Equation_1matrix.h

Go to the documentation of this file.

/// \file Equation_1matrix.h
/// A templated class for equations that can be inherited from
/// to allow instantiation of PDE_IBVP objects (amongst others).
 
#ifndef EQUATION_1MATRIX_H
#define EQUATION_1MATRIX_H
 
#include <Residual_with_coords.h>
 
namespace CppNoddy {
 
  /// An equation object base class used in the IBVP classes (and others).
  /// An equation object is essentially a ('square') residual object with an independent variable
  /// data member and access methods. By 'square' we mean that it defines
  /// N residuals and N state variables. The equation is defined
  /// using an NxN matrix that multiplies the derivative of unknowns and a residual RHS.
  template < typename _Type, typename _Xtype = double >
  class Equation_1matrix : public Residual_with_coords<_Type, _Xtype> {
   public:
    /// Constructor for equation class.
    /// \param order The order of the system
    explicit Equation_1matrix(const unsigned &order);
 
    /// An empty destructor, virtual since we have virtual methods.
    virtual ~Equation_1matrix();
 
    /// Update the Equation object for the current set of state variables
    /// \param state The state vector at which to set the equation object
    void update(const DenseVector<_Type> &state);
 
    /// Return a handle to the matrix
    const DenseMatrix<_Type>& matrix0() const;
 
    /// Return the product of the Jacobian-of-the-matrix and a vector 'vec'
    /// when the equation has a given 'state'. The user should overload this
    /// if concerned about performance of the solver. If not overloaded, the
    /// default is to finite difference the Jacobian-of-the-matrix.
    /// \param state The current state variables -- used for clarity when
    /// overloaded by the user instead of expecting the user to access the member data.
    /// \param vec The vector that will be multiplied by the Jacobian-of-the-matrix
    /// \param h The resulting 2D matrix
    virtual void get_jacobian_of_matrix0_mult_vector(const DenseVector<_Type> &state,
        const DenseVector<_Type> &vec, DenseMatrix<_Type> &h) const;
 
 
   protected:
 
    /// Define the matrix in terms of the current state vector.
    /// \param x The current state vector.
    /// \param m The matrix.
    virtual void matrix0(const DenseVector<_Type> &x, DenseMatrix<_Type> &m) const {
      std::string problem;
      problem = "The equation::matrix0 method has not been implemented!\n";
      problem += "You have to implement this method to define the equation.\n";
      throw ExceptionRuntime(problem);
    }
 
   private:
    /// Matrix0 evaluated for the last state vector
    DenseMatrix<_Type> MATRIX0_AT_LAST_STATE;
 
  }
  ; // end class
 
  template <typename _Type, typename _Xtype>
  inline const DenseMatrix<_Type>& Equation_1matrix<_Type, _Xtype>::matrix0() const {
    return MATRIX0_AT_LAST_STATE;
  }
 
} // end namespace
 
#endif