An interface declaration for DiscreteFunctionSpace which removes the size of the Codomain. More...

#include <ptems/space.hpp>

Inheritance diagram for ptems::DiscreteFunctionSpaceInterface< DIM, X >:

Collaboration diagram for ptems::DiscreteFunctionSpaceInterface< DIM, X >:

Public Member Functions
virtual std::size_t	NumberGlobalDoFs () const =0
	Gets the global number of degrees of freedom for the space. More...

std::unordered_map< std::size_t, X >	StronglyImposedDoFs () const
	Computes the set of global DoFs with strongly imposed Dirichlet boundary conditions. More...

std::vector< std::size_t >	StronglyImposedDofMapping (std::size_t &size) const
	Create mapping from global dof number to DoF number of the reduced set of dofs with strongly imposed boundary conditions Dofs removed (Dirichlet) More...

virtual bool	IsContinuous () const =0
	Gets if the functions space is continuous over element boundaries. More...

virtual bool	CanIncrementPolynomialDegree () const
	Gets whether the space can be modified by incrementing/decrementing the polynomial degree uniformly for any component. More...

virtual bool	CanIncrementPolynomialDegree ([[maybe_unused]] std::size_t component) const
	Gets whether the space can be modified by incrementing/decrementing the polynomial degree uniformly for the specified codomain component. More...

virtual bool	SupportsVariablePolynomialDegree () const
	Gets whether the space can be modified with varying polynomial degree for each element for any component. More...

virtual bool	SupportsVariablePolynomialDegree ([[maybe_unused]] std::size_t component) const
	Gets whether the space can be modified with varying polynomial degree for each element for the specified codomain component. More...

std::uintptr_t	ID () const
	Gets a unique ID for the space (actually just the pointer address) More...

Static Public Attributes
static constexpr std::size_t	IndexStronglyImposedDof = -1
	Index in the mapping returned by StronglyImposedDofMapping if the dof is strongly imposed. More...

Protected Member Functions
virtual void	ComputeStronglyImposedDoFs ([[maybe_unused]] std::unordered_map< std::size_t, X > &dofs, [[maybe_unused]] std::size_t offset) const
	Computes the set of global DoFs with strongly imposed Dirichlet boundary conditions. More...

virtual void	ComputeGlobalDoFOffset (std::size_t *dofOffset, std::size_t offset) const =0
	Computes the offset onto the global degrees of freedom for each component. More...

virtual std::size_t *	ComputeDoFMapping (std::size_t *dofMapping, std::size_t elementIdx, std::size_t offset) const =0
	Computes the mapping between local dof numbers for an element and the global dof numbers. More...

virtual X *	ComputeBasisFunctions (X *basis, std::size_t elementIdx, const Vector< DIM > &pt)=0
	Computes the basis functions for each component at the specified point of the specified element. More...

virtual FuncAndGradData< DIM, X > *	ComputeGradBasisFunctions (FuncAndGradData< DIM, X > *basis, std::size_t elementIdx, const Vector< DIM > &pt)=0
	Computes the basis functions and first order derivatives for each component at the specified point of the specified element. More...

virtual FuncAndGradData< DIM, X > *	ComputeGradValueBasisFunctions (FuncAndGradData< DIM, X > *basis, std::size_t elementIdx, const Vector< DIM > &pt)
	Computes the basis functions and first order derivatives of those basis functions for each component at the specified point of the specified element. More...

virtual FuncGradAndHessianData< DIM, X > *	ComputeHessianBasisFunctions ([[maybe_unused]] FuncGradAndHessianData< DIM, X > *basis, [[maybe_unused]] std::size_t elementIdx, [[maybe_unused]] const Vector< DIM > &pt)
	Computes the basis functions, first order derivatives, and second order derivatives for each component at the specified point of the specified element. More...

virtual FuncThirdOrderData< DIM, X > *	ComputeThirdOrderBasisFunctions ([[maybe_unused]] FuncThirdOrderData< DIM, X > *basis, [[maybe_unused]] std::size_t elementIdx, [[maybe_unused]] const Vector< DIM > &pt)
	Computes the basis functions and first, second, and third order derivatives for each component at the specified point of the specified element. More...

