moab
Public Member Functions | Protected Attributes | Static Protected Attributes
moab::Element::LinearTet Class Reference

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:
moab::Element::Map

List of all members.

Public Member Functions

 LinearTet (const std::vector< CartVect > &vertices)
 LinearTet ()
virtual ~LinearTet ()
virtual CartVect evaluate (const CartVect &xi) const
 Evaluate the map on (calculate $ x = F($ )$ )
virtual CartVect ievaluate (const CartVect &x) const
virtual Matrix3 jacobian (const CartVect &) const
 Evaluate the map's Jacobi matrix.
virtual Matrix3 ijacobian (const CartVect &) const
 Evaluate the inverse of the Jacobi matrix.
virtual double det_jacobian (const CartVect &) const
 Evaluate the determinate of the Jacobi matrix.
virtual double det_ijacobian (const CartVect &) const
 Evaluate the determinate of the inverse 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.
virtual void set_vertices (const std::vector< CartVect > &v)
 Set vertices.
virtual bool inside_nat_space (const CartVect &xi, double &tol) const
 decide if within the natural param space, with a tolerance

Protected Attributes

Matrix3 T
Matrix3 T_inverse
double det_T
double det_T_inverse

Static Protected Attributes

static const double corner [4][3]

Detailed Description

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

Definition at line 169 of file ElemUtil.hpp.

Constructor & Destructor Documentation

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

Definition at line 171 of file ElemUtil.hpp.

: Map(vertices){ LinearTet::set_vertices(vertex);};
moab::Element::LinearTet::LinearTet ( )

Definition at line 752 of file ElemUtil.cpp.

                       : Map(0) {

  }// LinearTet::LinearTet()
moab::Element::LinearTet::~LinearTet ( ) [virtual]

Definition at line 757 of file ElemUtil.cpp.

    {}

Member Function Documentation

virtual double moab::Element::LinearTet::det_ijacobian ( const CartVect &  xi) const [inline, virtual]

Evaluate the determinate of the inverse Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 180 of file ElemUtil.hpp.

{return this->det_T_inverse;};
virtual double moab::Element::LinearTet::det_jacobian ( const CartVect &  xi) const [inline, virtual]

Evaluate the determinate of the Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 179 of file ElemUtil.hpp.

{return this->det_T;};
virtual CartVect moab::Element::LinearTet::evaluate ( const CartVect &  xi) const [inline, virtual]

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

Implements moab::Element::Map.

Definition at line 175 of file ElemUtil.hpp.

{return this->vertex[0] + this->T*xi;};
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 771 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()
virtual CartVect moab::Element::LinearTet::ievaluate ( const CartVect &  x) const [inline, virtual]

Definition at line 176 of file ElemUtil.hpp.

{return this->T_inverse*(x-this->vertex[0]);};
virtual Matrix3 moab::Element::LinearTet::ijacobian ( const CartVect &  xi) const [inline, virtual]

Evaluate the inverse of the Jacobi matrix.

Reimplemented from moab::Element::Map.

Definition at line 178 of file ElemUtil.hpp.

{return this->T_inverse;};
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 788 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);
  }
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 780 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()
virtual Matrix3 moab::Element::LinearTet::jacobian ( const CartVect &  xi) const [inline, virtual]

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 177 of file ElemUtil.hpp.

{return this->T;};
void moab::Element::LinearTet::set_vertices ( const std::vector< CartVect > &  v) [virtual]

Set vertices.

Reimplemented from moab::Element::Map.

Definition at line 760 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 = (0.0 == this->det_T ? HUGE : 1.0/this->det_T);
  }// LinearTet::set_vertices()

Member Data Documentation

const double moab::Element::LinearTet::corner [static, protected]
Initial value:
 { {0,0,0},
                                           {1,0,0},
                                           {0,1,0},
                                           {0,0,1}}

Definition at line 189 of file ElemUtil.hpp.

double moab::Element::LinearTet::det_T [protected]

Definition at line 191 of file ElemUtil.hpp.

double moab::Element::LinearTet::det_T_inverse [protected]

Definition at line 191 of file ElemUtil.hpp.

Matrix3 moab::Element::LinearTet::T [protected]

Definition at line 190 of file ElemUtil.hpp.

Matrix3 moab::Element::LinearTet::T_inverse [protected]

Definition at line 190 of file ElemUtil.hpp.

The documentation for this class was generated from the following files:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines