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rAKA/fem/element_classes/element_class_triangle_1.cc
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element_class_triangle_1.cc
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/**
* @file element_class_triangle_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 _triangle_1
*
* @section LICENSE
*
* <insert license here>
*
*/
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_triangle_1>::nb_nodes_per_element;
template<> UInt ElementClass<_triangle_1>::nb_quadrature_points;
template<> UInt ElementClass<_triangle_1>::spatial_dimension;
/* -------------------------------------------------------------------------- */
template<> inline void ElementClass<_triangle_1>::shapeFunctions(const Real * x,
Real * shape,
Real * shape_deriv,
Real * jacobian) {
/**
* t
* ^
* |
* x (0,0,1)
* |`
* | `
* | q `
| ° `
* x--------x-----> s
* (1,0,0) (0,1,0)
*
* N1 = 1 - s - t
* N2 = s
* N3 = t
*/
Real weight = .5;
/// shape functions
shape[0] = 1./3.; //N1(q_0)
shape[1] = 1./3.; //N2(q_0)
shape[2] = 1./3.; //N3(q_0)
/*
* / dN1/ds dN2/ds dN3/ds \
* dnds = | |
* \ dN1/dt dN2/dt dN3/dt /
*/
Real dnds[nb_nodes_per_element*spatial_dimension];
dnds[0] = -1.; dnds[1] = 1.; dnds[2] = 0.;
dnds[3] = -1.; dnds[4] = 0.; dnds[5] = 1.;
/// J = dxds = dnds * x
Real dxds[spatial_dimension*spatial_dimension];
Math::matrix_matrix(spatial_dimension, spatial_dimension, nb_nodes_per_element,
dnds, x, dxds);
Real det_dxds = dxds[0] * dxds[3] - dxds[2] * dxds[1];
/// dxds = J^{-1}
Real inv_dxds[spatial_dimension*spatial_dimension];
Math::inv2(dxds,inv_dxds);
jacobian[0] = det_dxds * weight;
Math::matrixt_matrixt(nb_nodes_per_element, spatial_dimension, spatial_dimension,
dnds, inv_dxds, shape_deriv);
}
/* -------------------------------------------------------------------------- */
template<> inline Real ElementClass<_triangle_1>::getInradius(const Real * coord) {
return Math::triangle_inradius(coord);
}
/* -------------------------------------------------------------------------- */
template<> inline void ElementClass<_triangle_1>::changeDimension(const Real * coord, UInt dim, UInt n_points, Real * local_coord) {
AKANTU_DEBUG_ERROR("TO IMPLEMENT");
}
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