BasisFunction.h

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#ifndef BasisFunction_included
#define BasisFunction_included
 
#include <Quadrature_base.h>
#include <Option_DG.h>
#include <Domaine_DG.h>
#include <Matrice_Dense.h>
#include <Matrice_Morse.h>
 
 
/**
 * @brief Manages the local polynomial basis functions for Discontinuous Galerkin elements.
 *
 * This class builds, stores, and evaluates the local polynomial basis {phi_i} used in
 * the DG discretization on each element. It supports orders 0, 1, and 2 in 2D
 * (3D is not yet implemented and throws at runtime).
 *
 * **Basis definition**
 * The raw (non-orthonormalized) basis is defined on each element T as scaled monomials
 * centered at the element barycenter xp and normalized by the characteristic length h_T:
 *   - order 0: { 1 }
 *   - order 1: { 1, (x-xp)/h, (y-yp)/h }
 *   - order 2: { 1, (x-xp)/h, (y-yp)/h, xy/h^2, x^2/h^2, y^2/h^2 }
 *
 * **Gram-Schmidt orthonormalization**
 * If orthonormalization is requested (gram_schmidt flag in initialize()), the raw basis
 * is transformed into an L2-orthonormal basis on each element via the modified Gram-Schmidt
 * process (gramSchmidt()). The change-of-basis coefficients are stored in a sparse
 * transition_matrix_ (block-diagonal, one nb_bfunc x nb_bfunc block per element), which
 * is then applied on-the-fly by orthonormalize() whenever a basis or gradient is evaluated.
 *
 * **Global DOF indexing**
 * indices_glob_elem_(e) gives the first global DOF index for element e.  For scalar
 * fields (dim=1) this maps directly; for vector fields (dim=2 or 3) the index is scaled
 * accordingly via the indices_glob_elem(dim) accessor.
 *
 * **Stabilization parameters**
 * compute_stab_param() fills two arrays used by the SIP penalty term:
 *   - eta_elem(e): element-local penalty coefficient, computed from the polynomial order
 *     and element geometry (sharp formula for triangles, conservative estimate otherwise).
 *   - eta_facet(f): face-local penalty, equal to eta_elem for boundary faces and to the
 *     harmonic mean of the two adjacent element values for internal faces.
 *
 * **Evaluation methods**
 * All eval_* methods fill a pre-allocated output DoubleTab with values at the quadrature
 * points provided by a Quadrature_base object. If the basis is orthonormalized, the
 * transition matrix is applied automatically after the raw evaluation.
 *
 * @note 3D support is declared but not yet implemented; calling any eval_* method in 3D
 *       will throw at runtime.
 */
class BasisFunction
{
public:
  BasisFunction() = default;
  virtual ~BasisFunction() {}
 
  void initialize(const Domaine_DG& dom, const int& order, const bool& gram_schmidt);
 
  inline const int& get_order() const { return order_; }
  inline const int& get_default_quadrature_order() const { return default_quad_order_; }
  inline const IntTab& indices_glob_elem(const int dim = 1) const
  {
    switch (dim)
      {
      case 1:
        return indices_glob_elem_;
      case 2:
        if (indices_glob_elem_2D_.size() == 0)
          {
            indices_glob_elem_2D_ = indices_glob_elem_;
            indices_glob_elem_2D_ *= 2;
          }
        return indices_glob_elem_2D_;
      case 3:
        if (indices_glob_elem_3D_.size() == 0)
          {
            indices_glob_elem_3D_ = indices_glob_elem_;
            indices_glob_elem_3D_ *= 2;
          }
        return indices_glob_elem_3D_;
      default:
        Cerr << "[DG] indices_glob_elem is incorrectly sized" << finl;
        throw;
      }
  }
  inline const int& nb_bfunc() const { return nb_bfunc_; }
 
  //Evaluation of the basis functions on integration points for elements and facets
  void eval_bfunc(const Quadrature_base& quad, const int& nelem, DoubleTab& fbasis) const;
  void eval_bfunc_on_facets(const Quadrature_base& quad, const int& nelem, const int& num_face, DoubleTab& grad_fbasis) const;
  void eval_bfunc(const DoubleTab& coord, const int& nelem, DoubleTab& fbasis) const;
 
  //Evaluation of the gradient of the basis functions on integration points for elements and facets
  void eval_grad_bfunc(const Quadrature_base& quad, const int& nelem, DoubleTab& fbasis) const;
  void eval_grad_bfunc_on_facets(const Quadrature_base& quad, const int& nelem, const int& num_face, DoubleTab& grad_fbasis) const;
 
  //Evaluation of the divergence of the basis functions (need to indicate which scalar component we are using) on integration points for elements and facets
  void eval_div_bfunc_on_facets(const Quadrature_base& quad, const int& nelem, const int& num_face, DoubleTab& div_fbasis) const;
  void eval_div_bfunc(const Quadrature_base& quad, const int& nelem, DoubleTab& div_fbasis) const;
 
  const Matrice_Dense eval_invMassMatrix(const Quadrature_base& quad, const int& nelem) const;
 
  inline const DoubleTab& get_eta_elem() const { return eta_elem; }
  inline const DoubleTab& get_eta_facet() const { return eta_facet; }
 
protected:
  void allocate_transition_matrix();
  void compute_stab_param();
 
  const Matrice_Dense build_local_mass_matrix(const Quadrature_base& quad, const int nelem) const;
 
  void build_mass_matrix();
  void build_transition_matrix();
  void orthonormalize(const int& nelem, const int& nb_pts_integ, DoubleTab& fbasis) const;
 
  void gramSchmidt(DoubleTab& fbase, const Quadrature_base& quad, const int& num_elem, const int& current_indice, const int& nb_pts_integ, const double& volume, int index);
 
  OBS_PTR(Domaine_DG) dom_;
  int order_ = 1;
  bool is_orthonormalized_ = true;
  bool is_diagonal_ = true;
  int nb_bfunc_ = -1;
  int default_quad_order_ = -1;
 
  IntTab indices_glob_elem_;
  mutable IntTab indices_glob_elem_2D_;
  mutable IntTab indices_glob_elem_3D_;
 
 
  Matrice_Morse transition_matrix_;
 
  DoubleTab eta_elem;
  DoubleTab eta_facet;
 
};
 
 
#endif /* BasisFunction_included */