A class representing a Nedelec space for finite element methods on a structured, rectilinear grid. More...

#include <NedelecSpace.h>

Inheritance diagram for ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >:

Collaboration diagram for ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >:

Public Types
typedef FiniteElementSpace< T, Dim, numElementDOFs, ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >::indices_t	indices_t

typedef FiniteElementSpace< T, Dim, numElementDOFs, ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >::point_t	point_t

typedef FiniteElementSpace< T, Dim, numElementDOFs, ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >::vertex_points_t	vertex_points_t

typedef FieldLayout< Dim >	Layout_t

typedef detail::ViewType< T, 1 >::view_type	ViewType

typedef detail::ViewType< T, 1, Kokkos::MemoryTraits< Kokkos::Atomic > >::view_type	AtomicViewType

Public Types inherited from ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >
typedef Vector< size_t, Dim >	indices_t

typedef Vector< T, Dim >	point_t

typedef Vector< size_t, numElementVertices >	vertex_indices_t

typedef Vector< indices_t, numElementVertices >	indices_list_t

typedef Vector< point_t, numElementVertices >	vertex_points_t

Public Member Functions
	NedelecSpace (UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature, const Layout_t &layout)
	Construct a new NedelecSpace object.

	NedelecSpace (UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature)
	Construct a new NedelecSpace object (without layout) This constructor is made to work with the default constructor in FEMPoissonSolver.h such that it is compatible with alpine.

void	initialize (UniformCartesian< T, Dim > &mesh, const Layout_t &layout)
	Initialize a NedelecSpace object created with the default constructor.

void	initializeElementIndices (const Layout_t &layout)
	Initialize a Kokkos view containing the element indices.

NDIndex< Dim >	getLocalNDIndex () const
	Return the local NDIndex of this rank's subdomain.

KOKKOS_FUNCTION size_t	numGlobalDOFs () const override
	Degree of Freedom operations //////////////////////////////////////.

KOKKOS_FUNCTION size_t	getLocalDOFIndex (const size_t &elementIndex, const size_t &globalDOFIndex) const override
	Get the elements local DOF from the element index and global DOF index.

KOKKOS_FUNCTION size_t	getGlobalDOFIndex (const size_t &elementIndex, const size_t &localDOFIndex) const override
	Get the global DOF index from the element index and local DOF.

KOKKOS_FUNCTION Vector< size_t, numElementDOFs >	getLocalDOFIndices () const override
	Get the local DOF indices (vector of local DOF indices) They are independent of the specific element because it only depends on the reference element type.

KOKKOS_FUNCTION Vector< size_t, numElementDOFs >	getGlobalDOFIndices (const size_t &elementIndex) const override
	Get the global DOF indices (vector of global DOF indices) of an element.

KOKKOS_FUNCTION Vector< size_t, numElementDOFs >	getGlobalDOFIndices (const indices_t &elementIndex) const
	Get the global DOF indices (vector of global DOF indices) of an element.

KOKKOS_FUNCTION Vector< size_t, numElementDOFs >	getFEMVectorDOFIndices (const size_t &elementIndex, NDIndex< Dim > ldom) const
	Get the DOF indices (vector of indices) corresponding to the position inside the FEMVector of an element.

KOKKOS_FUNCTION Vector< size_t, numElementDOFs >	getFEMVectorDOFIndices (indices_t elementIndex, NDIndex< Dim > ldom) const
	Get the DOF indices (vector of indices) corresponding to the position inside the FEMVector of an element.

KOKKOS_FUNCTION point_t	getLocalDOFPosition (size_t localDOFIndex) const
	Get the cartesion position of a local DOF in the reference element.

KOKKOS_FUNCTION point_t	evaluateRefElementShapeFunction (const size_t &localDOF, const point_t &localPoint) const
	Basis functions and gradients /////////////////////////////////////.

KOKKOS_FUNCTION point_t	evaluateRefElementShapeFunctionCurl (const size_t &localDOF, const point_t &localPoint) const
	Evaluate the curl of the shape function of a local degree of of freedom at ta given point in the reference element.

template<typename F >
FEMVector< T >	evaluateAx (FEMVector< T > &x, F &evalFunction) const
	Assembly operations ///////////////////////////////////////////////.

