CppNoddy::Example::Karman_equations Class Reference

Define the Karman equations. More...

Inheritance diagram for CppNoddy::Example::Karman_equations:

Public Member Functions
	Karman_equations ()
	The Karman system is a 5th order real system of ODEs. More...
void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define the Karman system. More...
void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...
	Karman_equations ()
	The Karman system is a 5th order real system of ODEs. More...
void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define the Karman system. More...
void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...
	Karman_equations ()
	The Karman system is a 5th order real system of ODEs. More...
void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define the Karman system. More...
void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...
	Karman_equations ()
	The Karman system is a 5th order real system of ODEs. More...
void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	Define the Karman system. More...
void	jacobian (const DenseVector< double > &z, DenseMatrix< double > &jac) const
	Provide the exact Jacobian of above RHS rather than using finite-differences. More...
void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...
	Karman_equations ()
	The problem is 5th 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 BVP deriv by providing the 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_1matrix< double >
	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< double > &state)
	Update the Equation object for the current set of state variables. More...
const DenseMatrix< double > &	matrix0 () const
	Return a handle to the matrix. More...
virtual void	get_jacobian_of_matrix0_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::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...
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...

Additional Inherited Members
virtual void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &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...
virtual void	matrix1 (const DenseVector< double > &state, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...
virtual void	matrix0 (const DenseVector< _Type > &x, DenseMatrix< _Type > &m) const
	Define the matrix in terms of the current state vector. 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

Define the Karman equations.

Definition at line 27 of file BVPKarman.cpp.

Constructor & Destructor Documentation

Karman_equations() [1/5]

CppNoddy::Example::Karman_equations::Karman_equations ( )

inline

The Karman system is a 5th order real system of ODEs.

Definition at line 32 of file BVPKarman.cpp.

: Equation_1matrix<double>( 5 ) {}

Karman_equations() [2/5]

CppNoddy::Example::Karman_equations::Karman_equations ( )

inline

The Karman system is a 5th order real system of ODEs.

Definition at line 31 of file BVPKarmanAdaptive.cpp.

: Equation_1matrix<double>( 5 ) {}

Karman_equations() [3/5]

CppNoddy::Example::Karman_equations::Karman_equations ( )

inline

The Karman system is a 5th order real system of ODEs.

Definition at line 38 of file BVPKarmanArclength.cpp.

: Equation_1matrix<double>( 5 ) {}

Karman_equations() [4/5]

CppNoddy::Example::Karman_equations::Karman_equations ( )

inline

The Karman system is a 5th order real system of ODEs.

Definition at line 30 of file BVPKarmanJacobian.cpp.

: Equation_1matrix<double>( 5 ) {}

Karman_equations() [5/5]

CppNoddy::Example::Karman_equations::Karman_equations ( )

inline

The problem is 5th order and real.

Definition at line 37 of file IBVPKarman.cpp.

: Equation_2matrix<double> ( 5 ) {}

Member Function Documentation

get_jacobian_of_matrix0_mult_vector()

void CppNoddy::Example::Karman_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 62 of file IBVPKarman.cpp.

      {
        // blank definition leads to a zero result
      }

get_jacobian_of_matrix1_mult_vector()

void CppNoddy::Example::Karman_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 75 of file IBVPKarman.cpp.

      {
        // blank definition leads to a zero result
      }

jacobian()

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

inline

Provide the exact Jacobian of above RHS rather than using finite-differences.

Definition at line 44 of file BVPKarmanJacobian.cpp.

      {
        jac( 0, Ud ) = 1.0;
        jac( 1, U ) = 2 * z[ U ];
        jac( 1, Ud ) = z[ V ];
        jac( 1, V ) = z[ Ud ];
        jac( 1, W ) = -2 * z[ W ];
        jac( 2, U ) = -2.0;
        jac( 3, Wd ) = 1.0;
        jac( 4, U ) = 2 * z[ W ];
        jac( 4, V ) = z[ Wd ];
        jac( 4, W ) = 2 * z[ U ];
        jac( 4, Wd ) = z[ V ];
      }

References U, Ud, V, W, Wd, and CppNoddy::Example::z().

matrix0() [1/5]

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

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 45 of file BVPKarman.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

matrix0() [2/5]

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

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 44 of file BVPKarmanAdaptive.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

matrix0() [3/5]

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

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 51 of file BVPKarmanArclength.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

matrix0() [4/5]

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

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 59 of file BVPKarmanJacobian.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

matrix0() [5/5]

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

inlinevirtual

Define the BVP deriv by providing the matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 51 of file IBVPKarman.cpp.

