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

#include <LagrangeSpace.h>

Inheritance diagram for ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >:

Collaboration diagram for ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >:

Classes
struct	DeviceStruct
	Device struct for copies //////////////////////////////////////////. More...

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

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

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

typedef FieldLayout< Dim >	Layout_t

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

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

Public Types inherited from ippl::FiniteElementSpace< T, Dim, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >
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
	LagrangeSpace (UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature, Layout_t &layout)
	Construct a new LagrangeSpace object.

	LagrangeSpace (UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature)
	Construct a new LagrangeSpace 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, Layout_t &layout)
	Initialize a LagrangeSpace object created with the default constructor.

void	initializeElementIndices (Layout_t &layout)
	Initialize a Kokkos view containing the element indices. This distributes the elements among MPI ranks.

void	updateLayout (Layout_t &layout)
	Function to update the element partition and the layout of fields in the LagrangeSpace if the layout has been changed during the simulation (for example by the load balancer).

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 &element_index) const override
	Get the global DOF indices (vector of global DOF indices) of an element.

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

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

KOKKOS_FUNCTION point_t	getInverseTransposeTransformationJacobian (vertex_points_t pt) const
	Functions to access element info from outside /////////////////////.

template<typename F >
FieldLHS	evaluateAx (FieldLHS &field, F &evalFunction)
	Assembly operations ///////////////////////////////////////////////.

template<typename F >
FieldLHS	evaluateAx_lower (FieldLHS &field, F &evalFunction)

template<typename F >
FieldLHS	evaluateAx_upper (FieldLHS &field, F &evalFunction)

template<typename F >
FieldLHS	evaluateAx_upperlower (FieldLHS &field, F &evalFunction)

template<typename F >
FieldLHS	evaluateAx_inversediag (FieldLHS &field, F &evalFunction)

template<typename F >
FieldLHS	evaluateAx_diag (FieldLHS &field, F &evalFunction)

template<typename F >
FieldLHS	evaluateAx_lift (FieldLHS &field, F &evalFunction)
	Assemble the left stiffness matrix A of the system but only for the boundary values, so that they can be subtracted from the RHS for treatment of Dirichlet BCs.

void	evaluateLoadVector (FieldRHS &field) const
	Assemble the load vector b of the system Ax = b.

void	evaluateLumpedMass (FieldRHS &field) const
	Functions for error computations, etc. ////////////////////////////.

template<typename F >
T	computeErrorL2 (const FieldLHS &u_h, const F &u_sol) const
	Error norm computations ///////////////////////////////////////////.

T	computeAvg (const FieldLHS &u_h) const
	Given a field, compute the average.

DeviceStruct	getDeviceMirror () const
	Device struct definitions /////////////////////////////////////////.

Public Member Functions inherited from ippl::FiniteElementSpace< T, Dim, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >
	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 = getLagrangeNumElementDOFs(Dim, Order)

static constexpr unsigned	dim

static constexpr unsigned	order = Order

static constexpr unsigned	numElementVertices

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

static constexpr unsigned	numElementVertices

static constexpr unsigned	numElementDOFs

Additional Inherited Members
Public Attributes inherited from ippl::FiniteElementSpace< T, Dim, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >
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 FieldLHS, typename FieldRHS>
class ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >

A class representing a Lagrange 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 Lagrange space
QuadratureType	The type of the quadrature rule
FieldLHS	The type of the left hand side field
FieldRHS	The type of the right hand side field

Constructor & Destructor Documentation

◆ LagrangeSpace() [1/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

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

Construct a new LagrangeSpace 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

◆ LagrangeSpace() [2/2]

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::LagrangeSpace	(	UniformCartesian< T, Dim > &	mesh,
		ElementType &	ref_element,
		const QuadratureType &	quadrature
	)

Construct a new LagrangeSpace 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

◆ computeAvg()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

T ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::computeAvg ( const FieldLHS & u_h ) const

Given a field, compute the average.

