Class representing a map (diffeomorphism) F parameterizing a 3D element by its canonical preimage. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::Map:

Collaboration diagram for moab::Element::Map:

Classes
class	ArgError

class	EvaluationError

Public Member Functions
	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 ()

virtual CartVect	evaluate (const CartVect &xi) const =0
	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 bool	inside_nat_space (const CartVect &xi, double &tol) const =0
	decide if within the natural param space, with a tolerance More...

virtual Matrix3	jacobian (const CartVect &xi) const =0
	Evaluate the map's Jacobi matrix. More...

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

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

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

virtual double	evaluate_scalar_field (const CartVect &xi, const double *field_vertex_values) const =0
	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 =0
	Integrate a scalar field over the element given field values at the vertices. More...

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

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

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

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

Protected Attributes
std::vector< CartVect >	vertex

Detailed Description

Class representing a map (diffeomorphism) F parameterizing a 3D element by its canonical preimage.

Definition at line 51 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ Map() [1/2]

moab::Element::Map::Map ( const std::vector< CartVect > & v )

inline

Construct a Map defined by the given std::vector of vertices.

Definition at line 55 of file ElemUtil.hpp.

  {
  this->vertex.resize( v.size() );
  this->set_vertices( v );
  };

References set_vertices().

◆ Map() [2/2]

moab::Element::Map::Map ( const unsigned int n )

inline

Construct a Map defined by n vertices.

Definition at line 61 of file ElemUtil.hpp.

  {
  this->vertex = std::vector< CartVect >( n );
  };

◆ ~Map()

moab::Element::Map::~Map ( )

virtual

Definition at line 396 of file ElemUtil.cpp.

396 {}

Member Function Documentation

◆ det_ijacobian()

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

inlinevirtual

Evaluate the determinate of the inverse Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 92 of file ElemUtil.hpp.

  {
  return this->jacobian( xi ).inverse().determinant();
  };

References moab::Matrix3::determinant(), moab::Matrix3::inverse(), and jacobian().

◆ det_jacobian()

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

inlinevirtual

Evaluate the determinate of the Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 85 of file ElemUtil.hpp.

  {
  return this->jacobian( xi ).determinant();
  };

References moab::Matrix3::determinant(), and jacobian().

Referenced by moab::Element::LinearHex::integrate_scalar_field(), moab::Element::LinearQuad::integrate_scalar_field(), and moab::Element::LinearEdge::integrate_scalar_field().

◆ evaluate()

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

pure virtual

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

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

Referenced by ievaluate().

◆ evaluate_scalar_field()

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

pure virtual

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

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

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

◆ get_vertices()

const std::vector< CartVect > & moab::Element::Map::get_vertices ( )

inline

Retrieve vertices.

Definition at line 398 of file ElemUtil.cpp.

  {
  return this->vertex;
  }

References vertex.

◆ ievaluate()

CartVect moab::Element::Map::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 in moab::Element::SpectralQuad, moab::Element::SphericalTri, moab::Element::LinearTri, moab::Element::SphericalQuad, moab::Element::SpectralHex, and moab::Element::LinearTet.

Definition at line 421 of file ElemUtil.cpp.

  {
  // TODO: should differentiate between epsilons used for
  // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
  // right now, fix the tolerance used for NR
  tol = 1.0e-10;
  const double error_tol_sqr = tol * tol;
  double det;
  CartVect xi = x0;
  CartVect delta = evaluate( xi ) - x;
  Matrix3 J;
  
  int iters = 0;
  while( delta % delta > error_tol_sqr )
  {
  if( ++iters > 10 ) throw Map::EvaluationError( x, vertex );
  
  J = jacobian( xi );
  det = J.determinant();
  if( det < std::numeric_limits< double >::epsilon() ) throw Map::EvaluationError( x, vertex );
  xi -= J.inverse() * delta;
  delta = evaluate( xi ) - x;
  }
  return xi;
  } // Map::ievaluate()

References moab::Matrix3::determinant(), evaluate(), moab::Matrix3::inverse(), and jacobian().

Referenced by moab::Element::SphericalQuad::ievaluate(), moab::Coupler::nat_param(), test_hex(), and test_hex_nat_coords().

◆ ijacobian()

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

inlinevirtual

Evaluate the inverse of the Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 79 of file ElemUtil.hpp.

  {
  return this->jacobian( xi ).inverse();
  };

References moab::Matrix3::inverse(), and jacobian().

◆ inside_box()

bool moab::Element::Map::inside_box	(	const CartVect &	xi,
		double &	tol
	)		const

virtual

Reimplemented in moab::Element::SphericalTri, and moab::Element::SphericalQuad.

Definition at line 412 of file ElemUtil.cpp.

  {
  // bail out early, before doing an expensive NR iteration
  // compute box
  BoundBox box( this->vertex );
  return box.contains_point( xi.array(), tol );
  }

References moab::CartVect::array(), and moab::BoundBox::contains_point().

Referenced by moab::Element::SphericalQuad::inside_box(), moab::Element::SphericalTri::inside_box(), moab::Coupler::nat_param(), test_hex(), and test_linear_tri().

◆ inside_nat_space()

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

pure virtual

decide if within the natural param space, with a tolerance

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

◆ integrate_scalar_field()

virtual double moab::Element::Map::integrate_scalar_field ( const double * field_vertex_values ) const

pure virtual

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

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

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

◆ jacobian()

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

pure virtual

Evaluate the map's Jacobi matrix.

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::QuadraticHex, moab::Element::LinearHex, moab::Element::LinearTri, and moab::Element::LinearTet.

Referenced by det_ijacobian(), det_jacobian(), ievaluate(), and ijacobian().

◆ set_vertices()

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

virtual

Set vertices.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 403 of file ElemUtil.cpp.

  {
  if( v.size() != this->vertex.size() )
  {
  throw ArgError();
  }
  this->vertex = v;
  }

Referenced by Map(), moab::Element::LinearTet::set_vertices(), moab::Element::LinearTri::set_vertices(), and test_spectral_quad().

◆ size()

unsigned int moab::Element::Map::size ( )

inline

Size of the vertices vector.

Definition at line 103 of file ElemUtil.hpp.

  {
  return this->vertex.size();
  }

Referenced by moab::Element::SpectralQuad::get_gl_points().

Member Data Documentation

◆ vertex

std::vector< CartVect > moab::Element::Map::vertex

protected

Definition at line 141 of file ElemUtil.hpp.

Referenced by get_vertices().

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

Classes

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Map() [1/2]

◆ Map() [2/2]

◆ ~Map()

Member Function Documentation

◆ det_ijacobian()

◆ det_jacobian()

◆ evaluate()

◆ evaluate_scalar_field()

◆ get_vertices()

◆ ievaluate()

◆ ijacobian()

◆ inside_box()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

◆ set_vertices()

◆ size()

Member Data Documentation

◆ vertex