Finite Element Assembly Using an Embedded Domain Specific Language

Listing 13

Element type for first order line elements of the Lagrange family.

(/// 1D Line shape function

()  struct line1d

()  {

()   static const int nb_nodes = 2; // Number of nodes

()   static const int dimension = 1;

()  

()   // Type of the mapped coordinates

()   typedef Eigen::Matrix<double, 1, dimension> coord_t;

()   // Type of the shape function vector

() typedef Eigen::Matrix<double, 1, nb_nodes> shape_func_t;

() // Type of the coordinates matrix

() typedef Eigen::Matrix<double, nb_nodes, dimension> coord_mat_t;

()  

() // Compute the shape function vector at mapped coordinate c

() static shape_func_t shape_function(const coord_t& c)

() {

()  const double xi = c[];

()  shape_func_t result;

()  result[] = 0.5*(1.−xi);

()  result[] = 0.5*(1.+xi);

()  return result;

() }

()  

() // Compute the jacobian determinant

() static double jacobian_determinant(const coord_t& mapped_coord, const coord_mat_t&

     node_coords)

() {

()  return 0.5*(node_coords[] − node_coords[]);

() }

()  

() static const int nb_gauss_points = 2;

() // Type of the matrix with the Gauss points

() typedef Eigen::Matrix<double, nb_gauss_points, 1> gauss_points_t;

() // The Gauss points for the current shape function (definition omitted)

() static const gauss_points_t gauss_points();

() // Type for the weights

() typedef Eigen::Matrix<double, nb_gauss_points, 1> gauss_weights_t;

() // The Gauss weights (definition omitted)

() static const gauss_weights_t gauss_weights();

() };