EC2D1T3 Class Reference

Eddy current problems in 2-D domains using solenoidal approximation. More...

#include <EC2D1T3.h>

Inheritance diagram for EC2D1T3:

Public Member Functions
	EC2D1T3 ()
	Default constructor.
	EC2D1T3 (Mesh &ms)
	Constructor using mesh.
	EC2D1T3 (Mesh &ms, Vect< real_t > &u)
	Constructor using mesh and solution vector.
	~EC2D1T3 ()
	Destructor.
void	setData (real_t omega, real_t volt)
	Define data for equation.
void	build ()
	Build the linear system of equations.
void	Magnetic (real_t coef=1.)
	Add magnetic contribution to matrix.
void	Electric (real_t coef=1.)
	Add electric contribution to matrix.
real_t	Joule ()
	Compute Joule density in element.
void	IntegMF (real_t &vr, real_t &vi)
	Add element integral contribution.
void	IntegND (const Vect< real_t > &h, real_t &vr, real_t &vi)
	Compute integral of normal derivative on edge.
real_t	VacuumArea ()
	Add contribution to vacuum area calculation.
Public Member Functions inherited from Equation< NEN_, NEE_, NSN_, NSE_ >
	Equation ()
	Equation (Mesh &mesh)
	Constructor with mesh instance.
	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector.
	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.
	~Equation ()
	Destructor.
void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.
void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.
void	LocalNodeVector (Vect< real_t > &b)
	Localize element vector from a Vect instance.
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize element vector from a Vect instance.
void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize side vector from a Vect instance.
void	SideSideVector (const Vect< real_t > &b, vector< real_t > &bs)
	Localize side vector from a Vect instance.
void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance.
void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance.
void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance.
void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize element vector.
void	SideVector (const Vect< real_t > &b, vector< real_t > &sb)
	Localize side vector.
void	ElementNodeCoordinates ()
	Localize coordinates of element nodes.
void	SideNodeCoordinates ()
	Localize coordinates of side nodes.
void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one.
void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one.
void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one.
void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.
void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.
void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one.
void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one.
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.
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.
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.
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.
LinearSolver &	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.
void	setMatrixType (int t)
	Choose type of matrix.
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.
int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side.
void	LinearSystemInfo ()
	Print info on linear system solver.

Additional Inherited Members
Protected Member Functions inherited from Equa_Electromagnetics< 3, 6, 2, 4 >
void	MagneticPermeability (const real_t &mu)
	Set (constant) magnetic permeability.
void	MagneticPermeability (const string &exp)
	Set magnetic permeability given by an algebraic expression.
void	ElectricConductivity (const real_t &sigma)
	Set (constant) electric conductivity.
void	ElectricConductivity (const string &exp)
	set electric conductivity given by an algebraic expression
void	setMaterial ()
	Set material properties.

Detailed Description

Eddy current problems in 2-D domains using solenoidal approximation.

Builds finite element arrays for time harmonic eddy current problems in 2-D domains with solenoidal configurations (Magnetic field has only one nonzero component). Magnetic field is constant in the vacuum, and then zero in the outer vacuum.
Uses 3-Node triangles.

The unknown is the time-harmonic magnetic induction (complex valued) but stored in 2-degree of freedom real-valued vector. Therefore, mesh must be defined with 2 degrees of freedom per node

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Constructor & Destructor Documentation

EC2D1T3() [1/2]

EC2D1T3

(

Mesh &

ms

)

Constructor using mesh.

Parameters

[in]

ms

Mesh instance

EC2D1T3() [2/2]

EC2D1T3	(	Mesh &	ms,
		Vect< real_t > &	u
	)

Constructor using mesh and solution vector.

Parameters

[in]	ms	Mesh instance
[in,out]	u	Reference to solution vector instance

Member Function Documentation

build()

void build

(

)

Build the linear system of equations.

Before using this function, one must have properly selected appropriate options for:

• The choice of a steady state or transient analysis. By default, the analysis is stationary
• In the case of transient analysis, the choice of a time integration scheme and a lumped or consistent capacity matrix. If transient analysis is chosen, the lumped capacity matrix option is chosen by default, and the implicit Euler scheme is used by default for time integration.

Electric()

void Electric

(

real_t

coef = 1.

)

Add electric contribution to matrix.

Parameters

[in]

coef

Coefficient to multiply by [Default: 1]

IntegND()

void IntegND	(	const Vect< real_t > &	h,
		real_t &	vr,
		real_t &	vi
	)

Compute integral of normal derivative on edge.

Parameters

[in]	h	Vect instance containing magnetic field at nodes
[in]	vr	Real part of the integral
[in]	vi	Imaginary part of the integral

Note

This member function is to be called within each element, it detects boundary sides as the ones with nonzero code

Magnetic()

void Magnetic

(

real_t

coef = 1.

)

Add magnetic contribution to matrix.

Parameters

[in]

coef

Coefficient to multiply by [Default: 1]

setData()

void setData	(	real_t	omega,
		real_t	volt
	)

Define data for equation.

Parameters

[in]	omega	Angular frequency
[in]	volt	Voltage