FEMVector< T >	evaluateLoadVector (const FEMVector< point_t > &f) const
	Assemble the load vector b of the system Ax = b, given a field of the right hand side defined at the Nédélec DOF positions. If a functor instead of a field should be used, use the function `NedelecSpace::evaluateLoadVectorFunctor`.

template<typename F >
FEMVector< T >	evaluateLoadVectorFunctor (const F &f) const
	Assemble the load vector b of the system Ax = b, given a functional of the rhs. If a field instead of a functor should be used, use the function `NedelecSpace::evaluateLoadVector`.

FEMVector< T >	createFEMVector () const
	FEMVector conversion and creation//////////////////////////////////.

Kokkos::View< point_t * >	reconstructToPoints (const Kokkos::View< point_t * > &positions, const FEMVector< T > &coef) const
	Reconstructs function values at arbitrary points in the mesh given the Nedelec DOF coefficients.

template<typename F >
T	computeError (const FEMVector< T > &u_h, const F &u_sol) const
	Error norm computations ///////////////////////////////////////////.

KOKKOS_FUNCTION bool	isDOFOnBoundary (const size_t &dofIdx) const
	Check if a DOF is on the boundary of the mesh.

KOKKOS_FUNCTION int	getBoundarySide (const size_t &dofIdx) const
	Returns which side the boundary is on.

Public Member Functions inherited from ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >
	FiniteElementSpace (UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature)
	Construct a new FiniteElementSpace object.

void	setMesh (UniformCartesian< T, Dim > &mesh)

KOKKOS_FUNCTION size_t	numElements () const
	Mesh and Element operations ///////////////////////////////////////.

KOKKOS_FUNCTION size_t	numElementsInDim (const size_t &dim) const
	Get the number of elements in a given dimension.

KOKKOS_FUNCTION indices_t	getMeshVertexNDIndex (const size_t &vertex_index) const
	Get the NDIndex of a mesh vertex.

KOKKOS_FUNCTION size_t	getMeshVertexIndex (const indices_t &vertex_nd_index) const
	Get the global index of a mesh vertex given its NDIndex.

KOKKOS_FUNCTION indices_t	getElementNDIndex (const size_t &elementIndex) const
	Get the NDIndex (vector of indices for each dimension) of a mesh element.

KOKKOS_FUNCTION size_t	getElementIndex (const indices_t &ndindex) const
	Get the global index of a mesh element given the NDIndex.

KOKKOS_FUNCTION vertex_indices_t	getElementMeshVertexIndices (const indices_t &elementNDIndex) const
	Get all the global vertex indices of an element (given by its NDIndex).

KOKKOS_FUNCTION indices_list_t	getElementMeshVertexNDIndices (const indices_t &elementNDIndex) const
	Get all the NDIndices of the vertices of an element (given by its NDIndex).

KOKKOS_FUNCTION vertex_points_t	getElementMeshVertexPoints (const indices_t &elementNDIndex) const
	Get all the global vertex points of an element (given by its NDIndex).

Static Public Attributes
static constexpr unsigned	numElementDOFs = getNedelecNumElementDOFs(Dim, Order)

static constexpr unsigned	dim

static constexpr unsigned	order = Order

static constexpr unsigned	numElementVertices

Static Public Attributes inherited from ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >
static constexpr unsigned	dim

static constexpr unsigned	numElementVertices

static constexpr unsigned	numElementDOFs

Additional Inherited Members
Public Attributes inherited from ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >
UniformCartesian< T, Dim > &	mesh_m
	Member variables //////////////////////////////////////////////////.

ElementType	ref_element_m

const QuadratureType &	quadrature_m

Vector< size_t, Dim >	nr_m

Vector< double, Dim >	hr_m

Vector< double, Dim >	origin_m

Detailed Description

template<typename T, unsigned Dim, unsigned Order, typename ElementType, typename QuadratureType, typename FieldType>
class ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >

A class representing a Nedelec space for finite element methods on a structured, rectilinear grid.

