moab::ElemUtil::LinearHexMap Class Reference

Shape function for trilinear hexahedron. More...

Inheritance diagram for moab::ElemUtil::LinearHexMap:

Collaboration diagram for moab::ElemUtil::LinearHexMap:

Public Member Functions
	LinearHexMap (const CartVect *corner_coords)
virtual CartVect	center_xi () const
	Return $\vec \xi$ corresponding to logical center of element. More...
virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate mapping function (calculate $\vec x = F($\vec \xi)$ ) More...
virtual double	evaluate_scalar_field (const CartVect &xi, const double *f_vals) const
virtual Matrix3	jacobian (const CartVect &xi) const
	Evaluate Jacobian of mapping function. More...
Public Member Functions inherited from moab::ElemUtil::VolMap
bool	solve_inverse (const CartVect &x, CartVect &xi, double tol) const
	Evaluate inverse of mapping function (calculate $\vec \xi = F^-1($\vec x)$ ) More...

Private Attributes
const CartVect *	corners

Static Private Attributes
static const double	corner_xi [8][3]

Detailed Description

Shape function for trilinear hexahedron.

Definition at line 48 of file ElemUtil.cpp.

Constructor & Destructor Documentation

LinearHexMap()

moab::ElemUtil::LinearHexMap::LinearHexMap ( const CartVect *  corner_coords )

inline

Definition at line 51 of file ElemUtil.cpp.

   51 : corners( corner_coords ) {}

Member Function Documentation

center_xi()

CartVect moab::ElemUtil::LinearHexMap::center_xi ( ) const

virtual

Return $\vec \xi$ corresponding to logical center of element.

Implements moab::ElemUtil::VolMap.

Definition at line 64 of file ElemUtil.cpp.

   65     {
   66         return CartVect( 0.0 );
   67     }

evaluate()

CartVect moab::ElemUtil::LinearHexMap::evaluate ( const CartVect &  xi ) const

virtual

Evaluate mapping function (calculate $\vec x = F($\vec \xi)$ )

Implements moab::ElemUtil::VolMap.

Definition at line 69 of file ElemUtil.cpp.

   70     {
   71         CartVect x( 0.0 );
   72         for( unsigned i = 0; i < 8; ++i )
   73         {
   74             const double N_i =
   75                 ( 1 + xi[0] * corner_xi[i][0] ) * ( 1 + xi[1] * corner_xi[i][1] ) * ( 1 + xi[2] * corner_xi[i][2] );
   76             x += N_i * corners[i];
   77         }
   78         x *= 0.125;
   79         return x;
   80     }

References corner_xi, and corners.

evaluate_scalar_field()

double moab::ElemUtil::LinearHexMap::evaluate_scalar_field ( const CartVect &  xi, const double *  f_vals  ) const

virtual

Definition at line 82 of file ElemUtil.cpp.

   83     {
   84         double f( 0.0 );
   85         for( unsigned i = 0; i < 8; ++i )
   86         {
   87             const double N_i =
   88                 ( 1 + xi[0] * corner_xi[i][0] ) * ( 1 + xi[1] * corner_xi[i][1] ) * ( 1 + xi[2] * corner_xi[i][2] );
   89             f += N_i * f_vals[i];
   90         }
   91         f *= 0.125;
   92         return f;
   93     }

References corner_xi.

Referenced by moab::ElemUtil::integrate_trilinear_hex().

jacobian()

Matrix3 moab::ElemUtil::LinearHexMap::jacobian ( const CartVect &  xi ) const

virtual

Evaluate Jacobian of mapping function.

Implements moab::ElemUtil::VolMap.

Definition at line 95 of file ElemUtil.cpp.

   96     {
   97         Matrix3 J( 0.0 );
   98         for( unsigned i = 0; i < 8; ++i )
   99         {
  100             const double xi_p      = 1 + xi[0] * corner_xi[i][0];
  101             const double eta_p     = 1 + xi[1] * corner_xi[i][1];
  102             const double zeta_p    = 1 + xi[2] * corner_xi[i][2];
  103             const double dNi_dxi   = corner_xi[i][0] * eta_p * zeta_p;
  104             const double dNi_deta  = corner_xi[i][1] * xi_p * zeta_p;
  105             const double dNi_dzeta = corner_xi[i][2] * xi_p * eta_p;
  106             J( 0, 0 ) += dNi_dxi * corners[i][0];
  107             J( 1, 0 ) += dNi_dxi * corners[i][1];
  108             J( 2, 0 ) += dNi_dxi * corners[i][2];
  109             J( 0, 1 ) += dNi_deta * corners[i][0];
  110             J( 1, 1 ) += dNi_deta * corners[i][1];
  111             J( 2, 1 ) += dNi_deta * corners[i][2];
  112             J( 0, 2 ) += dNi_dzeta * corners[i][0];
  113             J( 1, 2 ) += dNi_dzeta * corners[i][1];
  114             J( 2, 2 ) += dNi_dzeta * corners[i][2];
  115         }
  116         return J *= 0.125;
  117     }

References corner_xi, and corners.

Referenced by moab::ElemUtil::integrate_trilinear_hex().

Member Data Documentation

corner_xi

const double moab::ElemUtil::LinearHexMap::corner_xi

staticprivate

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 } }

Definition at line 59 of file ElemUtil.cpp.

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

corners

const CartVect* moab::ElemUtil::LinearHexMap::corners

private

Definition at line 58 of file ElemUtil.cpp.

Referenced by evaluate(), and jacobian().

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

• ElemUtil.cpp