#include <tetra.h>

Inheritance diagram for Tetra::Tet:

Public Member Functions
	Tet (const std::vector< Nodes::Node > &_p_node, const int _idx, const std::initializer_list< int > _i)

void	interpolation (const std::function< double(Nodes::Node)> &getter, Eigen::Ref< Eigen::Matrix< double, NPI, 1 >> result) const

void	interpolation (const std::function< Eigen::Vector3d(Nodes::Node)> &getter, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> result, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> Tx, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> Ty, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> Tz) const

void	interpolation_field (const std::function< double(Nodes::Node)> &getter, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> X) const

void	interpolation (const std::function< double(Nodes::Node, Nodes::index)> &getter, const Nodes::index idx, Eigen::Ref< Eigen::Matrix< double, Tetra::NPI, 1 >> result) const

void	lumping (const Eigen::Ref< const Eigen::Matrix< double, NPI, 1 >> alpha_eff, double prefactor, Eigen::Ref< Eigen::Matrix< double, 3 N, 3 N >> AE) const

Eigen::Matrix< double, N, N >	calcDiagBlock (const double c, const Eigen::Matrix< double, N, 1 > &x) const

Eigen::Matrix< double, N, 1 >	calcOffDiagBlock (const Nodes::index idx) const

void	DMI_bulk_OffDiag (timing const &prm_t, const double DMIbulk_bis, Eigen::Ref< Eigen::Matrix< double, 3 N, 3 N >> AE) const

void	DMI_bulk_BE (const double cst, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> U, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dUdx, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dUdy, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dUdz, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, N >> BE) const

void	add_drift_BE (const Eigen::Ref< const Eigen::Matrix< double, NPI, 1 >> alpha, double s_dt, double Vdrift, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> U, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> V, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dUd_, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dVd_, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, N >> BE) const

Eigen::Matrix< double, NPI, 1 >	calc_aniso_uniax (const Eigen::Ref< const Eigen::Vector3d > uk, const double Kbis, const double s_dt, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> U, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> V, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> H_aniso) const

Eigen::Matrix< double, NPI, 1 >	calc_aniso_cub (const Eigen::Ref< const Eigen::Matrix3d > e, const double K3bis, const double s_dt, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> U, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> V, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> H_aniso) const

Eigen::Matrix< double, Nodes::DIM, NPI >	Hst_order2_contribution (const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >> Hst, const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >> U, const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >> V) const

void	integrales (const Tetra::prm &param, const timing &prm_t, const std::function< Eigen::Matrix< double, Nodes::DIM, NPI >(void)> &calc_Hext, Nodes::index idx_dir, double Vdrift, const AbsorbingEnds &absorb)

double	exchangeEnergy (const Tetra::prm &param, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudx, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudy, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudz) const

double	DMIBulkEnergy (const Tetra::prm &param, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> u, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudx, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudy, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudz) const

double	uniaxialAnisotropyEnergy (const Tetra::prm &param, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> u) const

double	cubicAnisotropyEnergy (const Tetra::prm &param, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> u) const

Eigen::Matrix< double, Tetra::NPI, 1 >	charges (const double &Ms, const std::function< Eigen::Vector3d(const Nodes::Node &)> &getter) const override

double	demagEnergy (const Tetra::prm &param, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudx, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudy, Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> dudz, Eigen::Ref< Eigen::Matrix< double, NPI, 1 >> phi) const

double	zeemanEnergy (const Tetra::prm &param, const Eigen::Ref< const Eigen::Vector3d > Hext, const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >> u) const

double	zeemanEnergy (const Tetra::prm &param, double fieldAmp, const std::vector< Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >> &spaceField, const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >> u) const

double	Jacobian (Eigen::Ref< Eigen::Matrix3d > J) const

double	calc_vol (void) const

Eigen::Matrix< double, Nodes::DIM, NPI >	getPtGauss (void) const override

Eigen::Matrix< double, Nodes::DIM, NPI >	gradV (const std::vector< double > &V) const