Parameters

u_h	The numerical solution found using FEM

Returns: avg The average of the field on the domain

◆ computeErrorL2()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

template<typename F >

T ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::computeErrorL2	(	const FieldLHS &	u_h,
		const F &	u_sol
	)		const

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

Given two fields, compute the L2 norm error

Parameters

u_h	The numerical solution found using FEM
u_sol	The analytical solution (functor)

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

◆ evaluateAx()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

template<typename F >

FieldLHS ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx	(	FieldLHS &	field,
		F &	evalFunction
	)

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

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

Parameters

field	The field to assemble the matrix for
evalFunction	The lambda telling us the form which A takes

Returns: FieldLHS - The LHS field containing A*x

◆ evaluateAx_lift()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

template<typename F >

FieldLHS ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_lift	(	FieldLHS &	field,
		F &	evalFunction
	)

Assemble the left stiffness matrix A of the system but only for the boundary values, so that they can be subtracted from the RHS for treatment of Dirichlet BCs.

Parameters

field	The field to assemble the matrix for
evalFunction	The lambda telling us the form which A takes

Returns: FieldLHS - The LHS field containing A*x

◆ evaluateLoadVector()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

void ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateLoadVector ( FieldRHS & field ) const

Assemble the load vector b of the system Ax = b.

Parameters

field The field to set with the load vector

◆ evaluateRefElementShapeFunction()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION T ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::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

◆ evaluateRefElementShapeFunctionGradient()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::point_t ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateRefElementShapeFunctionGradient	(	const size_t &	localDOF,
		const point_t &	localPoint
	)		const

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

◆ getGlobalDOFIndex()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION size_t ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::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, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >.

◆ getGlobalDOFIndices()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION Vector< size_t, LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::numElementDOFs > ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::getGlobalDOFIndices ( const size_t & element_index ) const

overridevirtual

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

Parameters

element_index size_t - The index of the element

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

Implements ippl::FiniteElementSpace< T, Dim, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >.

◆ getLocalDOFIndex()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION size_t ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::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, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >.

◆ getLocalDOFIndices()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION Vector< size_t, LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::numElementDOFs > ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::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, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >.

◆ initialize()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

void ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::initialize	(	UniformCartesian< T, Dim > &	mesh,
		Layout_t &	layout
	)

Initialize a LagrangeSpace object created with the default constructor.

Parameters

mesh	Reference to the mesh
layout	Reference to the field layout

◆ numGlobalDOFs()

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

KOKKOS_FUNCTION size_t ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::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, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >.

Member Data Documentation

◆ dim

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

constexpr unsigned ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::dim

staticconstexpr

Initial value:

= FiniteElementSpace<T, Dim, numElementDOFs, ElementType,

QuadratureType, FieldLHS, FieldRHS>::dim

ippl::FiniteElementSpace< T, Dim, getLagrangeNumElementDOFs(Dim, Order), ElementType, QuadratureType, FieldLHS, FieldRHS >::FiniteElementSpace

FiniteElementSpace(UniformCartesian< T, Dim > &mesh, ElementType &ref_element, const QuadratureType &quadrature)

Construct a new FiniteElementSpace object.

Definition FiniteElementSpace.hpp:6

◆ numElementVertices

template<typename T , unsigned Dim, unsigned Order, typename ElementType , typename QuadratureType , typename FieldLHS , typename FieldRHS >

constexpr unsigned ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::numElementVertices

staticconstexpr

Initial value:

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

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

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

Classes

Public Types

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LagrangeSpace() [1/2]

◆ LagrangeSpace() [2/2]

Member Function Documentation

◆ computeAvg()

◆ computeErrorL2()

◆ evaluateAx()

◆ evaluateAx_lift()

◆ evaluateLoadVector()

◆ evaluateRefElementShapeFunction()

◆ evaluateRefElementShapeFunctionGradient()

◆ getGlobalDOFIndex()

◆ getGlobalDOFIndices()

◆ getLocalDOFIndex()

◆ getLocalDOFIndices()

◆ initialize()

◆ numGlobalDOFs()

Member Data Documentation

◆ dim

◆ numElementVertices