Equation< NEN_, NEE_, NSN_, NSE_ > Class Template Reference

Abstract class for all equation classes. More...

#include <Equation.h>

Inheritance diagram for Equation< NEN_, NEE_, NSN_, NSE_ >:

Public Member Functions
	Equation ()
	Equation (Mesh &mesh)
	Constructor with mesh instance. More...
	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector. More...
	Equation (Mesh &mesh, Vect< real_t > &u, real_t &init_time, real_t &final_time, real_t &time_step)
	Constructor with mesh instance, matrix and right-hand side. More...
	~Equation ()
	Destructor.
void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions. More...
void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique. More...
void	LocalNodeVector (Vect< real_t > &b)
	Localize Element Vector from a Vect instance. More...
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize Element Vector from a Vect instance. More...
void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize Side Vector from a Vect instance. More...
void	SideSideVector (const Vect< real_t > &b, std::valarray< real_t > &bs)
	Localize Side Vector from a Vect instance. More...
void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance. More...
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance. More...
void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance. More...
void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize Element Vector. More...
void	SideVector (const Vect< real_t > &b, std::valarray< real_t > &sb)
	Localize Side Vector. More...
void	ElementNodeCoordinates ()
	Localize coordinates of element nodes. More...
void	SideNodeCoordinates ()
	Localize coordinates of side nodes. More...
void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one. More...
void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one. More...
void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one. More...
void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one. More...
void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one. More...
void	AxbAssembly (const Element &el, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of element matrix by element vector into global vector. More...
void	AxbAssembly (const Side &sd, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of side matrix by side vector into global vector. More...
size_t	getNbNodes () const
	Return number of element nodes.
size_t	getNbEq () const
	Return number of element equations.
real_t	setMaterialProperty (const string &exp, const string &prop)
	Define a material property by an algebraic expression. More...
Public Member Functions inherited from Equa
	Equa ()
	Default constructor.
virtual	~Equa ()
	Destructor.
void	setMesh (Mesh &m)
	Define mesh and renumber DOFs after removing imposed ones.
Mesh &	getMesh () const
	Return reference to Mesh instance. More...
LinearSolver< real_t > &	getLinearSolver ()
	Return reference to linear solver instance.
Matrix< real_t > *	getMatrix () const
	Return pointer to matrix.
void	setSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
	Choose solver for the linear system. More...
void	setLinearSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
	Choose solver for the linear system. More...
void	setMatrixType (int t)
	Choose type of matrix. More...
int	solveLinearSystem (Matrix< real_t > *A, Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given matrix and right-hand side. More...
int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side. More...

Detailed Description

template<size_t NEN_, size_t NEE_, size_t NSN_, size_t NSE_>
class OFELI::Equation< NEN_, NEE_, NSN_, NSE_ >

Abstract class for all equation classes.

Template Arguments:

• NEN_ : Number of element nodes
• NEE_ : Number of element equations
• NSN_ : Number of side nodes
• NSN_ : Number of side equations

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Constructor & Destructor Documentation

Equation() [1/4]

Equation

(

)

Default constructor. Constructs an "empty" equation

Equation() [2/4]

Equation

(

Mesh &

mesh

)

Constructor with mesh instance.

Parameters

[in]

mesh

Mesh instance

Equation() [3/4]

Equation	(	Mesh &	mesh,
		Vect< real_t > &	u
	)

Constructor with mesh instance and solution vector.

Parameters

[in]	mesh	Mesh instance
[in]	u	Vect instance containing solution.

Equation() [4/4]

Equation	(	Mesh &	mesh,
		Vect< real_t > &	u,
		real_t &	init_time,
		real_t &	final_time,
		real_t &	time_step
	)

Constructor with mesh instance, matrix and right-hand side.

Parameters

[in]	mesh	Mesh instance
[in]	u	Vect instance containing Right-hand side.
[in]	init_time	Initial Time value
[in]	final_time	Final Time value
[in]	time_step	Time step value

Member Function Documentation

AxbAssembly() [1/2]

void AxbAssembly	(	const Element &	el,
		const Vect< real_t > &	x,
		Vect< real_t > &	b
	)

Assemble product of element matrix by element vector into global vector.

Parameters

[in]	el	Reference to Element instance
[in]	x	Global vector to multiply by (Vect instance)
[out]	b	Global vector to add (Vect instance)

AxbAssembly() [2/2]

void AxbAssembly	(	const Side &	sd,
		const Vect< real_t > &	x,
		Vect< real_t > &	b
	)

Assemble product of side matrix by side vector into global vector.

