sxgrad.hpp

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#ifndef SXGRAD_HPP
#define SXGRAD_HPP
 
#include <variabledofspace.hpp>
#include <ddrcore.hpp>
#include <integralweight.hpp>
#include <xgrad.hpp>
#include <serendipity_problem.hpp>
 
namespace HArDCore2D
{
 
  class SXGrad : public VariableDOFSpace
  {
  public:
    typedef std::function<double(const Eigen::Vector2d &)> FunctionType;
 
 
    struct TransferOperators
    {
      TransferOperators(
                     const Eigen::MatrixXd & _serendipity,    
                     const Eigen::MatrixXd & _extension,     
                     const Eigen::MatrixXd & _reduction      
                     )
        : serendipity(_serendipity),
          extension(_extension),
          reduction(_reduction)
      {
        // Do nothing
      }
 
      Eigen::MatrixXd serendipity;
      Eigen::MatrixXd extension;
      Eigen::MatrixXd reduction;
    };
 
    SXGrad(const DDRCore & ddr_core, const SerendipityProblem & ser_pro, bool use_threads = true, std::ostream & output = std::cout);
 
    const Mesh & mesh() const
    {
      return m_ddr_core.mesh();
    }
    
    const size_t & degree() const
    {
      return m_ddr_core.degree();
    }
 
    Eigen::VectorXd interpolate(
                                const FunctionType & q, 
                                const int deg_quad = -1 
                                ) const;
 
    //---------------------------------//
    
    //---------------------------------//
    //---- Cell transfer operators -----//
    inline const Eigen::MatrixXd & SgradCell(size_t iT) const
    {
      return (*m_cell_transfer_operators[iT]).serendipity;
    }
 
    inline const Eigen::MatrixXd & EgradCell(size_t iT) const
    {
      return (*m_cell_transfer_operators[iT]).extension;
    }
 
    inline const Eigen::MatrixXd & RgradCell(size_t iT) const
    {
      return (*m_cell_transfer_operators[iT]).reduction;
    }
 
    inline const Eigen::MatrixXd & SgradCell(const Cell & T) const
    {
      return SgradCell(T.global_index());
    }
 
    inline const Eigen::MatrixXd & EgradCell(const Cell & T) const
    {
      return EgradCell(T.global_index());
    }
 
    inline const Eigen::MatrixXd & RgradCell(const Cell & T) const
    {
      return RgradCell(T.global_index());
    }
    inline const TransferOperators & cellOperators(size_t iT) const
    {
      return *m_cell_transfer_operators[iT];
    }
 
    inline const TransferOperators & cellOperators(const Cell & T) const
    {
      return *m_cell_transfer_operators[T.global_index()];
    }
 
 
    //---------------------------------------------------------------------//
    //---- Full gradient and potential reconstructions, and L2 product ----//
    
    inline const Eigen::MatrixXd edgeGradient(size_t iE) const
    {
      return m_xgrad.edgeOperators(iE).gradient;
    }
    
    inline const Eigen::MatrixXd edgeGradient(const Edge & E) const
    {
      return edgeGradient(E.global_index());
    }
 
    inline const Eigen::MatrixXd edgePotential(size_t iE) const
    {
      return m_xgrad.edgeOperators(iE).potential;
    }
 
    inline const Eigen::MatrixXd edgePotential(const Edge & E) const
    {
      return edgePotential(E.global_index());
    }
 
    inline const Eigen::MatrixXd cellGradient(size_t iT) const
    {
      return m_xgrad.cellOperators(iT).gradient * EgradCell(iT);
    }
 
    inline const Eigen::MatrixXd cellGradient(const Cell & T) const
    {
      return cellGradient(T.global_index());
    }
 
    inline const Eigen::MatrixXd cellPotential(size_t iT) const
    {
      return m_xgrad.cellOperators(iT).potential * EgradCell(iT);
    }
 
    inline const Eigen::MatrixXd cellPotential(const Cell & T) const
    {
      return cellPotential(T.global_index());
    }
 
    Eigen::MatrixXd computeL2Product(
                                     const size_t iT, 
                                     const double & penalty_factor = 1., 
                                     const Eigen::MatrixXd & mass_Pk2_T = Eigen::MatrixXd::Zero(1,1), 
                                     const IntegralWeight & weight = IntegralWeight(1.) 
                                     ) const
    {
      return EgradCell(iT).transpose() 
                * m_xgrad.computeL2Product(iT, penalty_factor, mass_Pk2_T, weight)
                  *EgradCell(iT);  
    }
    
    double computeL2Norm(const Eigen::VectorXd & v) const;   
 
    Eigen::MatrixXd computeStabilisation(
                                     const size_t iT, 
                                     const IntegralWeight & weight = IntegralWeight(1.) 
                                     ) const
    {
      return EgradCell(iT).transpose() 
                * m_xgrad.computeStabilisation(iT, weight)
                  * EgradCell(iT);
    }
 
    
    std::vector<double> computeVertexValues(
                  const Eigen::VectorXd & u   
                  ) const;
 
         
         
    //-----------------------//       
    //---- Getters ----------//
 
    inline const DDRCore::CellBases & cellBases (size_t iT) const
    {
      return m_ddr_core.cellBases(iT);
    }
 
    inline const DDRCore::CellBases & cellBases (const Cell & T) const
    {
      return  m_ddr_core.cellBases(T.global_index());
    }
    
    
    inline const DDRCore::EdgeBases & edgeBases(size_t iE) const
    {
      return m_ddr_core.edgeBases(iE);
    }
 
    inline const DDRCore::EdgeBases & edgeBases(const Edge & E) const
    {
      return m_ddr_core.edgeBases(E.global_index());
    }
 
  private:
    TransferOperators _compute_cell_transfer_operators(size_t iT);
    double _compute_squared_l2_norm(size_t iT, const Eigen::VectorXd & vT) const;
    const DDRCore & m_ddr_core;
    const SerendipityProblem & m_ser_pro;
    const XGrad m_xgrad;
       
    // Containers for serendipity, extension and reduction operators
    std::vector<std::shared_ptr<TransferOperators> > m_cell_transfer_operators;
 
    bool m_use_threads;
    std::ostream & m_output;
 
  };
 
} // end of namespace HArDCore2D
#endif