virtual FuncFourthOrderData< DIM, X > *	ComputeFourthOrderBasisFunctions ([[maybe_unused]] FuncFourthOrderData< DIM, X > *basis, [[maybe_unused]] std::size_t elementIdx, [[maybe_unused]] const Vector< DIM > &pt)
	Computes the basis functions and first, second, third, and fourth order derivatives for each component at the specified point of the specified element. More...

virtual std::vector< X > *	ComputeDoFAtBasis (std::vector< X > *dofs, [[maybe_unused]] std::size_t elementIdx)
	Computes the basis functions of the space evaluated by the functional for each degree of freedom. More...

virtual std::vector< X > *	ComputeDoFAtBasisProjection (std::vector< X > *dofs, std::size_t elementIdx)
	Computes the value projection of the basis functions of the space evaluated by the functional for each degree of freedom. More...

virtual Vector< DIM > *	ComputeLocalAnalyticityEstimate (Vector< DIM > analyticity, [[maybe_unused]] std::size_t elementIdx, [[maybe_unused]] const X dofs)
	Computes the local analyticity estimate of the element using Legendre coefficients. More...

virtual std::size_t	CodomainDimensionSize () const =0
	Gets ths size of the codomain of the fuctions in the space. More...

virtual std::size_t *	FillPolynomialDegree (std::size_t element, std::size_t *nextPolydeg) const =0
	Populates an array with polynomial degree for each component of the result for the specified element. More...

virtual void	SetPolynomialDegree ([[maybe_unused]] const std::map< std::size_t, const std::size_t * > &elementPolydegs, const DoFChangeList< X > &dofs)
	Set the polynomial degree of the specified elements and update the DoFs of the specified functions. More...

virtual void	SetPolynomialDegree ([[maybe_unused]] const std::size_t *polydeg, const DoFChangeList< X > &dofs)
	Set the polynomial degree of the all elements and update the DoFs of the specified functions. More...

virtual void	ComputeNumberLocalDoFs (std::size_t elementIdx, std::size_t *numberDofs) const =0
	Gets the number of degrees of freedom for an element in the space per component. More...

virtual std::vector< X >::iterator	Interpolate (typename std::vector< X >::iterator dofsBegin, typename std::vector< X >::iterator dofsEnd, const X *value) const =0
	Fill the degrees of freedom for this space by interpolating the specified constant function. More...

virtual std::vector< X >::iterator	Interpolate ([[maybe_unused]] typename std::vector< X >::iterator dofsBegin, [[maybe_unused]] typename std::vector< X >::iterator dofsEnd, [[maybe_unused]] const std::function< X(const Vector< DIM > &, std::size_t)> &func) const
	Fill the degrees of freedom for this space by interpolating the specified function. More...

virtual void	OnMeshChanged (const PFEMesh< DIM > &previousMesh, DiscreteFunctionSpaceInterface< DIM, X > *previousSpace, const typename FEMesh< DIM >::Modifications &changes, const DoFChangeList< X > &dofs)=0
	Event notification from mesh that the mesh has been changed. More...

virtual DiscreteFunctionSpaceInterface< DIM, X > *	CreateClone (const PFEMesh< DIM > &mesh)=0
	Creates a clone of the space. More...

Friends
template<std::size_t D, typename T , std::size_t N>
class	DiscreteCartesianProductSpace

Detailed Description

template<std::size_t DIM, typename X>
class ptems::DiscreteFunctionSpaceInterface< DIM, X >

An interface declaration for DiscreteFunctionSpace which removes the size of the Codomain.

Template Parameters

DIM	The dimension of the domain (and mesh)
X	The type of the result of the functions (double, std::complex, etc)

Member Function Documentation

◆ CanIncrementPolynomialDegree() [1/2]

template<std::size_t DIM, typename X >

virtual bool ptems::DiscreteFunctionSpaceInterface< DIM, X >::CanIncrementPolynomialDegree ( ) const

inlinevirtual

Gets whether the space can be modified by incrementing/decrementing the polynomial degree uniformly for any component.