Template Parameters

T	The floating point number type of the field values
Dim	The dimension of the mesh
Order	The order of the Nedelec space
QuadratureType	The type of the quadrature rule
FieldType	The type of field to use.

Constructor & Destructor Documentation

◆ NedelecSpace() [1/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::NedelecSpace	(	UniformCartesian< T, Dim > &	mesh,
		ElementType &	ref_element,
		const QuadratureType &	quadrature,
		const Layout_t &	layout
	)

Construct a new NedelecSpace object.

Parameters

mesh	Reference to the mesh
ref_element	Reference to the reference element
quadrature	Reference to the quadrature rule
layout	Reference to the field layout

◆ NedelecSpace() [2/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::NedelecSpace	(	UniformCartesian< T, Dim > &	mesh,
		ElementType &	ref_element,
		const QuadratureType &	quadrature
	)

Construct a new NedelecSpace object (without layout) This constructor is made to work with the default constructor in FEMPoissonSolver.h such that it is compatible with alpine.

Parameters

mesh	Reference to the mesh
ref_element	Reference to the reference element
quadrature	Reference to the quadrature rule

Member Function Documentation

◆ computeError()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

template<typename F >

T ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::computeError	(	const FEMVector< T > &	u_h,
		const F &	u_sol
	)		const

Error norm computations ///////////////////////////////////////////.

Given the Nedelec space DoF coefficients and an analytical solution computes the L2 norm error.

Parameters

u_h	The basis function coefficients obtained via FEM.
u_sol	The analytical solution (functor)

Returns: error - The error ||u_h - u_sol||_L2

◆ createFEMVector()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

FEMVector< T > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::createFEMVector ( ) const

FEMVector conversion and creation//////////////////////////////////.

FEMVector conversion //////////////////////////////////////////////.

Creates and empty FEMVector.

Creates and empty FEMVector which corresponds to the domain this MPI rank owns (according to the ippl layout created for this mesh). To this extend it will also setup all the information needed to exchange halo cells.

Returns: An empty FEMVector for this domain.

◆ evaluateAx()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

template<typename F >

FEMVector< T > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::evaluateAx	(	FEMVector< T > &	x,
		F &	evalFunction
	)		const

Assembly operations ///////////////////////////////////////////////.

Assemble the left stiffness matrix A of the system Ax = b

Parameters

x	The vector which we want to multiply
evalFunction	The element-wise operator evaluation functor

Returns: The vector containing A*x

◆ evaluateLoadVector()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

FEMVector< T > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::evaluateLoadVector ( const FEMVector< point_t > & f ) const

Assemble the load vector b of the system Ax = b, given a field of the right hand side defined at the Nédélec DOF positions. If a functor instead of a field should be used, use the function NedelecSpace::evaluateLoadVectorFunctor.

Parameters

f	The source field defined at the Nédélec degrees fo freedom.

Returns: The resulting rhs b of the Galerkin discretization.

◆ evaluateLoadVectorFunctor()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

template<typename F >

FEMVector< T > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::evaluateLoadVectorFunctor ( const F & f ) const

Assemble the load vector b of the system Ax = b, given a functional of the rhs. If a field instead of a functor should be used, use the function NedelecSpace::evaluateLoadVector.

Parameters

f	The source function, which can be evaluated at arbitrary points.

Template Parameters

F	The functor type.

Returns: The resulting rhs b of the Galerkin discretization.

◆ evaluateRefElementShapeFunction()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::point_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::evaluateRefElementShapeFunction	(	const size_t &	localDOF,
		const point_t &	localPoint
	)		const

Basis functions and gradients /////////////////////////////////////.

Evaluate the shape function of a local degree of freedom at a given point in the reference element

Parameters

localDOF	size_t - The local degree of freedom index
localPoint	point_t (Vector<T, Dim>) - The point in the reference element

Returns: T - The value of the shape function at the given point

◆ evaluateRefElementShapeFunctionCurl()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::point_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::evaluateRefElementShapeFunctionCurl	(	const size_t &	localDOF,
		const point_t &	localPoint
	)		const

Evaluate the curl of the shape function of a local degree of of freedom at ta given point in the reference element.

