An equation object base class used in the IBVP classes (and others). More...

#include <Equation_1matrix.h>

Inheritance diagram for CppNoddy::Equation_1matrix< _Type, _Xtype >:

Public Member Functions
	Equation_1matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_1matrix ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< _Type > &state)
	Update the Equation object for the current set of state variables. More...

const DenseMatrix< _Type > &	matrix0 () const
	Return a handle to the matrix. More...

virtual void	get_jacobian_of_matrix0_mult_vector (const DenseVector< _Type > &state, const DenseVector< _Type > &vec, DenseMatrix< _Type > &h) const
	Return the product of the Jacobian-of-the-matrix and a vector 'vec' when the equation has a given 'state'. More...

Public Member Functions inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
	Residual_with_coords (const unsigned &order, const unsigned &ncoords)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual_with_coords (const unsigned &order, const unsigned &nvars, const unsigned &ncoords)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual_with_coords ()
	An empty destructor. More...

_Xtype &	coord (const unsigned &i)
	General handle access to the coordinates. More...

const _Xtype &	coord (const unsigned &i) const
	General handle access to the coordinates. More...

Public Member Functions inherited from CppNoddy::Residual< _Type >
	Residual (const unsigned &order)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual (const unsigned &order, const unsigned &nvars)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< _Type > &state)
	Update the Residual object for the current set of state variables. More...

const DenseVector< _Type > &	residual () const
	Return a handle to the residuals corresponding to the last update state. More...

const DenseMatrix< _Type > &	jacobian () const
	Retrun a handle to the Jacobian of the residual corresponding to the last update state. More...

_Type &	delta ()

const _Type &	delta () const

unsigned	get_order () const
	Get the order of the residual vector. More...

unsigned	get_number_of_vars () const
	Get the number of variables that this residual condition is defined for. More...

virtual void	residual_fn (const DenseVector< _Type > &state, DenseVector< _Type > &f) const
	A blank virtual residual function method. More...

Protected Member Functions
virtual void	matrix0 (const DenseVector< _Type > &x, DenseMatrix< _Type > &m) const
	Define the matrix in terms of the current state vector. More...

Protected Member Functions inherited from CppNoddy::Residual< _Type >
virtual void	jacobian (const DenseVector< _Type > &state, DenseMatrix< _Type > &jac) const
	Because the residual evaluation at the current state is assumed to have already been done by the 'update' method, this routine is protected. More...

Additional Inherited Members
Protected Attributes inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
std::vector< _Xtype >	coords
	The coordinates stored for this residual. More...

Protected Attributes inherited from CppNoddy::Residual< _Type >
DenseMatrix< _Type >	JAC_AT_LAST_STATE
	Jacobian for the last state vector. More...

DenseVector< _Type >	FN_AT_LAST_STATE
	Residual for the last state vector. More...

DenseVector< _Type >	LAST_STATE
	The last state vector. More...

_Type	DELTA
	A default step for FD computation of the Jacobian. More...

unsigned	ORDER_OF_SYSTEM
	The order of the system of equations. More...

unsigned	NUMBER_OF_VARS
	The number of elements in the state vector. More...

Detailed Description

template<typename _Type, typename _Xtype = double>
class CppNoddy::Equation_1matrix< _Type, _Xtype >

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.

Definition at line 18 of file Equation_1matrix.h.

Constructor & Destructor Documentation

◆ Equation_1matrix()

template<typename _Type , typename _Xtype >

CppNoddy::Equation_1matrix< _Type, _Xtype >::Equation_1matrix ( const unsigned & order )

explicit

Constructor for equation class.

Parameters

order The order of the system

Definition at line 12 of file Equation_1matrix.cpp.

                                                                         :
    Residual_with_coords<_Type, _Xtype>(order, 1) {
    MATRIX0_AT_LAST_STATE = DenseMatrix<_Type>(this -> ORDER_OF_SYSTEM, this -> ORDER_OF_SYSTEM, 0.0);
  }

References CppNoddy::Residual< _Type >::ORDER_OF_SYSTEM.

◆ ~Equation_1matrix()

template<typename _Type , typename _Xtype >

CppNoddy::Equation_1matrix< _Type, _Xtype >::~Equation_1matrix

virtual

An empty destructor, virtual since we have virtual methods.