Note: Must return true if SupportsVariablePolynomialDegree() returns true

Returns: true if the polynomial degree can be uniformly incremented; false otherwise

Reimplemented in ptems::DiscreteCartesianProductSpace< DIM, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< DIM, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< 1, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< 2, X, N >, and ptems::VariableDegreeDiscreteFunctionSpace< DIM, double, 1 >.

◆ CanIncrementPolynomialDegree() [2/2]

template<std::size_t DIM, typename X >

virtual bool ptems::DiscreteFunctionSpaceInterface< DIM, X >::CanIncrementPolynomialDegree ( [[maybe_unused] ] std::size_t component ) const

inlinevirtual

Gets whether the space can be modified by incrementing/decrementing the polynomial degree uniformly for the specified codomain component.

Parameters

component Index of component to check

Returns: true if the polynomial degree of the specified component can be uniformly incremented; false otherwise

◆ CodomainDimensionSize()

template<std::size_t DIM, typename X >

virtual std::size_t ptems::DiscreteFunctionSpaceInterface< DIM, X >::CodomainDimensionSize ( ) const

protectedpure virtual

Gets ths size of the codomain of the fuctions in the space.

Implemented in ptems::DiscreteFunctionSpace< DIM, X, N >, and ptems::DiscreteFunctionSpace< DIM, double, 1 >.

◆ ComputeBasisFunctions()

template<std::size_t DIM, typename X >

virtual X* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeBasisFunctions	(	X *	basis,
		std::size_t	elementIdx,
		const Vector< DIM > &	pt
	)

protectedpure virtual

Computes the basis functions for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element) or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Note: For virtual element the returned values are the value projections of the basis functions

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

Implemented in ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeDoFAtBasis()

template<std::size_t DIM, typename X >

virtual std::vector<X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeDoFAtBasis	(	std::vector< X > *	dofs,
		[[maybe_unused] ] std::size_t	elementIdx
	)

inlineprotectedvirtual

Computes the basis functions of the space evaluated by the functional for each degree of freedom.

Parameters

dofs Pointer to the vector to store each basis for the first DoF functional to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.. Each vector will already be sized to same size as ComputeNumberLocalDoFs() for the component and filled wth zero

elementIdx The element index to get the basis functions/dofs for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to dofs+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

◆ ComputeDoFAtBasisProjection()

template<std::size_t DIM, typename X >

virtual std::vector<X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeDoFAtBasisProjection	(	std::vector< X > *	dofs,
		std::size_t	elementIdx
	)

inlineprotectedvirtual

Computes the value projection of the basis functions of the space evaluated by the functional for each degree of freedom.

Note: This function is only relevant for virtual element spaces. For finite element spaces it simply returns EvaluateDoFAtBasis();

Parameters

dofs Pointer to the vector to store each basis for the first DoF functional to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc. Each vector will already be sized to same size as ComputeNumberLocalDoFs() for the component and filled wth zero

elementIdx The element index to get the basis functions/dofs for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to dofs+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

Reimplemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeDoFMapping()

template<std::size_t DIM, typename X >

virtual std::size_t* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeDoFMapping	(	std::size_t *	dofMapping,
		std::size_t	elementIdx,
		std::size_t	offset
	)		const

protectedpure virtual

Computes the mapping between local dof numbers for an element and the global dof numbers.

The passed pointer is a continuous array of all the dofs for the first component, followed by all the dofs for the second etc. The number of dofs MUST be the same as ComputeNumberLocalDoFs calculates

Note: Implementations of this function can cache this value for performance IF the number only changes when the mesh changes. The implementation must then invalidate the cached value when OnMeshChanged is called.

