MOAB: Mesh Oriented datABase  (version 5.4.1)

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

#include <ElemUtil.hpp>

Public Member Functions

LinearQuad (const std::vector< CartVect > &vertices)
virtual CartVect evaluate (const CartVect &xi) const
Evaluate the map on $$x_i$$ (calculate $$\vec x = F(\vec \xi)$$ )
virtual bool inside_nat_space (const CartVect &xi, double &tol) const
decide if within the natural param space, with a tolerance
virtual Matrix3 jacobian (const CartVect &xi) const
Evaluate the map's Jacobi matrix.
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.
virtual double integrate_scalar_field (const double *field_vertex_values) const
Integrate a scalar field over the element given field values at the vertices.

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

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

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

Definition at line 287 of file ElemUtil.hpp.

: Map( vertices ){};


Definition at line 1146 of file ElemUtil.cpp.

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

 moab::Element::LinearQuad::~LinearQuad ( )  [virtual]

Definition at line 1148 of file ElemUtil.cpp.

{}


Member Function Documentation

 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.

References corner, and corner_count.

    {
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];
}
return x;

 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.

References corner, and corner_count.

Referenced by integrate_scalar_field().

    {
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];
}
return f;

 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.

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

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

 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;

 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.

References corner, and corner_count.

    {
// 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 */
return J;


Member Data Documentation

 const double moab::Element::LinearQuad::corner = { { -1, -1, 0 }, { 1, -1, 0 }, { 1, 1, 0 }, { -1, 1, 0 } } [static, protected]

Definition at line 300 of file ElemUtil.hpp.

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

 const unsigned int moab::Element::LinearQuad::corner_count = 4 [static, protected]

Definition at line 302 of file ElemUtil.hpp.

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

 const double moab::Element::LinearQuad::gauss = { { 2.0, 0.0 } } [static, protected]

Definition at line 301 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

 const unsigned int moab::Element::LinearQuad::gauss_count = 1 [static, protected]

Definition at line 303 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

List of all members.

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