Tool kit for the Whitney-1 (Nedelec) based FE discretization of the rot-rot operators. More...

#include <nedelec_local_ass.h>

Public Types
typedef TDomain::grid_type	grid_type
	type of the grid More...

typedef TDomain::position_type	position_type
	type of the geometric positions (WDim-vectors) More...

typedef reference_element_traits< TElem >::reference_element_type	ref_elem_type
	type of reference element More...

typedef LagrangeP1< ref_elem_type >	W0_shapes_type
	shapes and derivatives of the Whitney-0 (Lagrange P1) shape functions More...

Static Public Member Functions
static void	curl (const TDomain domain, TElem elem, const position_type *corners, const number dofs[], MathVector< WDim > &curl_vec)
	computes the curl of the grid functions (in 2d represented as \((z, 0)\) instead of \((0, 0, z)\)) More...

static void	get_shapes (const TDomain domain, TElem elem, const position_type *corners, const MathVector< dim > local, MathVector< WDim > shapes[])
	computes the Nedelec shapes at a given point More...

static void	interpolate (const TDomain domain, TElem elem, const position_type *corners, const number dofs[], const MathVector< dim > local[], const size_t n_pnt, MathVector< WDim > values[])
	computes of the values of the grid functions More...

static void	local_div_matrix (const TDomain domain, TElem elem, const position_type *corners, number B[][numEdges])
	assembles the discrete weak div operator More...

static void	local_mass (const TDomain domain, TElem elem, const position_type *corners, number M[maxNumEdges][maxNumEdges])
	assembles the local mass matrix of the Nedelec elements More...

static void	local_stiffness_and_mass (const TDomain domain, TElem elem, const position_type *corners, number S[maxNumEdges][maxNumEdges], number M[maxNumEdges][maxNumEdges])
	assembles the local stiffness and the mass matrices of the rot-rot operator More...

Static Public Attributes
static const int	dim = ref_elem_type::dim
	dimension of reference element More...

static const size_t	maxNumEdges = (size_t) element_list_traits<typename domain_traits<WDim>::DimElemList>::maxEdges
	max. number of the edges of the full-dimensional elements in the domain More...

static const size_t	numCorners = ref_elem_type::numCorners
	total number of the corners More...

static const size_t	numEdges = ref_elem_type::numEdges
	total number of the edges More...

static const int	WDim = TDomain::dim
	world dimention More...

Detailed Description

template<typename TDomain, typename TElem>
class ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >

Tool kit for the Whitney-1 (Nedelec) based FE discretization of the rot-rot operators.

Class for the local discretization of the rot-rot operator using the Nedelec-type-1 (Whitney-1) elements. This class may not contain any member except for static functions, so no instances of this class need to be created.

This basic class template does not contain any numerical algorithms as they are specific for different types of the elements. Cf. the specializations for simplices (

See also: NedelecT1_LDisc_forSimplex).

Remarks: Note that the definition of the Whitney-1 function depends on the ordering of the nodes in the element. More precisely, for a different ordering, the shape function \(w^{(1)}_e\) may have a different sign. Thus, the ordering should be consistent in all the elements: If two elements \(T_1\) and \(T_2\) share the edge \(e\) with the ends at corners \(i\) and \(j\) (that are shared, too) then this edge should be \(e = (i, j)\) for both the elements (and not for example \(e = (i, j)\) for \(T_1\) but \(e = (j, i)\) for \(T_2\)). In all the other respects, the ordering does not play any essential role. In particular, the singes of the degrees of freedom in the solution depend on the global ordering of the corners (but the absolute values of these dofs are invariant). For this, the solution of the discretized system may be only considered in connection with the given ordering of the corners (in the edges).

Member Typedef Documentation

◆ grid_type

template<typename TDomain , typename TElem >

typedef TDomain::grid_type ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::grid_type

type of the grid

◆ position_type

template<typename TDomain , typename TElem >

typedef TDomain::position_type ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::position_type

type of the geometric positions (WDim-vectors)

◆ ref_elem_type

template<typename TDomain , typename TElem >

typedef reference_element_traits<TElem>::reference_element_type ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::ref_elem_type

type of reference element

◆ W0_shapes_type

template<typename TDomain , typename TElem >

typedef LagrangeP1<ref_elem_type> ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::W0_shapes_type

shapes and derivatives of the Whitney-0 (Lagrange P1) shape functions

Member Function Documentation

◆ curl()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::curl	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		const number	dofs[],
		MathVector< WDim > &	curl_vec
	)

inlinestatic

computes the curl of the grid functions (in 2d represented as \((z, 0)\) instead of \((0, 0, z)\))

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[in]	dofs	arrays of values of the Nedelec degrees of freedom
[out]	curl_vec	where to store the computed curl

References UG_THROW.

