Inheritance diagram for CppNoddy::Example::nonlinear:

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

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define a nonlinear advection diffusion problem. More...

void	matrix0 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Define the BVP terms. More...

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

void	matrix2 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Define the unsteady terms by providing the mass matrix for x evolution. More...

void	jacobian (const DenseVector< double > &z, DenseMatrix< double > &jac) const
	Provide the exact Jacobian rather than using finite-differences. More...

void	get_jacobian_of_matrix0_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &h) const

void	get_jacobian_of_matrix1_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &h) const

void	get_jacobian_of_matrix2_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...

	nonlinear ()
	The problem is 2nd order and real. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define a nonlinear advection diffusion problem. More...

void	matrix0 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Define the unsteady terms by providing the mass matrix for t evolution. More...

void	matrix1 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Providing the matrix for t evolution. More...

void	matrix2 (const DenseVector< double > &z, DenseMatrix< double > &m) const
	Providing the matrix for x evolution. More...

Public Member Functions inherited from CppNoddy::Equation_3matrix< double >
	Equation_3matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_3matrix ()
	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 > &	matrix2 () const
	Return a handle to the matrix member data. More...

virtual void	get_jacobian_of_matrix2_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_2matrix< _Type, _Xtype >
	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< _Type > &state)
	Update the Equation object for the current set of state variables. More...

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

virtual void	get_jacobian_of_matrix1_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::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	matrix2 (const DenseVector< double > &state, DenseMatrix< double > &m) const
	Define the matrix for the current state vector. More...

Protected Member Functions inherited from CppNoddy::Equation_2matrix< _Type, _Xtype >
virtual void	matrix1 (const DenseVector< _Type > &state, DenseMatrix< _Type > &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 33 of file IBVPNonlinearFast.cpp.

Constructor & Destructor Documentation

◆ nonlinear() [1/2]

CppNoddy::Example::nonlinear::nonlinear ( )

inline

The problem is 2nd order and real.

Definition at line 37 of file IBVPNonlinearFast.cpp.

37: Equation_3matrix<double> ( 2 ) {}

CppNoddy::Equation_3matrix

An equation object base class used in the PDE_double_IBVP class.

Definition: Equation_3matrix.h:21

◆ nonlinear() [2/2]

CppNoddy::Example::nonlinear::nonlinear ( )

inline

The problem is 2nd order and real.

Definition at line 35 of file IBVPNonlinearSlower.cpp.

35: Equation_3matrix<double> ( 2 ) {}

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

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

inline

Definition at line 75 of file IBVPNonlinearFast.cpp.

      {
        // constant matrix
      }

◆ get_jacobian_of_matrix1_mult_vector()

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

inline

Definition at line 79 of file IBVPNonlinearFast.cpp.

      {
        h( 1, U ) = - vec[ 0 ];
      }

References h, and U.

◆ get_jacobian_of_matrix2_mult_vector()

void CppNoddy::Example::nonlinear::get_jacobian_of_matrix2_mult_vector	(	const DenseVector< double > &	state,
		const DenseVector< double > &	vec,
		DenseMatrix< double > &	h
	)		const

inlinevirtual

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

Reimplemented from CppNoddy::Equation_3matrix< double >.

Definition at line 83 of file IBVPNonlinearFast.cpp.

      {
        // constant matrix
      }

◆ jacobian()

void CppNoddy::Example::nonlinear::jacobian	(	const DenseVector< double > &	z,
		DenseMatrix< double > &	jac
	)		const

inline

Provide the exact Jacobian rather than using finite-differences.

Definition at line 71 of file IBVPNonlinearFast.cpp.

      {
        jac( 0, Ud ) = 1.0;
      }

References Ud.

◆ matrix0() [1/2]

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

inline

Define the BVP terms.

Definition at line 49 of file IBVPNonlinearFast.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

◆ matrix0() [2/2]

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

inline

Define the unsteady terms by providing the mass matrix for t evolution.

Definition at line 46 of file IBVPNonlinearSlower.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

◆ matrix1() [1/2]

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

inline

Define the unsteady terms by providing the mass matrix for t evolution.

Definition at line 55 of file IBVPNonlinearFast.cpp.

      {
        // eqn 1 variable 0
        m( 1, 0 ) = -1.0;
      }

References m.

◆ matrix1() [2/2]

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

inline

Providing the matrix for t evolution.

Definition at line 52 of file IBVPNonlinearSlower.cpp.

      {
        // eqn 1 variable 0
        m( 1, 0 ) = -1.0;
      }

References m.

◆ matrix2() [1/2]

void CppNoddy::Example::nonlinear::matrix2	(	const DenseVector< double > &	z,
		DenseMatrix< double > &	m
	)		const

inlinevirtual

Define the unsteady terms by providing the mass matrix for x evolution.

Reimplemented from CppNoddy::Equation_3matrix< double >.

Definition at line 62 of file IBVPNonlinearFast.cpp.

      {
        // eqn 1 variable 0
        m( 1, 0 ) = -z[ U ];
      }

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

◆ matrix2() [2/2]

void CppNoddy::Example::nonlinear::matrix2	(	const DenseVector< double > &	z,
		DenseMatrix< double > &	m
	)		const

inlinevirtual

Providing the matrix for x evolution.

Reimplemented from CppNoddy::Equation_3matrix< double >.

Definition at line 59 of file IBVPNonlinearSlower.cpp.

      {
        // eqn 1 variable 0
        m( 1, 0 ) = -z[ U ];
      }

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

◆ residual_fn() [1/2]

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

inline

Define a nonlinear advection diffusion problem.

Definition at line 40 of file IBVPNonlinearFast.cpp.

      {
        // The system
        f[ U ] = z[ Ud ];
        // x,y,t
        f[ Ud ] = source( coord(2), coord(0), coord(1) );
      }

References CppNoddy::Residual_with_coords< _Type, _Xtype >::coord(), f, CppNoddy::Example::source(), U, Ud, and CppNoddy::Example::z().

◆ residual_fn() [2/2]

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

inline

Define a nonlinear advection diffusion problem.

Definition at line 38 of file IBVPNonlinearSlower.cpp.

      {
        // The system
        f[ U ] = z[ Ud ];
        f[ Ud ] = source( coord(2), coord(0), coord(1) );
      }

References CppNoddy::Residual_with_coords< _Type, _Xtype >::coord(), f, CppNoddy::Example::source(), U, Ud, and CppNoddy::Example::z().

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

Tests/double_IBVP/IBVPNonlinearFast.cpp
Tests/double_IBVP/IBVPNonlinearSlower.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ nonlinear() [1/2]

◆ nonlinear() [2/2]

Member Function Documentation

◆ get_jacobian_of_matrix0_mult_vector()

◆ get_jacobian_of_matrix1_mult_vector()

◆ get_jacobian_of_matrix2_mult_vector()

◆ jacobian()

◆ matrix0() [1/2]

◆ matrix0() [2/2]

◆ matrix1() [1/2]

◆ matrix1() [2/2]

◆ matrix2() [1/2]

◆ matrix2() [2/2]

◆ residual_fn() [1/2]

◆ residual_fn() [2/2]