MOAB: Mesh Oriented datABase  (version 5.2.1)
moab::GeomUtil::LinearHexMap Class Reference

Shape function for trilinear hexahedron. More...

+ Inheritance diagram for moab::GeomUtil::LinearHexMap:
+ Collaboration diagram for moab::GeomUtil::LinearHexMap:

Public Member Functions

 LinearHexMap (const CartVect *corner_coords)
virtual CartVect center_xi () const
 Return \(\vec \xi\) corresponding to logical center of element.
virtual CartVect evaluate (const CartVect &xi) const
 Evaluate mapping function (calculate \(\vec x = F($\vec \xi)\) )
virtual Matrix3 jacobian (const CartVect &xi) const
 Evaluate Jacobian of mapping function.

Private Attributes

const CartVectcorners

Static Private Attributes

static const double corner_xi [8][3]

Detailed Description

Shape function for trilinear hexahedron.

Definition at line 1400 of file GeomUtil.cpp.


Constructor & Destructor Documentation

moab::GeomUtil::LinearHexMap::LinearHexMap ( const CartVect corner_coords) [inline]

Definition at line 1403 of file GeomUtil.cpp.

: corners( corner_coords ) {}

Member Function Documentation

Return \(\vec \xi\) corresponding to logical center of element.

Implements moab::GeomUtil::VolMap.

Definition at line 1415 of file GeomUtil.cpp.

    {
        return CartVect( 0.0 );
    }
CartVect moab::GeomUtil::LinearHexMap::evaluate ( const CartVect xi) const [virtual]

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

Implements moab::GeomUtil::VolMap.

Definition at line 1420 of file GeomUtil.cpp.

References corner_xi, and corners.

    {
        CartVect x( 0.0 );
        for( unsigned i = 0; i < 8; ++i )
        {
            const double N_i =
                ( 1 + xi[0] * corner_xi[i][0] ) * ( 1 + xi[1] * corner_xi[i][1] ) * ( 1 + xi[2] * corner_xi[i][2] );
            x += N_i * corners[i];
        }
        x *= 0.125;
        return x;
    }
Matrix3 moab::GeomUtil::LinearHexMap::jacobian ( const CartVect xi) const [virtual]

Evaluate Jacobian of mapping function.

Implements moab::GeomUtil::VolMap.

Definition at line 1433 of file GeomUtil.cpp.

References corner_xi, and corners.

    {
        Matrix3 J( 0.0 );
        for( unsigned i = 0; i < 8; ++i )
        {
            const double xi_p      = 1 + xi[0] * corner_xi[i][0];
            const double eta_p     = 1 + xi[1] * corner_xi[i][1];
            const double zeta_p    = 1 + xi[2] * corner_xi[i][2];
            const double dNi_dxi   = corner_xi[i][0] * eta_p * zeta_p;
            const double dNi_deta  = corner_xi[i][1] * xi_p * zeta_p;
            const double dNi_dzeta = corner_xi[i][2] * xi_p * eta_p;
            J( 0, 0 ) += dNi_dxi * corners[i][0];
            J( 1, 0 ) += dNi_dxi * corners[i][1];
            J( 2, 0 ) += dNi_dxi * corners[i][2];
            J( 0, 1 ) += dNi_deta * corners[i][0];
            J( 1, 1 ) += dNi_deta * corners[i][1];
            J( 2, 1 ) += dNi_deta * corners[i][2];
            J( 0, 2 ) += dNi_dzeta * corners[i][0];
            J( 1, 2 ) += dNi_dzeta * corners[i][1];
            J( 2, 2 ) += dNi_dzeta * corners[i][2];
        }
        return J *= 0.125;
    }

Member Data Documentation

const double moab::GeomUtil::LinearHexMap::corner_xi [static, private]
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 1410 of file GeomUtil.cpp.

Referenced by evaluate(), and jacobian().

Definition at line 1409 of file GeomUtil.cpp.

Referenced by evaluate(), and jacobian().

List of all members.


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