Public Member Functions inherited from element< N, NPI >
	element (const std::vector< Nodes::Node > &_p_node, const int _idx, const std::initializer_list< int > &_i)

constexpr int	getN (void) const

constexpr int	getNPI (void) const

void	buildMatP (Eigen::Ref< Eigen::Matrix< double, 2 N, 3 N >> P)

void	infos (void) const

bool	existNodes (void) const

Public Attributes
Eigen::Matrix< double, N, Nodes::DIM >	da

int	idx

std::function< void(Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >> H)>	extraField

Public Attributes inherited from element< N, NPI >
std::array< int, N >	ind

int	idxPrm

Eigen::Matrix< double, NPI, 1 >	weight

Eigen::Matrix< double, 2 N, 2 N >	Kp

Eigen::Matrix< double, 2 *N, 1 >	Lp

Private Member Functions
void	orientate (void) override

Additional Inherited Members
Protected Member Functions inherited from element< N, NPI >
const Nodes::Node &	getNode (const int i) const

Detailed Description

Tet is a tetrahedron. It must not be flat. The list of its nodes is ordered in a way that enforces this spatial orientation:

0───1
│╲ ╱│
│ ╲ │
│╱ ╲│
3───2

The face (0, 1, 2) is oriented inwards: the nodes are arranged counterclockwise when seen from inside the tetrahedron. The orientation of the other faces are:

(1, 2, 3): outwards
(2, 3, 0): inwards
(3, 0, 1): outwards

Constructor & Destructor Documentation

◆ Tet()

Tetra::Tet::Tet	(	const std::vector< Nodes::Node > &	_p_node,
		const int	_idx,
		const std::initializer_list< int >	_i
	)

inline

constructor. It initializes weight hat function with weights \( w_i = |J| p_i \) with \( p_i = pds[i] = (D,E,E,E,E) \) and dad(x|y|z) if \( | detJ | < \epsilon \) jacobian is considered degenerated If NPI=1 (single Gauss point) then w[0] is the tetrahedron volume unit tests : Tet_constructor; Tet_inner_tables

Parameters

	_p_node	vector of nodes
[in]	_idx	region index in region vector
[in]	_i	node index

Member Function Documentation

◆ add_drift_BE()

void Tet::add_drift_BE	(	const Eigen::Ref< const Eigen::Matrix< double, NPI, 1 >>	alpha,
		double	s_dt,
		double	Vdrift,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	U,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	V,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dUd_,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dVd_,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, N >>	BE
	)		const

add drift contribution due to eventual recentering to vectors BE, Vdrift is the drift velocity in reduced time (physical velocity divided by gamma0), alpha is the damping at the Gauss points

◆ calc_aniso_cub()

Eigen::Matrix< double, NPI, 1 > Tet::calc_aniso_cub	(	const Eigen::Ref< const Eigen::Matrix3d >	e,
		const double	K3bis,
		const double	s_dt,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	U,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	V,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	H_aniso
	)		const

append(+=) H_aniso for cubic anisotropy contribution, returns contribution to uHeff (used to compute the stabilizing effective damping)

Parameters

[in]	e	base vectors
[in]	K3bis	cubic anisotropy coefficient
[in]	s_dt	THETA*dt
[in]	U	magnetization
[in]	V
[out]	H_aniso	effective cubic anisotropy field

◆ calc_aniso_uniax()

Eigen::Matrix< double, NPI, 1 > Tet::calc_aniso_uniax	(	const Eigen::Ref< const Eigen::Vector3d >	uk,
		const double	Kbis,
		const double	s_dt,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	U,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	V,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	H_aniso
	)		const

append(+=) H_aniso for uniaxial anisotropy contribution, returns contribution to uHeff (used to compute the stabilizing effective damping)

◆ calc_vol()

double Tet::calc_vol ( void ) const

returns volume of the tetrahedron ; unit test Tet_calc_vol

◆ calcDiagBlock()

Eigen::Matrix< double, N, N > Tet::calcDiagBlock	(	const double	c,
		const Eigen::Matrix< double, N, 1 > &	x
	)		const

computes elementary N*N matrix block returns Id⊗x + c Sum_i w_i da*transpose(da)

◆ calcOffDiagBlock()

Eigen::Matrix< double, N, 1 > Tet::calcOffDiagBlock ( const Nodes::index idx ) const

computes elementary diagonal elementary block (stored in a N vector) returns m(idx) on the nodes, with m(idx) a component of the magnetization

◆ charges()

Eigen::Matrix< double, Tetra::NPI, 1 > Tet::charges	(	const double &	Ms,
		const std::function< Eigen::Vector3d(const Nodes::Node &)> &	getter
	)		const

overridevirtual

computes volume charges, the divergence of the magnetization, returns result

Implements element< N, NPI >.