Referenced by ug::Electromagnetism::NedelecInterpolation< TDomain, 2, 2 >::curl(), ug::Electromagnetism::NedelecInterpolation< TDomain, 3, 3 >::curl(), and ug::Electromagnetism::NedelecInterpolation< TDomain, 3, 3 >::curl_flux().

◆ get_shapes()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::get_shapes	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		const MathVector< dim >	local,
		MathVector< WDim >	shapes[]
	)

inlinestatic

computes the Nedelec shapes at a given point

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[in]	local	local coordinates of the point where to compute
[out]	shapes	array for the shapes

References UG_THROW.

Referenced by ug::Electromagnetism::NedelecProlongationMatrixHelper< TDomain, TAlgebra, TElem >::assemble_prolongation_matrix().

◆ interpolate()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::interpolate	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		const number	dofs[],
		const MathVector< dim >	local[],
		const size_t	n_pnt,
		MathVector< WDim >	values[]
	)

inlinestatic

computes of the values of the grid functions

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[in]	dofs	arrays of values of the Nedelec degrees of freedom
[in]	local	local coordinates of the points where to compute
[in]	n_pnt	number of the points where to compute
[out]	values	where to store the computed n_pnt values

References UG_THROW.

Referenced by ug::Electromagnetism::NedelecInterpolation< TDomain, 2, 2 >::value(), and ug::Electromagnetism::NedelecInterpolation< TDomain, 3, 3 >::value().

◆ local_div_matrix()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::local_div_matrix	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		number	B[][numEdges]
	)

inlinestatic

assembles the discrete weak div operator

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[out]	B	local weak divergence operator matrix

References UG_THROW.

Referenced by ug::Electromagnetism::NedelecProject< TDomain, TAlgebra >::weak_div_elem_type().

◆ local_mass()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::local_mass	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		number	M[maxNumEdges][maxNumEdges]
	)

inlinestatic

assembles the local mass matrix of the Nedelec elements

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[out]	M	local mass matrix

References UG_THROW.

Referenced by ug::Electromagnetism::CalcVolPowerElemHelperClass< TGridFunc, TElem >::calc_elem_power().

◆ local_stiffness_and_mass()

template<typename TDomain , typename TElem >

static void ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::local_stiffness_and_mass	(	const TDomain *	domain,
		TElem *	elem,
		const position_type *	corners,
		number	S[maxNumEdges][maxNumEdges],
		number	M[maxNumEdges][maxNumEdges]
	)

inlinestatic

assembles the local stiffness and the mass matrices of the rot-rot operator

Parameters

[in]	domain	the domain
[in]	elem	element
[in]	corners	array of the global corner coordinates
[out]	S	local stiffness matrix
[out]	M	local mass matrix

References UG_THROW.

Referenced by ug::Electromagnetism::EddyCurrent_E_Nedelec< TDomain, TAlgebra >::prepare_element().

Member Data Documentation

◆ dim

template<typename TDomain , typename TElem >

const int ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::dim = ref_elem_type::dim

static

dimension of reference element

◆ maxNumEdges

template<typename TDomain , typename TElem >

const size_t ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::maxNumEdges = (size_t) element_list_traits<typename domain_traits<WDim>::DimElemList>::maxEdges

static

max. number of the edges of the full-dimensional elements in the domain

◆ numCorners

template<typename TDomain , typename TElem >

const size_t ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::numCorners = ref_elem_type::numCorners

static

total number of the corners

◆ numEdges

template<typename TDomain , typename TElem >

const size_t ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::numEdges = ref_elem_type::numEdges

static

total number of the edges

◆ WDim

template<typename TDomain , typename TElem >

const int ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >::WDim = TDomain::dim

static

world dimention

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

/home/runner/work/docs/docs/ug4/plugins/Electromagnetism/nedelec_local_ass.h

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename TDomain, typename TElem> class ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >

Member Typedef Documentation

◆ grid_type

◆ position_type

◆ ref_elem_type

◆ W0_shapes_type

Member Function Documentation

◆ curl()

◆ get_shapes()

◆ interpolate()

◆ local_div_matrix()

◆ local_mass()

◆ local_stiffness_and_mass()

Member Data Documentation

◆ dim

◆ maxNumEdges

◆ numCorners

◆ numEdges

◆ WDim

template<typename TDomain, typename TElem>
class ug::Electromagnetism::NedelecT1_LDisc< TDomain, TElem >