Parameters

[in]	sd	Reference to Side instance
[in]	x	Global vector to multiply by (Vect instance)
[out]	b	Global vector (Vect instance)

DGElementAssembly() [1/5]

void DGElementAssembly

(

Matrix< real_t > *

A

)

Assemble element matrix into global one for the Discontinuous Galerkin approximation.

Parameters

A	Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)

Warning

The element pointer is given by the global variable theElement

DGElementAssembly() [2/5]

void DGElementAssembly

(

SkMatrix< real_t > &

A

)

Assemble element matrix into global one for the Discontinuous Galerkin approximation.

Parameters

[in]

A

Global matrix stored as an SkMatrix instance

Warning

The element pointer is given by the global variable theElement

DGElementAssembly() [3/5]

void DGElementAssembly

(

SkSMatrix< real_t > &

A

)

Assemble element matrix into global one for the Discontinuous Galerkin approximation.

Parameters

A	Global matrix stored as an SkSMatrix instance

Warning

The element pointer is given by the global variable theElement

DGElementAssembly() [4/5]

void DGElementAssembly

(

SpMatrix< real_t > &

A

)

Assemble element matrix into global one for the Discontinuous Galerkin approximation.

Parameters

[in]

A

Global matrix stored as an SpMatrix instance

Warning

The element pointer is given by the global variable theElement

DGElementAssembly() [5/5]

void DGElementAssembly

(

TrMatrix< real_t > &

A

)

Assemble element matrix into global one for the Discontinuous Galerkin approximation.

Parameters

[in]

A

Global matrix stored as an TrMatrix instance

Warning

The element pointer is given by the global variable theElement

DiagBC()

void DiagBC	(	DOFSupport	dof_type = NODE_DOF,
		int	dof = 0
	)

Update element matrix to impose bc by diagonalization technique.

Parameters

[in]	dof_type	DOF type option. To choose among the enumerated values: NODE_DOF, DOFs are supported by nodes [Default] ELEMENT_DOF, DOFs are supported by elements SIDE_DOF, DOFs are supported by sides
[in]	dof	DOF setting: = 0, All DOFs are taken into account [Default] != 0, Only DOF No. dof is handled in the system

ElementAssembly() [1/7]

void ElementAssembly

(

BMatrix< real_t > &

A

)

Assemble element matrix into global one.

Parameters

A	Global matrix stored as a BMatrix instance

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [2/7]

void ElementAssembly

(

Matrix< real_t > *

A

)

Assemble element matrix into global one.

Parameters

A	Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [3/7]

void ElementAssembly

(

SkMatrix< real_t > &

A

)

Assemble element matrix into global one.

Parameters

[in]

A

Global matrix stored as an SkMatrix instance

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [4/7]

void ElementAssembly

(

SkSMatrix< real_t > &

A

)

Assemble element matrix into global one.

Parameters

A	Global matrix stored as an SkSMatrix instance

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [5/7]

void ElementAssembly

(

SpMatrix< real_t > &

A

)

Assemble element matrix into global one.

Parameters

[in]

A

Global matrix stored as an SpMatrix instance

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [6/7]

void ElementAssembly

(

TrMatrix< real_t > &

A

)

Assemble element matrix into global one.

Parameters

[in]

A

Global matrix stored as an TrMatrix instance

Warning

The element pointer is given by the global variable theElement

ElementAssembly() [7/7]

void ElementAssembly

(

Vect< real_t > &

v

)

Assemble element vector into global one.

Parameters

[in]

v

Global vector (Vect instance)

Warning

The element pointer is given by the global variable theElement

ElementNodeCoordinates()

void ElementNodeCoordinates

(

)

Localize coordinates of element nodes.

Coordinates are stored in array _x[0], _x[1], ... which are instances of class Point<real_t>

Remarks

This member function uses the Side pointer _theSide

ElementNodeVector() [1/2]

void ElementNodeVector	(	const Vect< real_t > &	b,
		LocalVect< real_t, NEE_ > &	be
	)

Localize Element Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	be	Local vector, the length of which is the total number of element equations.

Remarks

All degrees of freedom are transferred to the local vector

ElementNodeVector() [2/2]

void ElementNodeVector	(	const Vect< real_t > &	b,
		LocalVect< real_t, NEN_ > &	be,
		int	dof
	)

Localize Element Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	be	Local vector, the length of which is the total number of element equations.
[in]	dof	Degree of freedom to transfer to the local vector

Remarks

Only yhe dega dof is transferred to the local vector

ElementNodeVectorSingleDOF()

void ElementNodeVectorSingleDOF	(	const Vect< real_t > &	b,
		LocalVect< real_t, NEN_ > &	be
	)

Localize Element Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	be	Local vector, the length of which is the total number of element equations.

Remarks

Vector b is assumed to contain only one degree of freedom by node.

