Shape function space for a linear tetrahedron, obtained by a pushforward of the canonical affine shape functions. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::LinearTet:

Collaboration diagram for moab::Element::LinearTet:

Public Member Functions
	LinearTet (const std::vector< CartVect > &vertices)

	LinearTet ()

virtual	~LinearTet ()

virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ ) More...

virtual CartVect	ievaluate (const CartVect &x, double tol=1e-6, const CartVect &x0=CartVect(0.0)) const
	Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance) More...

virtual Matrix3	jacobian (const CartVect &) const
	Evaluate the map's Jacobi matrix. More...

virtual Matrix3	ijacobian (const CartVect &) const
	Evaluate the inverse of the Jacobi matrix. More...

virtual double	det_jacobian (const CartVect &) const
	Evaluate the determinate of the Jacobi matrix. More...

virtual double	det_ijacobian (const CartVect &) const
	Evaluate the determinate of the inverse Jacobi matrix. More...

virtual double	evaluate_scalar_field (const CartVect &xi, const double *field_vertex_values) const
	Evaluate a scalar field at a point given field values at the vertices. More...

virtual double	integrate_scalar_field (const double *field_vertex_values) const
	Integrate a scalar field over the element given field values at the vertices. More...

virtual void	set_vertices (const std::vector< CartVect > &v)
	Set vertices. More...

virtual bool	inside_nat_space (const CartVect &xi, double &tol) const
	decide if within the natural param space, with a tolerance More...

Public Member Functions inherited from moab::Element::Map
	Map (const std::vector< CartVect > &v)
	Construct a Map defined by the given std::vector of vertices. More...

	Map (const unsigned int n)
	Construct a Map defined by n vertices. More...

virtual	~Map ()

unsigned int	size ()
	Size of the vertices vector. More...

const std::vector< CartVect > &	get_vertices ()
	Retrieve vertices. More...

virtual bool	inside_box (const CartVect &xi, double &tol) const

Protected Attributes
Matrix3	T

Matrix3	T_inverse

double	det_T

double	det_T_inverse

Protected Attributes inherited from moab::Element::Map
std::vector< CartVect >	vertex

Static Protected Attributes
static const double	corner [4][3] = { { 0, 0, 0 }, { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } }

Detailed Description

Shape function space for a linear tetrahedron, obtained by a pushforward of the canonical affine shape functions.

Definition at line 197 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ LinearTet() [1/2]

moab::Element::LinearTet::LinearTet ( const std::vector< CartVect > & vertices )

inline

Definition at line 200 of file ElemUtil.hpp.

  : Map( vertices )
  {
  set_vertices( vertex );
  };

References set_vertices().

◆ LinearTet() [2/2]

moab::Element::LinearTet::LinearTet ( )

Definition at line 892 of file ElemUtil.cpp.

892 : Map( 0 ), det_T( 0.0 ), det_T_inverse( 0.0 ) {} // LinearTet::LinearTet()

◆ ~LinearTet()

moab::Element::LinearTet::~LinearTet ( )

virtual

Definition at line 894 of file ElemUtil.cpp.

894 {}

Member Function Documentation

◆ det_ijacobian()

virtual double moab::Element::LinearTet::det_ijacobian ( const CartVect & xi ) const

inlinevirtual

Evaluate the determinate of the inverse Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 224 of file ElemUtil.hpp.

  {
  return this->det_T_inverse;
  };

References det_T_inverse.

◆ det_jacobian()

virtual double moab::Element::LinearTet::det_jacobian ( const CartVect & xi ) const

inlinevirtual

Evaluate the determinate of the Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 220 of file ElemUtil.hpp.

  {
  return this->det_T;
  };

References det_T.

◆ evaluate()

virtual CartVect moab::Element::LinearTet::evaluate ( const CartVect & xi ) const

inlinevirtual

Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ )

Implements moab::Element::Map.

Definition at line 207 of file ElemUtil.hpp.

  {
  return this->vertex[0] + this->T * xi;
  };

References T.

◆ evaluate_scalar_field()

double moab::Element::LinearTet::evaluate_scalar_field	(	const CartVect &	xi,
		const double *	field_vertex_values
	)		const

virtual

Evaluate a scalar field at a point given field values at the vertices.

Implements moab::Element::Map.

Definition at line 907 of file ElemUtil.cpp.

  {
  double f0 = field_vertex_value[0];
  double f = f0;
  for( unsigned i = 1; i < 4; ++i )
  {
  f += ( field_vertex_value[i] - f0 ) * xi[i - 1];
  }
  return f;
  } // LinearTet::evaluate_scalar_field()

◆ ievaluate()

CartVect moab::Element::LinearTet::ievaluate	(	const CartVect &	x,
		double	tol = `1e-6`,
		const CartVect &	x0 = `CartVect( 0.0 )`
	)		const

virtual

Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance)

Reimplemented from moab::Element::Map.

