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rAKA/fem/element_classes/element_class_line_1.cc
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element_class_line_1.cc
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/**
* @file element_class_line_1.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Thu Jul 15 10:28:28 2010
*
* @brief Specialization of the element_class class for the type _line_1
*
* @section LICENSE
*
* \<insert license here\>
*
* @section DESCRIPTION
*
* @verbatim
q
--x--------|--------x---> x
-1 0 1
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* w_1(x) &=& 1/2(1 - x) \\
* w_2(x) &=& 1/2(1 + x)
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* x_{q} &=& 0
* @f}
*/
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_line_1>::nb_nodes_per_element;
template<> UInt ElementClass<_line_1>::nb_quadrature_points;
template<> UInt ElementClass<_line_1>::spatial_dimension;
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_line_1>::computeShapes(const Real * natural_coords,
Real * shapes){
/// natural coordinate
Real c = natural_coords[0];
/// shape functions
shapes[0] = 0.5*(1-c);
shapes[1] =0.5*(1+c);
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_line_1>::computeDNDS(__attribute__ ((unused))
const Real * natural_coords,
Real * dnds){
/// dN1/de
dnds[0] = - .5;
/// dN2/de
dnds[1] = .5;
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_line_1>::computeJacobian(const Real * dxds,
const UInt dimension,
Real & jac){
if (dimension == spatial_dimension){
Real weight = 2.;
jac = dxds[0]*weight;
}
else {
jac = Math::norm2(dxds);
}
}
/* -------------------------------------------------------------------------- */
template<> inline Real ElementClass<_line_1>::getInradius(const Real * coord) {
return sqrt((coord[0] - coord[1])*(coord[0] - coord[1]));
}
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