Parameters

localDOF	size_t - The local degree of freedom index
localPoint	point_t (Vector<T, Dim>) - The point in the reference element

Returns: point_t (Vector<T, Dim>) - The curl of the shape function at the given point

◆ getBoundarySide()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION int ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getBoundarySide ( const size_t & dofIdx ) const

Returns which side the boundary is on.

This function takes as input the global index of a DoF and then returns on which side of the domain boundary it is on, in 2d that would be either south, north, west, east and in 3d space and ground is added. The mapping is as follows: 0 = south 1 = west 2 = north 3 = east 4 = ground 5 = space -1 = not on a boundary.

Parameters

dofIdx the global DoF index for which the boundary side should be retrieved.

Returns: Which boundary side the DoF is on or -1 if on no boundary.

◆ getFEMVectorDOFIndices() [1/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION Vector< size_t, NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::numElementDOFs > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getFEMVectorDOFIndices	(	const size_t &	elementIndex,
		NDIndex< Dim >	ldom
	)		const

Get the DOF indices (vector of indices) corresponding to the position inside the FEMVector of an element.

Parameters

elementIndex	size_t - The index of the element
ldom	local domain used for FEMVector indexing

Returns: Vector<size_t, NumElementDOFs> - The DOF indices

◆ getFEMVectorDOFIndices() [2/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION Vector< size_t, numElementDOFs > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getFEMVectorDOFIndices	(	indices_t	elementIndex,
		NDIndex< Dim >	ldom
	)		const

Get the DOF indices (vector of indices) corresponding to the position inside the FEMVector of an element.

Parameters

elementIndex	indices_t - The index of the element
ldom	local domain used for FEMVector indexing

Returns: Vector<size_t, NumElementDOFs> - The DOF indices

◆ getGlobalDOFIndex()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION size_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getGlobalDOFIndex	(	const size_t &	elementIndex,
		const size_t &	localDOFIndex
	)		const

overridevirtual

Get the global DOF index from the element index and local DOF.

Parameters

elementIndex	size_t - The index of the element
localDOFIndex	size_t - The local DOF index

Returns: size_t - The global DOF index

Implements ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >.

◆ getGlobalDOFIndices() [1/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION Vector< size_t, numElementDOFs > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getGlobalDOFIndices ( const indices_t & elementIndex ) const

Get the global DOF indices (vector of global DOF indices) of an element.

Parameters

elementIndex indices_t - The index of the element

Returns: Vector<size_t, NumElementDOFs> - The global DOF indices

◆ getGlobalDOFIndices() [2/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION Vector< size_t, NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::numElementDOFs > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getGlobalDOFIndices ( const size_t & elementIndex ) const

overridevirtual

Get the global DOF indices (vector of global DOF indices) of an element.

Parameters

elementIndex size_t - The index of the element

Returns: Vector<size_t, NumElementDOFs> - The global DOF indices

Implements ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >.

◆ getLocalDOFIndex()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION size_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getLocalDOFIndex	(	const size_t &	elementIndex,
		const size_t &	globalDOFIndex
	)		const

overridevirtual

Get the elements local DOF from the element index and global DOF index.

Parameters

elementIndex	size_t - The index of the element
globalDOFIndex	size_t - The global DOF index

Returns: size_t - The local DOF index

Implements ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >.

◆ getLocalDOFIndices()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION Vector< size_t, NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::numElementDOFs > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getLocalDOFIndices ( ) const

overridevirtual

Get the local DOF indices (vector of local DOF indices) They are independent of the specific element because it only depends on the reference element type.

Returns: Vector<size_t, NumElementDOFs> - The local DOF indices

Implements ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >.

◆ getLocalDOFPosition()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::point_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getLocalDOFPosition ( size_t localDOFIndex ) const

Get the cartesion position of a local DOF in the reference element.

Given the local DOF index this function will return the cartesian position of this DOF with respect to the reference element.

◆ getLocalNDIndex()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

NDIndex< Dim > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::getLocalNDIndex ( ) const

inline

Return the local NDIndex of this rank's subdomain.

Exposed so that free-function assembly kernels (e.g. assemble_current_nedelec) can obtain the ldom needed by getFEMVectorDOFIndices without accessing the private layout_m.

