Inheritance diagram for CppNoddy::Example::Diffusion_equations:

Public Member Functions
	Diffusion_equations ()
	The problem is 2nd order and real. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define the Karman equations. More...

void	matrix0 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Define the domain-derivative terms by providing the mass matrix. More...

void	get_jacobian_of_matrix0_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &h) const
	To speed things up we'll overload this to say the mass matrix is constant. More...

void	matrix1 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Define the unsteady terms by providing the mass matrix. More...

void	get_jacobian_of_matrix1_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &h) const
	To speed things up we'll overload this to say the mass matrix is constant. More...

Public Member Functions inherited from CppNoddy::Equation_2matrix< double >
	Equation_2matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_2matrix ()
	An empty destructor, virtual since we have virtual methods. More...

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

const DenseMatrix< double > &	matrix1 () const
	Return a handle to the matrix member data. More...

virtual void	get_jacobian_of_matrix1_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &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::Equation_1matrix< _Type, _Xtype >
	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...

Additional Inherited Members
virtual void	matrix1 (const DenseVector< double > &state, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...

Protected Member Functions inherited from CppNoddy::Equation_1matrix< _Type, _Xtype >
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...

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

Definition at line 24 of file IBVPDiffusionNonlinear.cpp.

Constructor & Destructor Documentation

◆ Diffusion_equations()

CppNoddy::Example::Diffusion_equations::Diffusion_equations ( )

inline

The problem is 2nd order and real.

Definition at line 29 of file IBVPDiffusionNonlinear.cpp.

29: Equation_2matrix<double> ( 2 ) {}

CppNoddy::Equation_2matrix

An equation object base class used in the PDE_double_IBVP class.

Definition: Equation_2matrix.h:21

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

void CppNoddy::Example::Diffusion_equations::get_jacobian_of_matrix0_mult_vector	(	const DenseVector< double > &	state,
		const DenseVector< double > &	vec,
		DenseMatrix< double > &	h
	)		const

inline

To speed things up we'll overload this to say the mass matrix is constant.

Definition at line 50 of file IBVPDiffusionNonlinear.cpp.

      {
        // blank definition leads to a zero result
      }

◆ get_jacobian_of_matrix1_mult_vector()

void CppNoddy::Example::Diffusion_equations::get_jacobian_of_matrix1_mult_vector	(	const DenseVector< double > &	state,
		const DenseVector< double > &	vec,
		DenseMatrix< double > &	h
	)		const

inlinevirtual

To speed things up we'll overload this to say the mass matrix is constant.

Reimplemented from CppNoddy::Equation_2matrix< double >.

Definition at line 62 of file IBVPDiffusionNonlinear.cpp.

      {
        // blank definition leads to a zero result
      }

◆ matrix0()

void CppNoddy::Example::Diffusion_equations::matrix0	(	const DenseVector< double > &	z,
		DenseMatrix< double > &	m
	)		const

inline

Define the domain-derivative terms by providing the mass matrix.

Definition at line 42 of file IBVPDiffusionNonlinear.cpp.

      {
        // blank definition leads to a identity result
        m( 0, 0 ) = 1.0;
        m( 1, 1 ) = -z[ U ]/sigma;
      }

References m, CppNoddy::Example::sigma(), U, and CppNoddy::Example::z().

◆ matrix1()

void CppNoddy::Example::Diffusion_equations::matrix1	(	const DenseVector< double > &	z,
		DenseMatrix< double > &	m
	)		const

inlinevirtual

Define the unsteady terms by providing the mass matrix.

Reimplemented from CppNoddy::Equation_2matrix< double >.

Definition at line 56 of file IBVPDiffusionNonlinear.cpp.

      {
        m( 1, 0 ) = 1.0;
      }

References m.

◆ residual_fn()

void CppNoddy::Example::Diffusion_equations::residual_fn	(	const DenseVector< double > &	z,
		DenseVector< double > &	f
	)		const

inline

Define the Karman equations.

Definition at line 32 of file IBVPDiffusionNonlinear.cpp.

      { 
        double E( A*exp( -coord(1) ) );
        double Y( coord(0) );
        // we will add some source terms to give an exact solution
        f[ 0 ] = z[ Ud ];
        f[ 1 ] = -E*sin(M_PI*Y) + ((1+Y)+E*sin(M_PI*Y))*(M_PI*M_PI)*E*sin(M_PI*Y)/sigma;
      }

References CppNoddy::Example::A(), CppNoddy::Residual_with_coords< _Type, _Xtype >::coord(), E, f, CppNoddy::Example::sigma(), Ud, and CppNoddy::Example::z().

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

Tests/IBVP/IBVPDiffusionNonlinear.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Diffusion_equations()

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

◆ get_jacobian_of_matrix1_mult_vector()

◆ matrix0()

◆ matrix1()

◆ residual_fn()