◆ cubicAnisotropyEnergy()

double Tet::cubicAnisotropyEnergy	(	const Tetra::prm &	param,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	u
	)		const

cubic anisotropy energy of the tetrahedron

◆ demagEnergy()

double Tet::demagEnergy	(	const Tetra::prm &	param,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudx,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudy,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudz,
		Eigen::Ref< Eigen::Matrix< double, NPI, 1 >>	phi
	)		const

demagnetizing energy of the tetrahedron

◆ DMI_bulk_BE()

void Tet::DMI_bulk_BE	(	const double	cst,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	U,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dUdx,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dUdy,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dUdz,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, N >>	BE
	)		const

add DMI bulk contribution to BE

◆ DMI_bulk_OffDiag()

void Tet::DMI_bulk_OffDiag	(	timing const &	prm_t,
		const double	DMIbulk_bis,
		Eigen::Ref< Eigen::Matrix< double, 3 N, 3 N >>	AE
	)		const

computes off diagonal DMI bulk contributions and add them to matrix AE

◆ DMIBulkEnergy()

double Tet::DMIBulkEnergy	(	const Tetra::prm &	param,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	u,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudx,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudy,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudz
	)		const

DMI bulk energy of the tetrahedron

◆ exchangeEnergy()

double Tet::exchangeEnergy	(	const Tetra::prm &	param,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudx,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudy,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	dudz
	)		const

exchange energy of the tetrahedron

◆ getPtGauss()

Eigen::Matrix<double,Nodes::DIM,NPI> Tetra::Tet::getPtGauss ( void ) const

inlineoverridevirtual

returns gauss points

Implements element< N, NPI >.

◆ gradV()

Eigen::Matrix< double, Nodes::DIM, NPI > Tet::gradV ( const std::vector< double > & V ) const

returns grad(V)

◆ Hst_order2_contribution()

Eigen::Matrix< double, Nodes::DIM, NPI > Tet::Hst_order2_contribution	(	const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >>	Hst,
		const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >>	U,
		const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, NPI >>	V
	)		const

return the second order term of the spin accumulation field Hst: the derivative of its tangent part in the direction V, -(U.Hst) V; and V the velocity du/dtau, both in reduced time

Parameters

[in]	Hst
[in]	U	magnetization
[in]	V

◆ integrales()

void Tet::integrales	(	const Tetra::prm &	param,
		const timing &	prm_t,
		const std::function< Eigen::Matrix< double, Nodes::DIM, NPI >(void)> &	calc_Hext,
		Nodes::index	idx_dir,
		double	Vdrift,
		const AbsorbingEnds &	absorb
	)

computes the integral contribution of the tetrahedron to the evolution of the magnetization calc_Hext is a function that returns external H field defined on gauss points, absorb are the absorbing ends of the settings, used if param.absorbing is true

◆ interpolation() [1/3]

void Tetra::Tet::interpolation	(	const std::function< double(Nodes::Node)> &	getter,
		Eigen::Ref< Eigen::Matrix< double, NPI, 1 >>	result
	)		const

inline

interpolation for scalar field : the getter function is given as a parameter in order to know what part of the node you want to interpolate If single Gauss point evaluates scalar at barycenter

◆ interpolation() [2/3]

void Tetra::Tet::interpolation	(	const std::function< double(Nodes::Node, Nodes::index)> &	getter,
		const Nodes::index	idx,
		Eigen::Ref< Eigen::Matrix< double, Tetra::NPI, 1 >>	result
	)		const

inline

interpolation for the component idx of a field : the getter function is given as a parameter in order to know what part of the node you want to interpolate

◆ interpolation() [3/3]

void Tetra::Tet::interpolation	(	const std::function< Eigen::Vector3d(Nodes::Node)> &	getter,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	result,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	Tx,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	Ty,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	Tz
	)		const

inline

interpolation for 3D vector field and a tensor : getter function is given as a parameter to know what part of the node you want to interpolate