Exceptions

std::logic_error	If the underlying mesh is invalid for the type of space; e.g., nonconforming mesh for a conforming space.
std::out_of_range	if elementIdx is not less than the number of elements in the underlying mesh

Parameters

dofMapping	Pointer to the first global dof index to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	Index of the element to get the local to global mapping of the degrees of freedom for
offset	Offset to add to the global DoF numbers

Returns: Pointer to past the end of the array of global dof indices computed. Must be equal to dofMapping+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

Implemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::PiecewiseConstant< DIM, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::DiscontinuousSpace< LegendrePolynomials< DIM >, DIM, double, 1 >, ptems::DiscontinuousSpace< LagrangePolynomials< DIM >, DIM, double, 1 >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeFourthOrderBasisFunctions()

template<std::size_t DIM, typename X >

virtual FuncFourthOrderData<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeFourthOrderBasisFunctions	(	[[maybe_unused] ] FuncFourthOrderData< DIM, X > *	basis,
		[[maybe_unused] ] std::size_t	elementIdx,
		[[maybe_unused] ] const Vector< DIM > &	pt
	)

inlineprotectedvirtual

Computes the basis functions and first, second, third, and fourth order derivatives for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element), or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Note: Third and fourth order derivatives contaning the time variable are not yet supported

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Exceptions

std::logic_error If fourth order derivatives are not supported by the space

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

◆ ComputeGlobalDoFOffset()

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeGlobalDoFOffset	(	std::size_t *	dofOffset,
		std::size_t	offset
	)		const

protectedpure virtual

Computes the offset onto the global degrees of freedom for each component.

Note: Implementations of this function can cache this value for performance IF the number only changes when the mesh changes. The implementation must then invalidate the cached value when OnMeshChanged is called.

Exceptions

std::logic_error If the underlying mesh is invalid for the type of space; e.g., nonconforming mesh for a conforming space.

Parameters

dofOffset	Pointer to array of length of number of components + 1 to store the the offset into the global DoFs for the DoFs for each component (first N entries) and the total number of globals DoFs (last entry)
offset	Offset to add to the global DoF numbers

Implemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::PiecewiseConstant< DIM, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::DiscontinuousSpace< LegendrePolynomials< DIM >, DIM, double, 1 >, ptems::DiscontinuousSpace< LagrangePolynomials< DIM >, DIM, double, 1 >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeGradBasisFunctions()

template<std::size_t DIM, typename X >

virtual FuncAndGradData<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeGradBasisFunctions	(	FuncAndGradData< DIM, X > *	basis,
		std::size_t	elementIdx,
		const Vector< DIM > &	pt
	)

protectedpure virtual

Computes the basis functions and first order derivatives for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element) or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Note: For virtual element the returned values are the value and gradient projections of the basis functions

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

Implemented in ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeGradValueBasisFunctions()

template<std::size_t DIM, typename X >

virtual FuncAndGradData<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeGradValueBasisFunctions	(	FuncAndGradData< DIM, X > *	basis,
		std::size_t	elementIdx,
		const Vector< DIM > &	pt
	)

inlineprotectedvirtual

Computes the basis functions and first order derivatives of those basis functions for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element) or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Note: Only relevant for virtual element spaces - the returned values are the value and gradient of the value projection of the basis functions; for other methods this returns the same as ComputeGradBasisFunctions

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

◆ ComputeHessianBasisFunctions()

template<std::size_t DIM, typename X >

virtual FuncGradAndHessianData<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeHessianBasisFunctions	(	[[maybe_unused] ] FuncGradAndHessianData< DIM, X > *	basis,
		[[maybe_unused] ] std::size_t	elementIdx,
		[[maybe_unused] ] const Vector< DIM > &	pt
	)

inlineprotectedvirtual

Computes the basis functions, first order derivatives, and second order derivatives for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element), or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Exceptions

std::logic_error If second order derivatives are not supported by the space

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

◆ ComputeLocalAnalyticityEstimate()

template<std::size_t DIM, typename X >

virtual Vector<DIM>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeLocalAnalyticityEstimate	(	Vector< DIM > *	analyticity,
		[[maybe_unused] ] std::size_t	elementIdx,
		[[maybe_unused] ] const X *	dofs
	)

inlineprotectedvirtual

Computes the local analyticity estimate of the element using Legendre coefficients.

Parameters

elementIdx	Element to estimate analyticity
analyticity	Pointer to the array to store analyticity estimate, per variable, in range \((0,1]\) (or negative if analyticity cannot be computed)
dofs	Pointer to array containing degrees of freedom

Returns: Pointer to past the end of the array of analyticities computed

◆ ComputeNumberLocalDoFs()

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeNumberLocalDoFs	(	std::size_t	elementIdx,
		std::size_t *	numberDofs
	)		const

protectedpure virtual

Gets the number of degrees of freedom for an element in the space per component.

