Class to compute the magnetic induction from the current density using the Biot-Savart formula. More...

#include <BiotSavart.h>

Public Member Functions
	BiotSavart ()
	Default constructor.

	BiotSavart (Mesh &ms)
	Constructor using mesh data.

	BiotSavart (Mesh &ms, const Vect< real_t > &J, Vect< real_t > &B, int code=0)
	Constructor using mesh and vector of real current density.

	BiotSavart (Mesh &ms, const Vect< complex_t > &J, Vect< complex_t > &B, int code=0)
	Constructor using mesh and vector of complex current density.

	~BiotSavart ()
	Destructor.

void	setCurrentDensity (const Vect< real_t > &J)
	Set (real) current density given at elements.

void	setCurrentDensity (const Vect< complex_t > &J)
	Set (real) current density given at elements.

void	setMagneticInduction (Vect< real_t > &B)
	Transmit (real) magnetic induction vector given at nodes.

void	setMagneticInduction (Vect< complex_t > &B)
	Transmit (complex) magnetic induction vector given at nodes.

void	selectCode (int code)
	Choose code of faces or edges at which current density is given.

void	setPermeability (real_t mu)
	Set the magnetic permeability coefficient.

void	setBoundary ()
	Choose to compute the magnetic induction at boundary nodes only.

Point< real_t >	getB3 (Point< real_t > x)
	Compute the real magnetic induction at a given point using the volume Biot-Savart formula.

Point< real_t >	getB2 (Point< real_t > x)
	Compute the real magnetic induction at a given point using the surface Biot-Savart formula.

Point< real_t >	getB1 (Point< real_t > x)
	Compute the real magnetic induction at a given point using the line Biot-Savart formula.

Point< complex_t >	getBC3 (Point< real_t > x)
	Compute the complex magnetic induction at a given point using the volume Biot-Savart formula.

Point< complex_t >	getBC2 (Point< real_t > x)
	Compute the complex magnetic induction at a given point using the surface Biot-Savart formula.

Point< complex_t >	getBC1 (Point< real_t > x)
	Compute the complex magnetic induction at a given point using the line Biot-Savart formula.

int	run ()
	Run the calculation by the Biot-Savart formula.

Detailed Description

Class to compute the magnetic induction from the current density using the Biot-Savart formula.

Given a current density vector given at elements, a collection of sides of edges (piecewise constant), this class enables computing the magnetic induction vector (continuous and piecewise linear) using the Ampere equation. This magnetic induction is obtained by using the Biot-Savart formula which can be either a volume, surface or line formula depending on the nature of the current density vector.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ BiotSavart() [1/3]

BiotSavart ( Mesh & ms )

Constructor using mesh data.

Parameters

[in] ms Mesh instance

◆ BiotSavart() [2/3]

BiotSavart	(	Mesh &	ms,
		const Vect< real_t > &	J,
		Vect< real_t > &	B,
		int	code = `0`
	)

Constructor using mesh and vector of real current density.

The current density is assumed piecewise constant

Parameters

[in]	ms	Mesh instance
[in]	J	Sidewise vector of current density (`J` is a real valued vector), in the case of a surface supported current
[in]	B	Nodewise vector that contains, once the member function run is used, the magnetic induction
[in]	code	Only sides with given code support current [Default: `0`]

◆ BiotSavart() [3/3]

BiotSavart	(	Mesh &	ms,
		const Vect< complex_t > &	J,
		Vect< complex_t > &	B,
		int	code = `0`
	)

Constructor using mesh and vector of complex current density.

The current density is assumed piecewise constant

Parameters

[in]	ms	Mesh instance
[in]	J	Sidewise vector of current density (`J` is a complex valued vector), in the case of a surface supported current
[in]	B	Nodewise vector that contains, once the member function run is used, the magnetic induction
[in]	code	Only sides with given `code` support current [Default: `0`]

Member Function Documentation

◆ getB1()

Point< real_t > getB1 ( Point< real_t > x )

Compute the real magnetic induction at a given point using the line Biot-Savart formula.

This function computes a real valued magnetic induction for a real valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ getB2()

Point< real_t > getB2 ( Point< real_t > x )

Compute the real magnetic induction at a given point using the surface Biot-Savart formula.

This function computes a real valued magnetic induction for a real valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ getB3()

Point< real_t > getB3 ( Point< real_t > x )

Compute the real magnetic induction at a given point using the volume Biot-Savart formula.

This function computes a real valued magnetic induction for a real valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ getBC1()

Point< complex_t > getBC1 ( Point< real_t > x )

Compute the complex magnetic induction at a given point using the line Biot-Savart formula.

This function computes a complex valued magnetic induction for a complex valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ getBC2()

Point< complex_t > getBC2 ( Point< real_t > x )

Compute the complex magnetic induction at a given point using the surface Biot-Savart formula.

This function computes a complex valued magnetic induction for a complex valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ getBC3()

Point< complex_t > getBC3 ( Point< real_t > x )

Compute the complex magnetic induction at a given point using the volume Biot-Savart formula.

This function computes a complex valued magnetic induction for a complex valued current density field

Parameters

[in] x Coordinates of point at which the magnetic induction is computed

Returns: Value of the magnetic induction at x

◆ run()

int run ( )

Run the calculation by the Biot-Savart formula.

This function computes the magnetic induction, which is stored in the vector B given in the constructor

◆ setBoundary()

void setBoundary ( )

Choose to compute the magnetic induction at boundary nodes only.

By default the magnetic induction is computed (using the function run) at all mesh nodes

Note: This function has no effect for surface of line Biot-Savart formula

◆ setCurrentDensity() [1/2]

void setCurrentDensity ( const Vect< complex_t > & J )

Set (real) current density given at elements.

The current density is assumed piecewise constant and complex valued. This function can be used in the case of the volume Biot-Savart formula.

Parameters

[in] J Current density vector (Vect instance) of complex entries

◆ setCurrentDensity() [2/2]

void setCurrentDensity ( const Vect< real_t > & J )

Set (real) current density given at elements.

The current density is assumed piecewise constant and real valued. This function can be used in the case of the volume Biot-Savart formula.

Parameters

[in] J Current density vector (Vect instance) and real entries

◆ setMagneticInduction() [1/2]

void setMagneticInduction ( Vect< complex_t > & B )

Transmit (complex) magnetic induction vector given at nodes.

Parameters

[out] B Magnetic induction vector (Vect instance) and complex entries

◆ setMagneticInduction() [2/2]

void setMagneticInduction ( Vect< real_t > & B )

Transmit (real) magnetic induction vector given at nodes.

Parameters

[out] B Magnetic induction vector (Vect instance) and real entries

◆ setPermeability()

void setPermeability ( real_t mu )

Set the magnetic permeability coefficient.

Parameters

[in] mu Magnetic permeability

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ BiotSavart() [1/3]

◆ BiotSavart() [2/3]

◆ BiotSavart() [3/3]

Member Function Documentation

◆ getB1()

◆ getB2()

◆ getB3()

◆ getBC1()

◆ getBC2()

◆ getBC3()

◆ run()

◆ setBoundary()

◆ setCurrentDensity() [1/2]

◆ setCurrentDensity() [2/2]

◆ setMagneticInduction() [1/2]

◆ setMagneticInduction() [2/2]

◆ setPermeability()