moab::Element::LinearEdge Class Reference

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

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::LinearEdge:

List of all members.

Public Member Functions
	LinearEdge (const std::vector< CartVect > &vertices)
	LinearEdge ()
virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate the map on (calculate $ x = F($ )$ )
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 [2][3]
static const double	gauss [1][2] = { { 2.0, 0.0 } }
static const unsigned int	corner_count = 2
static const unsigned int	gauss_count = 1

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Detailed Description

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

Definition at line 252 of file ElemUtil.hpp.

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Constructor & Destructor Documentation

moab::Element::LinearEdge::LinearEdge

(

const std::vector< CartVect > &

vertices

)

[inline]

Definition at line 254 of file ElemUtil.hpp.

: Map(vertices){};

moab::Element::LinearEdge::LinearEdge

(

)

Definition at line 467 of file ElemUtil.cpp.

                         : Map(0) {

  }// LinearEdge::LinearEdge()

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Member Function Documentation

CartVect moab::Element::LinearEdge::evaluate

(

const CartVect &

xi

)

const [virtual]

Evaluate the map on (calculate $ x = F($ )$ )

Implements moab::Element::Map.

Definition at line 477 of file ElemUtil.cpp.

                                                          {
    CartVect x(0.0);
    for (unsigned i = 0; i < LinearEdge::corner_count; ++i) {
      const double N_i = (1.0 + xi[0]*corner[i][0]);
      x += N_i * this->vertex[i];
    }
    x /= LinearEdge::corner_count;
    return x;
  }// LinearEdge::evaluate

double moab::Element::LinearEdge::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 500 of file ElemUtil.cpp.

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

bool moab::Element::LinearEdge::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 522 of file ElemUtil.cpp.

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

double moab::Element::LinearEdge::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 511 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];
      CartVect x(x1,0.0,0.0);
      I += this->evaluate_scalar_field(x,field_vertex_values)*w1*this->det_jacobian(x);
    }
    return I;
  }// LinearEdge::integrate_scalar_field()

Matrix3 moab::Element::LinearEdge::jacobian

(

const CartVect &

xi

)

const [virtual]

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 487 of file ElemUtil.cpp.

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

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Member Data Documentation

const double moab::Element::LinearEdge::corner [static, protected]

Initial value:

 {  { -1, 0, 0 },
                                         {  1, 0, 0 } }

Definition at line 266 of file ElemUtil.hpp.

const unsigned int moab::Element::LinearEdge::corner_count = 2 [static, protected]

Definition at line 268 of file ElemUtil.hpp.

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

Definition at line 267 of file ElemUtil.hpp.

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

Definition at line 269 of file ElemUtil.hpp.

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

• ElemUtil.hpp
• ElemUtil.cpp