ElementSideVector()

void ElementSideVector	(	const Vect< real_t > &	b,
		LocalVect< real_t, NSE_ > &	be
	)

Localize Element Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	be	Local vector, the length of which is

ElementVector()

void ElementVector	(	const Vect< real_t > &	b,
		DOFSupport	dof_type = NODE_DOF,
		int	flag = 0
	)

Localize Element Vector.

Parameters

[in]	b	Global vector to be localized
[in]	dof_type	DOF type option. To choose among the enumerated values: NODE_DOF, DOFs are supported by nodes [Default] ELEMENT_DOF, DOFs are supported by elements SIDE_DOF, DOFs are supported by sides
[in]	flag	Option to set: = 0, All DOFs are taken into account [Default] != 0, Only DOF number dof is handled in the system The resulting local vector can be accessed by attribute ePrev.

Remarks

This member function is to be used if a constructor with Element was invoked. It uses the Element pointer _theElement

LocalNodeVector()

void LocalNodeVector

(

Vect< real_t > &

b

)

Localize Element Vector from a Vect instance.

Parameters

[in]

b

Reference to global vector to be localized. The resulting local vector can be accessed by attribute ePrev. This member function is to be used if a constructor with Element was invoked.

setMaterialProperty()

real_t setMaterialProperty	(	const string &	exp,
		const string &	prop
	)

Define a material property by an algebraic expression.

Parameters

[in]	exp	Algebraic expression
[in]	prop	Property name

Returns

Return value in expression evaluation:

• =0, Normal evaluation
• !=0, An error message is displayed

SideAssembly() [1/5]

void SideAssembly

(

Matrix< real_t > *

A

)

Assemble side (edge or face) matrix into global one.

Parameters

A	Pointer to global matrix (abstract class: can be any of classes SkSMatrix, SkMatrix, SpMatrix)

Warning

The side pointer is given by the global variable theSide

SideAssembly() [2/5]

void SideAssembly

(

SkMatrix< real_t > &

A

)

Assemble side (edge or face) matrix into global one.

Parameters

[in]

A

Global matrix stored as an SkMatrix instance

Warning

The side pointer is given by the global variable theSide

SideAssembly() [3/5]

void SideAssembly

(

SkSMatrix< real_t > &

A

)

Assemble side (edge or face) matrix into global one.

Parameters

[in]

A

Global matrix stored as an SkSMatrix instance

Warning

The side pointer is given by the global variable theSide

SideAssembly() [4/5]

void SideAssembly

(

SpMatrix< real_t > &

A

)

Assemble side (edge or face) matrix into global one.

Parameters

[in]

A

Global matrix stored as an SpMatrix instance

Warning

The side pointer is given by the global variable theSide

SideAssembly() [5/5]

void SideAssembly

(

Vect< real_t > &

v

)

Assemble side (edge or face) vector into global one.

Parameters

[in]

v

Global vector (Vect instance)

Warning

The side pointer is given by the global variable theSide

SideNodeCoordinates()

void SideNodeCoordinates

(

)

Localize coordinates of side nodes.

Coordinates are stored in array _x[0], _x[1], ... which are instances of class Point<real_t>

Remarks

This member function uses the Element pointer _theElement

SideNodeVector()

void SideNodeVector	(	const Vect< real_t > &	b,
		LocalVect< real_t, NSE_ > &	bs
	)

Localize Side Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	bs	Local vector, the length of which is the total number of side equations.

Remarks

All degrees of freedom are transferred to the local vector

SideSideVector()

void SideSideVector	(	const Vect< real_t > &	b,
		std::valarray< real_t > &	bs
	)

Localize Side Vector from a Vect instance.

Parameters

[in]	b	Global vector to be localized.
[out]	bs	Local constant value of vector at given side.

Remarks

All degrees of freedom are transferred to the local vector

SideVector()

void SideVector	(	const Vect< real_t > &	b,
		std::valarray< real_t > &	sb
	)

Localize Side Vector.

Parameters

[in]	b	Global vector to be localized NODE_DOF, DOFs are supported by nodes [ default ] ELEMENT_DOF, DOFs are supported by elements SIDE_DOF, DOFs are supported by sides BOUNDARY_SIDE_DOF, DOFs are supported by boundary sides
[out]	sb	Array in which local vector is stored The resulting local vector can be accessed by attribute ePrev.

Remarks

This member function is to be used if a constructor with Side was invoked. It uses the Side pointer _theSide

updateBC()

void updateBC	(	const Element &	el,
		const Vect< real_t > &	bc
	)

Update Right-Hand side by taking into account essential boundary conditions.

Parameters

[in]	el	Reference to current element instance
[in]	bc	Vector that contains imposed values at all DOFs