◆ initialize()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

void ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::initialize	(	UniformCartesian< T, Dim > &	mesh,
		const Layout_t &	layout
	)

Initialize a NedelecSpace object created with the default constructor.

Parameters

mesh	Reference to the mesh
layout	Reference to the field layout

◆ isDOFOnBoundary()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION bool ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::isDOFOnBoundary ( const size_t & dofIdx ) const

Check if a DOF is on the boundary of the mesh.

This function takes as input the global index of a DoF and returns if this DoF is on. If one would like to know which boundary this is the function NedelecSpace::getBoundarySide can be used.

Parameters

dofIdx The global DoF index for which should be checked if it is on the boundary.

Returns: true - If the DOF is on the domain boundary; false - If the DOF is not on the domain boundary

◆ numGlobalDOFs()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

KOKKOS_FUNCTION size_t ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::numGlobalDOFs ( ) const

overridevirtual

Degree of Freedom operations //////////////////////////////////////.

Get the number of global degrees of freedom in the space

Returns: size_t - unsigned integer number of global degrees of freedom

Implements ippl::FiniteElementSpace< T, Dim, getNedelecNumElementDOFs(Dim, Order), ElementType, QuadratureType, FEMVector< T >, FEMVector< T > >.

◆ reconstructToPoints()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

Kokkos::View< typename NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::point_t * > ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::reconstructToPoints	(	const Kokkos::View< point_t * > &	positions,
		const FEMVector< T > &	coef
	)		const

Reconstructs function values at arbitrary points in the mesh given the Nedelec DOF coefficients.

This function can be used to retrieve the values of a solution function at arbitrary points inside of the mesh given the Nedelec DOF coefficients which solved the problem using FEM.

Note: Currently the function is able to handle both cases, where we have that positions only contains positions which are inside of local domain of this MPI rank (i.e. each rank gets its own unique position ) and where positions contains the positions of all ranks (i.e. positions is the same for all ranks). If in the future it can be guaranteed, that each rank will get its own positions then certain parts of the function implementation can be removed. Instructions for this are given in the implementation itself.

Parameters

positions	The points at which the function should be evaluated. A `Kokkos::View` which stores in each element a 2D/3D point.
coef	The basis function coefficients obtained via FEM.

Returns: The function evaluated at the given points, stored inside of Kokkos::View where each element corresponts to the function value at the point described by the same element inside of positions.

Member Data Documentation

◆ dim

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

constexpr unsigned ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::dim

staticconstexpr

Initial value:

=
            FiniteElementSpace<T, Dim, numElementDOFs, ElementType, QuadratureType, FEMVector<T>,
                               FEMVector<T>>::dim

◆ numElementVertices

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldType >

constexpr unsigned ippl::NedelecSpace< T, Dim, Order, ElementType, QuadratureType, FieldType >::numElementVertices

staticconstexpr

Initial value:

=
            FiniteElementSpace<T, Dim, numElementDOFs, ElementType, QuadratureType, FEMVector<T>,
                               FEMVector<T>>::numElementVertices

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

ippl-src/src/FEM/NedelecSpace.h
ippl-src/src/FEM/NedelecSpace.hpp

Public Types

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NedelecSpace() [1/2]

◆ NedelecSpace() [2/2]

Member Function Documentation

◆ computeError()

◆ createFEMVector()

◆ evaluateAx()

◆ evaluateLoadVector()

◆ evaluateLoadVectorFunctor()

◆ evaluateRefElementShapeFunction()

◆ evaluateRefElementShapeFunctionCurl()

◆ getBoundarySide()

◆ getFEMVectorDOFIndices() [1/2]

◆ getFEMVectorDOFIndices() [2/2]

◆ getGlobalDOFIndex()

◆ getGlobalDOFIndices() [1/2]

◆ getGlobalDOFIndices() [2/2]

◆ getLocalDOFIndex()

◆ getLocalDOFIndices()

◆ getLocalDOFPosition()

◆ getLocalNDIndex()

◆ initialize()

◆ isDOFOnBoundary()

◆ numGlobalDOFs()

◆ reconstructToPoints()

Member Data Documentation

◆ dim

◆ numElementVertices