◆ interpolation_field()

void Tetra::Tet::interpolation_field	(	const std::function< double(Nodes::Node)> &	getter,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	X
	)		const

inline

interpolation for components of a field : the getter function is given as a parameter in order to know what part of the node you want to interpolate Computes gradient at single Gauss point, constant for linear tetrahedron

◆ Jacobian()

double Tet::Jacobian ( Eigen::Ref< Eigen::Matrix3d > J ) const

Returns: \( |J| \) build Jacobian \( J \)

◆ lumping()

void Tet::lumping	(	const Eigen::Ref< const Eigen::Matrix< double, NPI, 1 >>	alpha_eff,
		double	prefactor,
		Eigen::Ref< Eigen::Matrix< double, 3 N, 3 N >>	AE
	)		const

AE matrix filling with exchange contributions, diagonal contributions and magnetization contribution AE has a block structure: ( E -Z +Y) ( +Z E -X) ( -Y +X E) E X Y Z are N*N matrices E is the sum of the exchange contribution and modified alpha (scheme stabilizer) on its diagonal X Y Z are diagonal matrices with magnetization component contributions

◆ orientate()

void Tet::orientate ( void )

overrideprivatevirtual

Enforce the correct orientation by swapping nodes if needed.

Implements element< N, NPI >.

◆ uniaxialAnisotropyEnergy()

double Tet::uniaxialAnisotropyEnergy	(	const Tetra::prm &	param,
		Eigen::Ref< Eigen::Matrix< double, Nodes::DIM, NPI >>	u
	)		const

uniaxial anisotropy energy of the tetrahedron

◆ zeemanEnergy() [1/2]

double Tet::zeemanEnergy	(	const Tetra::prm &	param,
		const Eigen::Ref< const Eigen::Vector3d >	Hext,
		const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >>	u
	)		const

zeeman energy of the tetrahedron for a constant Hext

Parameters

[in]	param
[in]	Hext	constant applied field
[in]	u

◆ zeemanEnergy() [2/2]

double Tet::zeemanEnergy	(	const Tetra::prm &	param,
		double	fieldAmp,
		const std::vector< Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >> &	spaceField,
		const Eigen::Ref< const Eigen::Matrix< double, Nodes::DIM, Tetra::NPI >>	u
	)		const

zeeman energy of the tetrahedron for a varying Hext

Parameters

[in]	param
[in]	fieldAmp	applied field amplitude, may be time dependant
[in]	spaceField	space varying applied field
[in]	u	magnetization at Gauss points

Member Data Documentation

◆ da

Eigen::Matrix<double,N,Nodes::DIM> Tetra::Tet::da

local hat functions matrix, initialized by constructor: da = dadu * inverse(Jacobian) For linear tetrahedron, gradients are constant in the element

◆ extraField

std::function<void( Eigen::Ref<Eigen::Matrix<double,Nodes::DIM,NPI>> H)> Tetra::Tet::extraField

do a += to the effective field H, to add contributions as spin transfert torque Hst

◆ idx

int Tetra::Tet::idx

idx is the index of the tetrahedron in the vector of tetrahedron

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

src/tetra.h
src/tetra.cpp

Public Member Functions

Public Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Tet()

Member Function Documentation

◆ add_drift_BE()

◆ calc_aniso_cub()

◆ calc_aniso_uniax()

◆ calc_vol()

◆ calcDiagBlock()

◆ calcOffDiagBlock()

◆ charges()

◆ cubicAnisotropyEnergy()

◆ demagEnergy()

◆ DMI_bulk_BE()

◆ DMI_bulk_OffDiag()

◆ DMIBulkEnergy()

◆ exchangeEnergy()

◆ getPtGauss()

◆ gradV()

◆ Hst_order2_contribution()

◆ integrales()

◆ interpolation() [1/3]

◆ interpolation() [2/3]

◆ interpolation() [3/3]

◆ interpolation_field()

◆ Jacobian()

◆ lumping()

◆ orientate()

◆ uniaxialAnisotropyEnergy()

◆ zeemanEnergy() [1/2]

◆ zeemanEnergy() [2/2]

Member Data Documentation

◆ da

◆ extraField

◆ idx