Shape function space for trilinear hexahedron, obtained by a pushforward of the canonical linear (affine) functions. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::QuadraticHex:

List of all members.

Public Member Functions
	QuadraticHex (const std::vector< CartVect > &vertices)
	QuadraticHex ()
virtual	~QuadraticHex ()
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 int	corner [27][3]
static const double	gauss [8][2]
static const unsigned int	corner_count = 27
static const unsigned int	gauss_count = 8

Detailed Description

Shape function space for trilinear hexahedron, obtained by a pushforward of the canonical linear (affine) functions.

Definition at line 146 of file ElemUtil.hpp.

Constructor & Destructor Documentation

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

Definition at line 148 of file ElemUtil.hpp.

: Map(vertices){};

moab::Element::QuadraticHex::QuadraticHex ( )

Definition at line 656 of file ElemUtil.cpp.

                            :Map(0) {
  }

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

Definition at line 659 of file ElemUtil.cpp.

{}

Member Function Documentation

CartVect moab::Element::QuadraticHex::evaluate ( const CartVect & xi ) const [virtual]

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

Implements moab::Element::Map.

Definition at line 682 of file ElemUtil.cpp.

  {

    CartVect x(0.0);
    for (int i=0; i<27; i++)
    {
      const double sh= SH(corner[i][0], xi[0])
                      *SH(corner[i][1], xi[1])
                      *SH(corner[i][2], xi[2]);
      x+=sh* vertex[i];
    }

    return x;
  }

double moab::Element::QuadraticHex::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 728 of file ElemUtil.cpp.

  {
    double x=0.0;
    for (int i=0; i<27; i++)
    {
      const double sh= SH(corner[i][0], xi[0])
                *SH(corner[i][1], xi[1])
                *SH(corner[i][2], xi[2]);
      x+=sh* field_vertex_values[i];
    }

    return x;
  }

bool moab::Element::QuadraticHex::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 697 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) &&
           ( xi[2]>=-1.-tol) && (xi[2]<=1.+tol);
  }

double moab::Element::QuadraticHex::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 741 of file ElemUtil.cpp.

  {
    return 0.;// TODO: gaussian integration , probably 2x2x2
  }

Matrix3 moab::Element::QuadraticHex::jacobian ( const CartVect & xi ) const [virtual]

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 704 of file ElemUtil.cpp.

  {
    Matrix3 J(0.0);
    for (int i=0; i<27; i++)
    {
      const double sh[3]={ SH(corner[i][0], xi[0]),
                           SH(corner[i][1], xi[1]),
                           SH(corner[i][2], xi[2]) };
      const double dsh[3]={ DSH(corner[i][0], xi[0]),
                            DSH(corner[i][1], xi[1]),
                            DSH(corner[i][2], xi[2]) };


      for (int j=0; j<3; j++)
      {
        J(j,0)+=dsh[0]*sh[1]*sh[2]*vertex[i][j]; // dxj/dr first column
        J(j,1)+=sh[0]*dsh[1]*sh[2]*vertex[i][j]; // dxj/ds
        J(j,2)+=sh[0]*sh[1]*dsh[2]*vertex[i][j]; // dxj/dt
      }
    }


    return J;
  }

Member Data Documentation

const int moab::Element::QuadraticHex::corner [static, protected]

Initial value:

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

Definition at line 162 of file ElemUtil.hpp.

const unsigned int moab::Element::QuadraticHex::corner_count = 27 [static, protected]

Definition at line 164 of file ElemUtil.hpp.

const double moab::Element::QuadraticHex::gauss[8][2] [static, protected]

Definition at line 163 of file ElemUtil.hpp.

const unsigned int moab::Element::QuadraticHex::gauss_count = 8 [static, protected]

Definition at line 165 of file ElemUtil.hpp.

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

Public Member Functions

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation