Shape function space for bilinear quadrilateral, obtained from the canonical linear (affine) functions. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::LinearQuad:

Collaboration diagram for moab::Element::LinearQuad:

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

	LinearQuad ()

virtual	~LinearQuad ()

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

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

virtual Matrix3	jacobian (const CartVect &xi) const
	Evaluate the map's 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...

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 ()

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	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...

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

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

static const double	gauss [1][2] = { { 2.0, 0.0 } }

static const unsigned int	corner_count = 4

static const unsigned int	gauss_count = 1

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

Detailed Description

Shape function space for bilinear quadrilateral, obtained from the canonical linear (affine) functions.

Definition at line 284 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ LinearQuad() [1/2]

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

inline

Definition at line 287 of file ElemUtil.hpp.

287 : Map( vertices ){};

◆ LinearQuad() [2/2]

moab::Element::LinearQuad::LinearQuad ( )

Definition at line 1146 of file ElemUtil.cpp.

1146 : Map( 0 ) {} // LinearQuad::LinearQuad()

◆ ~LinearQuad()

moab::Element::LinearQuad::~LinearQuad ( )

virtual

Definition at line 1148 of file ElemUtil.cpp.

1148 {}

Member Function Documentation

◆ evaluate()

CartVect moab::Element::LinearQuad::evaluate ( const CartVect & xi ) const

virtual

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

Implements moab::Element::Map.

Definition at line 1156 of file ElemUtil.cpp.

  {
  CartVect x( 0.0 );
  for( unsigned i = 0; i < LinearQuad::corner_count; ++i )
  {
  const double N_i = ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] );
  x += N_i * this->vertex[i];
  }
  x /= LinearQuad::corner_count;
  return x;
  } // LinearQuad::evaluate

References corner, and corner_count.

◆ evaluate_scalar_field()

double moab::Element::LinearQuad::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 1188 of file ElemUtil.cpp.

  {
  double f( 0.0 );
  for( unsigned i = 0; i < LinearQuad::corner_count; ++i )
  {
  const double N_i = ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] );
  f += N_i * field_vertex_value[i];
  }
  f /= LinearQuad::corner_count;
  return f;
  } // LinearQuad::evaluate_scalar_field()

References corner, and corner_count.

Referenced by integrate_scalar_field().

◆ inside_nat_space()

bool moab::Element::LinearQuad::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 1218 of file ElemUtil.cpp.

  {
  // just look at the box+tol here
  return ( xi[0] >= -1. - tol ) && ( xi[0] <= 1. + tol ) && ( xi[1] >= -1. - tol ) && ( xi[1] <= 1. + tol );
  }

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

◆ integrate_scalar_field()

double moab::Element::LinearQuad::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 1200 of file ElemUtil.cpp.

  {
  double I( 0.0 );
  for( unsigned int j1 = 0; j1 < this->gauss_count; ++j1 )
  {
  double x1 = this->gauss[j1][1];
  double w1 = this->gauss[j1][0];
  for( unsigned int j2 = 0; j2 < this->gauss_count; ++j2 )
  {
  double x2 = this->gauss[j2][1];
  double w2 = this->gauss[j2][0];
  CartVect x( x1, x2, 0.0 );
  I += this->evaluate_scalar_field( x, field_vertex_values ) * w1 * w2 * this->det_jacobian( x );
  }
  }
  return I;
  } // LinearQuad::integrate_scalar_field()

References moab::Element::Map::det_jacobian(), evaluate_scalar_field(), gauss, and gauss_count.

◆ jacobian()

Matrix3 moab::Element::LinearQuad::jacobian ( const CartVect & xi ) const

virtual

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 1168 of file ElemUtil.cpp.

  {
  // this basically ignores the z component: xi[2] or vertex[][2]
  Matrix3 J( 0.0 );
  for( unsigned i = 0; i < LinearQuad::corner_count; ++i )
  {
  const double xi_p = 1 + xi[0] * corner[i][0];
  const double eta_p = 1 + xi[1] * corner[i][1];
  const double dNi_dxi = corner[i][0] * eta_p;
  const double dNi_deta = corner[i][1] * xi_p;
  J( 0, 0 ) += dNi_dxi * vertex[i][0];
  J( 1, 0 ) += dNi_dxi * vertex[i][1];
  J( 0, 1 ) += dNi_deta * vertex[i][0];
  J( 1, 1 ) += dNi_deta * vertex[i][1];
  }
  J( 2, 2 ) = 1.0; /* to make sure the Jacobian determinant is non-zero */
  J /= LinearQuad::corner_count;
  return J;
  } // LinearQuad::jacobian()

References corner, and corner_count.

Member Data Documentation

◆ corner

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

staticprotected

Definition at line 300 of file ElemUtil.hpp.

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

◆ corner_count

const unsigned int moab::Element::LinearQuad::corner_count = 4

staticprotected

Definition at line 302 of file ElemUtil.hpp.

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

◆ gauss

const double moab::Element::LinearQuad::gauss = { { 2.0, 0.0 } }

staticprotected

Definition at line 301 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

◆ gauss_count

const unsigned int moab::Element::LinearQuad::gauss_count = 1

staticprotected

Definition at line 303 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

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

Public Member Functions

Static Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LinearQuad() [1/2]

◆ LinearQuad() [2/2]

◆ ~LinearQuad()

Member Function Documentation

◆ evaluate()

◆ evaluate_scalar_field()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

Member Data Documentation

◆ corner

◆ corner_count

◆ gauss

◆ gauss_count