shape_function.hxx

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#pragma once  // Ensure that file is included only once in a single compilation.
 
#include <tpp/shape_function/tensorial.hxx>
 
namespace TPP
{
/*!*************************************************************************************************
 * \brief   Struct that handles different types of evaluation of shape functions.
 *
 * \tparam  shape_t   Type of shape functions.
 *
 * \authors   Andreas Rupp, Heidelberg University, 2021.
 **************************************************************************************************/
template <typename shape_t>
struct ShapeFunction
{
  /*!***********************************************************************************************
   * \brief   Make type of shape functions accessable to everyone.
   ************************************************************************************************/
  typedef shape_t shape_fun_t;
  /*!***********************************************************************************************
   * \brief   Number of shape functions that span the local polynomial space.
   ************************************************************************************************/
  static constexpr unsigned int n_fun() { return shape_t::n_fun(); }
  /*!***********************************************************************************************
   * \brief   Dimension of abscissas of the polynomials.
   ************************************************************************************************/
  static constexpr unsigned int dim() { return shape_t::dim(); }
  /*!***********************************************************************************************
   * \brief   Maximum degree of all polynomials.
   ************************************************************************************************/
  static constexpr unsigned int degree() { return shape_t::degree(); }
  /*!***********************************************************************************************
   * \brief   Evaluate value of shape function.
   ************************************************************************************************/
  template <typename return_t, typename point_t>
  static constexpr return_t fct_val(const unsigned int index, const point_t& point)
  {
    return shape_t::template fct_val<return_t>(index, point);
  }
  /*!***********************************************************************************************
   * \brief   Evaluate value of partial derivative of shape function.
   ************************************************************************************************/
  template <typename return_t, typename point_t>
  static constexpr return_t der_val(const unsigned int index,
                                    const point_t& point,
                                    const unsigned int der_dim)
  {
    return shape_t::template der_val<return_t>(index, point, der_dim);
  }
 
  /*!***********************************************************************************************
   * \brief   Evaluate value of gradient of shape function.
   ************************************************************************************************/
  template <typename return_t, typename point_t>
  static constexpr return_t grad_val(const unsigned int index, const point_t& point)
  {
    static_assert(return_t::size() == point_t::size(), "Gradient and point have same dimension.");
    static_assert(point_t::size() == dim(), "Gradient and dimension need to be equal.");
 
    return_t value;
    for (unsigned int der_dim = 0; der_dim < dim(); ++der_dim)
      value[der_dim] = der_val<return_t::value_type>(index, point, der_dim);
    return value;
  }
  /*!***********************************************************************************************
   * \brief   Evaluate value of divergence of shape function
   ************************************************************************************************/
  template <typename return_t, typename point_t>
  static constexpr return_t div_val(const unsigned int index, const point_t& point)
  {
    static_assert(point_t::size() == dim(), "Gradient and dimension need to be equal.");
 
    return_t value = 0.;
    for (unsigned int der_dim = 0; der_dim < dim(); ++der_dim)
      value += der_val<return_t>(index, point, der_dim);
    return value;
  }
 
  /*!***********************************************************************************************
   * \brief   Evaluate value linear combination of shape functions.
   ************************************************************************************************/
  template <typename return_t, typename coeffs_t, typename point_t>
  static constexpr return_t lin_comb_fct_val(const coeffs_t& coeffs, const point_t& point)
  {
    static_assert(point_t::size() == dim(), "Point needs to have correct dimension.");
    static_assert(coeffs_t::size() == n_fun(), "Coeffs size must coincide with poly space!");
 
    return_t value = 0.;
    for (unsigned int index = 0; index < coeffs.size(); ++index)
      value += coeffs[index] * fct_val<return_t>(index, point);
    return value;
  }
  /*!***********************************************************************************************
   * \brief   Evaluate value of partial derivative of linear combination of shape functions.
   ************************************************************************************************/
  template <typename return_t, typename coeffs_t, typename point_t>
  static constexpr return_t lin_comb_der_val(const coeffs_t& coeffs,
                                             const point_t& point,
                                             const unsigned int der_dim)
  {
    static_assert(point_t::size() == dim(), "Point needs to have correct dimension.");
    static_assert(coeffs_t::size() == n_fun(), "Coeffs size must coincide with poly space!");
 
    return_t value = 0.;
    for (unsigned int index = 0; index < coeffs.size(); ++index)
      value += coeffs[index] * der_val<return_t>(index, point, der_dim);
    return value;
  }
};  // end of struct ShapeFunction
 
}  // end of namespace TPP