uint  idx[]  )

inline

Constructor.

Creates a T matrix out of idx.

See also

concepts::TIndex

Parameters

cell	Cell of the element
idx	Describes the map local / global dof

Definition at line 84 of file triangle.hh.

Member Function Documentation

cell() [1/2]

virtual const concepts::Triangle2d& linDG2D::Triangle::cell ( ) const

inlinevirtualinherited

Returns the underlying geometrical triangle.

Implements linearFEM::Element.

Definition at line 45 of file triangle.hh.

cell() [2/2]

virtual const Cell& concepts::ElementWithCell< Real >::cell ( ) const

pure virtualinherited

Returns the cell on which the element is built.

Implemented in hp3D::Element< Real >, hp2D::Element< Real >, and hp1D::BaseElement< Real >.

elemMap() [1/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real  coord_local ) const

inlineinherited

Definition at line 86 of file element.hh.

elemMap() [2/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d &  coord_local ) const

inlineinherited

Definition at line 90 of file element.hh.

elemMap() [3/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d &  coord_local ) const

inlineinherited

Definition at line 94 of file element.hh.

graphics()

virtual const concepts::ElementGraphics<Real>* linDG2D::Triangle::graphics ( ) const

virtualinherited

Returns the element graphics object.

info()

virtual std::ostream& linDG2D::TriangleP1::info ( std::ostream &  os ) const

protectedvirtual

Reimplemented from linDG2D::Triangle.

shapeFct()

virtual Real linDG2D::TriangleP1::shapeFct ( const uint  i, const Real  xi1, const Real  xi2  ) const

virtual

Computes the value of the ith shape function in the point (xi1, xi2).

Precondition

xi1, xi2 >= 0 and xi2 <= xi1 <= 1

Parameters

i	Index of the shape fct. (0, 1, 2)
xi1	First coordinate
xi2	Second coordinate

Implements linDG2D::Triangle.

shapeFctGradient()

concepts::Real2d linDG2D::TriangleP1::shapeFctGradient

(

const uint

i

)

const

Returns the gradient of the ith shape function, transformed to real world coordinates.

The shape functions are linear and the gradient is constant. Therefore, no coordinates are necessary.

Parameters

i	Index of the shape fct. (0, 1, 2)

solution()

virtual Real linDG2D::TriangleP1::solution ( const concepts::Vector< Real > &  coeffs, const Real  xi1, const Real  xi2  ) const

virtual

Returns the value of a mesh function within this element.

Parameters

coeffs	Vector of coefficients representing the mesh function
xi1	first reference element coordinate, in [0,1]
xi2	second reference element coordinate, in [0,xi1]

Implements linDG2D::Triangle.

support()

virtual const concepts::Triangle& linDG2D::Triangle::support ( ) const

inlinevirtualinherited

Returns the topological triangle supporting the element.

Implements linearFEM::Element.

Definition at line 41 of file triangle.hh.

T() [1/2]

virtual const concepts::TMatrixBase<Real>& linearFEM::Element::T ( ) const

inlinevirtualinherited

Returns the T matrix of this element.

Definition at line 47 of file element.hh.

T() [2/2]

virtual const TMatrixBase<Real >& concepts::ElementWithCell< Real >::T ( ) const

pure virtualinherited

Returns the T matrix of the element.

Implemented in hp3D::Element< Real >, and hp2D::Element< Real >.

Member Data Documentation

cell_

const concepts::Triangle2d& linDG2D::Triangle::cell_

privateinherited

Cell under this element.

Definition at line 67 of file triangle.hh.

graphics_

std::unique_ptr<TriangleGraphics> linDG2D::Triangle::graphics_

staticprivateinherited

Graphics object of this element.

Definition at line 69 of file triangle.hh.

T_

std::unique_ptr<concepts::TMatrixBase<Real> > linearFEM::Element::T_

protectedinherited

T matrix of this element.

Definition at line 50 of file element.hh.

---

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

• linDG2D/triangle.hh