Definition at line 918 of file ElemUtil.cpp.

  {
  return this->T_inverse * ( x - this->vertex[0] );
  } // LinearTet::ievaluate

References T_inverse.

Referenced by moab::Coupler::nat_param().

◆ ijacobian()

virtual Matrix3 moab::Element::LinearTet::ijacobian ( const CartVect & xi ) const

inlinevirtual

Evaluate the inverse of the Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 216 of file ElemUtil.hpp.

  {
  return this->T_inverse;
  };

References T_inverse.

◆ inside_nat_space()

bool moab::Element::LinearTet::inside_nat_space	(	const CartVect &	xi,
		double &	tol
	)		const

virtual

decide if within the natural param space, with a tolerance

Implements moab::Element::Map.

Definition at line 933 of file ElemUtil.cpp.

  {
  // linear tet space is a tetra with vertices (0,0,0), (1,0,0), (0,1,0), (0, 0, 1)
  // first check if outside bigger box, then below the plane x+y+z=1
  return ( xi[0] >= -tol ) && ( xi[1] >= -tol ) && ( xi[2] >= -tol ) && ( xi[0] + xi[1] + xi[2] < 1.0 + tol );
  }

Referenced by moab::Coupler::nat_param().

◆ integrate_scalar_field()

double moab::Element::LinearTet::integrate_scalar_field ( const double * field_vertex_values ) const

virtual

Integrate a scalar field over the element given field values at the vertices.

Implements moab::Element::Map.

Definition at line 923 of file ElemUtil.cpp.

  {
  double I( 0.0 );
  for( unsigned int i = 0; i < 4; ++i )
  {
  I += field_vertex_values[i];
  }
  I *= this->det_T / 24.0;
  return I;
  } // LinearTet::integrate_scalar_field()

References det_T.

◆ jacobian()

virtual Matrix3 moab::Element::LinearTet::jacobian ( const CartVect & xi ) const

inlinevirtual

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 212 of file ElemUtil.hpp.

  {
  return this->T;
  };

References T.

◆ set_vertices()

void moab::Element::LinearTet::set_vertices ( const std::vector< CartVect > & v )

virtual

Set vertices.

Reimplemented from moab::Element::Map.

Definition at line 896 of file ElemUtil.cpp.

  {
  this->Map::set_vertices( v );
  this->T =
  Matrix3( v[1][0] - v[0][0], v[2][0] - v[0][0], v[3][0] - v[0][0], v[1][1] - v[0][1], v[2][1] - v[0][1],
  v[3][1] - v[0][1], v[1][2] - v[0][2], v[2][2] - v[0][2], v[3][2] - v[0][2] );
  this->T_inverse = this->T.inverse();
  this->det_T = this->T.determinant();
  this->det_T_inverse = ( this->det_T < 1e-12 ? std::numeric_limits< double >::max() : 1.0 / this->det_T );
  } // LinearTet::set_vertices()

References det_T, det_T_inverse, moab::Matrix3::determinant(), moab::Matrix3::inverse(), moab::Element::Map::set_vertices(), T, and T_inverse.

Referenced by LinearTet().

Member Data Documentation

◆ corner

const double moab::Element::LinearTet::corner = { { 0, 0, 0 }, { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } }

staticprotected

Definition at line 238 of file ElemUtil.hpp.

◆ det_T

double moab::Element::LinearTet::det_T

protected

Definition at line 240 of file ElemUtil.hpp.

Referenced by det_jacobian(), integrate_scalar_field(), and set_vertices().

◆ det_T_inverse

double moab::Element::LinearTet::det_T_inverse

protected

Definition at line 240 of file ElemUtil.hpp.

Referenced by det_ijacobian(), and set_vertices().

◆ T

Matrix3 moab::Element::LinearTet::T

protected

Definition at line 239 of file ElemUtil.hpp.

Referenced by evaluate(), jacobian(), and set_vertices().

◆ T_inverse

Matrix3 moab::Element::LinearTet::T_inverse

protected

Definition at line 239 of file ElemUtil.hpp.

Referenced by ievaluate(), ijacobian(), and set_vertices().

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

Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ LinearTet() [1/2]

◆ LinearTet() [2/2]

◆ ~LinearTet()

Member Function Documentation

◆ det_ijacobian()

◆ det_jacobian()

◆ evaluate()

◆ evaluate_scalar_field()

◆ ievaluate()

◆ ijacobian()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

◆ set_vertices()

Member Data Documentation

◆ corner

◆ det_T

◆ det_T_inverse

◆ T

◆ T_inverse