Definition at line 18 of file Equation_1matrix.cpp.

                                                     {
    // timer reporting is done via the Equation class this inherits from
  }

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

template<typename _Type , typename _Xtype >

void CppNoddy::Equation_1matrix< _Type, _Xtype >::get_jacobian_of_matrix0_mult_vector	(	const DenseVector< _Type > &	state,
		const DenseVector< _Type > &	vec,
		DenseMatrix< _Type > &	h
	)		const

virtual

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.

Parameters

state	The current state variables – used for clarity when overloaded by the user instead of expecting the user to access the member data.
vec	The vector that will be multiplied by the Jacobian-of-the-matrix
h	The resulting 2D matrix

Definition at line 23 of file Equation_1matrix.cpp.

                                                                                                                                                                       {
    // we dont need state in the default implementation as its already been set by the update method. You do need it for the user
    // to overload this method with an explicit analytical version however.
    //
    // copy some items for FD computation of Jacobian of matrix
    DenseVector<_Type> copy_of_state(this -> LAST_STATE);
    DenseMatrix<_Type> copy_of_matrix(MATRIX0_AT_LAST_STATE);
    std::vector< DenseMatrix<_Type> > jacmatrix;
    // update the Jacobian of the mass matrix
    for(std::size_t i = 0; i < this -> ORDER_OF_SYSTEM; ++i) {
      copy_of_state[ i ] += this -> DELTA;
      matrix0(copy_of_state, copy_of_matrix);
      copy_of_state[ i ] -= this -> DELTA;
      copy_of_matrix.sub(MATRIX0_AT_LAST_STATE);
      copy_of_matrix.scale(1. / this -> DELTA);
      // the 3D object that represents the Jacobian of the mass matrix
      jacmatrix.push_back(copy_of_matrix);
    }
    // evaluate the jacabian of mass contribution
    for(unsigned i = 0; i < this -> ORDER_OF_SYSTEM; ++i) {
      for(unsigned j = 0; j < this -> ORDER_OF_SYSTEM; ++j) {
        h(i, j) = Utility::dot(jacmatrix[ j ][ i ], vec);
      }
    }
  }

◆ matrix0() [1/2]

template<typename _Type , typename _Xtype >

const DenseMatrix< _Type > & CppNoddy::Equation_1matrix< _Type, _Xtype >::matrix0

inline

Return a handle to the matrix.

Definition at line 66 of file Equation_1matrix.h.

                                                                                  {
    return MATRIX0_AT_LAST_STATE;
  }

◆ matrix0() [2/2]

template<typename _Type , typename _Xtype = double>

virtual void CppNoddy::Equation_1matrix< _Type, _Xtype >::matrix0	(	const DenseVector< _Type > &	x,
		DenseMatrix< _Type > &	m
	)		const

inlineprotectedvirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Definition at line 51 of file Equation_1matrix.h.

                                                                                   {
      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);
    }

◆ update()

template<typename _Type , typename _Xtype >

void CppNoddy::Equation_1matrix< _Type, _Xtype >::update ( const DenseVector< _Type > & state )

Update the Equation object for the current set of state variables.

Parameters

state The state vector at which to set the equation object

Definition at line 50 of file Equation_1matrix.cpp.

                                                                              {
    // use the base class update to set LAST_STATE, FN_AT_LAST_STATE and JAC_AT_LAST_STATE
    Residual_with_coords<_Type, _Xtype>::update(state);
    // this has TIME ifdef to go after the base class update - otherwise we'll be
    // resuming the timer twice in a row
#ifdef TIME
    this -> T_UPDATER.start();
#endif
    // now we deal with the mass matrix separately to set MATRIX0_AT_LAST_STATE
    // and JAC_OF_MATRIX
    matrix0(state, MATRIX0_AT_LAST_STATE);
#ifdef TIME
    this -> T_UPDATER.stop();
#endif
  }

References CppNoddy::Residual< _Type >::update().

Referenced by CppNoddy::Equation_2matrix< _Type, double >::Equation_2matrix().

The documentation for this class was generated from the following files:

include/Equation_1matrix.h
src/Equation_1matrix.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Equation_1matrix()

◆ ~Equation_1matrix()

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

◆ matrix0() [1/2]

◆ matrix0() [2/2]

◆ update()