      {
        // identity matrix
        m( 0, 0 ) = 1.0;
        m( 1, 1 ) = 1.0;
        m( 2, 2 ) = 1.0;
        m( 3, 3 ) = 1.0;        
        m( 4, 4 ) = 1.0;        
      }

References m.

matrix1()

void CppNoddy::Example::Karman_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 68 of file IBVPKarman.cpp.

      {
        m( 1, 0 ) = -1.0;
        m( 4, 3 ) = -1.0;
      }

References m.

residual_fn() [1/5]

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

inline

Define the Karman system.

Definition at line 35 of file BVPKarman.cpp.

      {
        // The 5th order system for ( U, U', V, W, W' )
        f[ U ] = z[ Ud ];
        f[ Ud ] = z[ U ] * z[ U ] + z[ V ] * z[ Ud ] - z[ W ] * z[ W ];
        f[ V ] = -2 * z[ U ];
        f[ W ] = z[ Wd ];
        f[ Wd ] = 2 * z[ U ] * z[ W ] + z[ V ] * z[ Wd ];
      }

References f, U, Ud, V, W, Wd, and CppNoddy::Example::z().

residual_fn() [2/5]

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

inline

Define the Karman system.

Definition at line 34 of file BVPKarmanAdaptive.cpp.

      {
        // The 5th order system for ( U, U', V, W, W' )
        f[ U ] = z[ Ud ];
        f[ Ud ] = z[ U ] * z[ U ] + z[ V ] * z[ Ud ] - z[ W ] * z[ W ];
        f[ V ] = -2 * z[ U ];
        f[ W ] = z[ Wd ];
        f[ Wd ] = 2 * z[ U ] * z[ W ] + z[ V ] * z[ Wd ];
      }

References f, U, Ud, V, W, Wd, and CppNoddy::Example::z().

residual_fn() [3/5]

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

inline

Define the Karman system.

Definition at line 41 of file BVPKarmanArclength.cpp.

      {
        // The 5th order system for ( U, U', V, W, W' )
        f[ U ] = z[ Ud ];
        f[ Ud ] = z[ U ] * z[ U ] + z[ V ] * z[ Ud ] - z[ W ] * z[ W ] + s * s;
        f[ V ] = -2 * z[ U ];
        f[ W ] = z[ Wd ];
        f[ Wd ] = 2 * z[ U ] * z[ W ] + z[ V ] * z[ Wd ];
      }

References f, CppNoddy::Example::s, U, Ud, V, W, Wd, and CppNoddy::Example::z().

residual_fn() [4/5]

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

inline

Define the Karman system.

Definition at line 33 of file BVPKarmanJacobian.cpp.

      {
        // The 5th order system for ( U, U', V, W, W' )
        f[ U ] = z[ Ud ];
        f[ Ud ] = z[ U ] * z[ U ] + z[ V ] * z[ Ud ] - z[ W ] * z[ W ];
        f[ V ] = -2 * z[ U ];
        f[ W ] = z[ Wd ];
        f[ Wd ] = 2 * z[ U ] * z[ W ] + z[ V ] * z[ Wd ];
      }

References f, U, Ud, V, W, Wd, and CppNoddy::Example::z().

residual_fn() [5/5]

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

inline

Define the Karman equations.

Definition at line 40 of file IBVPKarman.cpp.

      {
        // The 5th order system for ( U, U', V, W, W' )
        f[ 0 ] = z[ 1 ];
        f[ 1 ] = z[ 0 ] * z[ 0 ] + z[ 2 ] * z[ 1 ] - z[ 3 ] * z[ 3 ] + W_inf * W_inf;
        f[ 2 ] = -2 * z[ 0 ];
        f[ 3 ] = z[ 4 ];
        f[ 4 ] = 2 * z[ 0 ] * z[ 3 ] + z[ 2 ] * z[ 4 ];
      }

References f, CppNoddy::Example::W_inf(), and CppNoddy::Example::z().

---

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

• Tests/BVP/BVPKarman.cpp
• Tests/BVP/BVPKarmanAdaptive.cpp
• Tests/BVP/BVPKarmanArclength.cpp
• Tests/BVP/BVPKarmanJacobian.cpp
• Tests/IBVP/IBVPKarman.cpp