Note: Implementations of this function can cache this value for performance IF the number only changes when the mesh changes. The implementation must then invalidate the cached value when OnMeshChanged is called.

Exceptions

std::logic_error	If the underlying mesh is invalid for the type of space; e.g., nonconforming mesh for a conforming space.
std::out_of_range	if elementIdx is not less than the number of elements in the underlying mesh

Parameters

elementIdx	Index of the element to get the number of local degrees of freedom for
numberDofs	Pointer to array of length of number of components to store the local number of degrees of freedom for the specified element per component

Implemented in ptems::PiecewiseConstant< DIM, X, N >, ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::DiscontinuousSpace< LegendrePolynomials< DIM >, DIM, double, 1 >, ptems::DiscontinuousSpace< LagrangePolynomials< DIM >, DIM, double, 1 >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ ComputeStronglyImposedDoFs()

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeStronglyImposedDoFs	(	[[maybe_unused] ] std::unordered_map< std::size_t, X > &	dofs,
		[[maybe_unused] ] std::size_t	offset
	)		const

inlineprotectedvirtual

Computes the set of global DoFs with strongly imposed Dirichlet boundary conditions.

Parameters

dofs	Set to update with global dof number and value for strongly imposed Dirichlet BC
offset	Offset to add to the global DoF numbers

◆ ComputeThirdOrderBasisFunctions()

template<std::size_t DIM, typename X >

virtual FuncThirdOrderData<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::ComputeThirdOrderBasisFunctions	(	[[maybe_unused] ] FuncThirdOrderData< DIM, X > *	basis,
		[[maybe_unused] ] std::size_t	elementIdx,
		[[maybe_unused] ] const Vector< DIM > &	pt
	)

inlineprotectedvirtual

Computes the basis functions and first, second, and third order derivatives for each component at the specified point of the specified element.

The point is the local point defined on the reference element (for elements with a single reference element), or the bounding box (for elements with multiple reference elements).

The passed pointer is a continuous array of all the basis functions for the first component, followed by all the basis functions for the second etc. The number of basis functions MUST be the same as ComputeNumberLocalDoFs calculates

Note: Third order derivatives contaning the time variable are not yet supported

Warning: Subclasses MUST add the number of basis given by ComputeNumberLocalDoFs for each component and return basis plus the sum of the number of basis functions of all components as computed by ComputeNumberLocalDoFs. Failure to do this is undefined behaviour (and could lead to segfaults)

Exceptions

std::logic_error If third order derivatives are not supported by the space

Parameters

basis	Pointer to the first basis function to compute. This pointer can be treated as if it is an array containing the number of DoFs for the first component as computed by ComputeNumberLocalDoFs(), followed by the number of DoFs for the second component as computed by ComputeNumberLocalDoFs(), etc.
elementIdx	The element index to get the basis functions for
pt	The local point in the reference element or bounding box to get the basis functions for

Returns: Pointer to past the end of the array of basis functions computed. Must be equal to basis+x, where x is the sum of the array entries computed by ComputeNumberLocalDoFs

◆ CreateClone()

template<std::size_t DIM, typename X >

virtual DiscreteFunctionSpaceInterface<DIM,X>* ptems::DiscreteFunctionSpaceInterface< DIM, X >::CreateClone ( const PFEMesh< DIM > & mesh )

protectedpure virtual

Creates a clone of the space.

Parameters

mesh	The mesh to use for the clone

Returns: The cloned space

Implemented in ptems::DiscreteFunctionSpace< DIM, X, N >, and ptems::DiscreteFunctionSpace< DIM, double, 1 >.

◆ FillPolynomialDegree()

template<std::size_t DIM, typename X >

virtual std::size_t* ptems::DiscreteFunctionSpaceInterface< DIM, X >::FillPolynomialDegree	(	std::size_t	element,
		std::size_t *	nextPolydeg
	)		const

protectedpure virtual

Populates an array with polynomial degree for each component of the result for the specified element.

Parameters

element	The index of the element to get the polynomial degree for
nextPolydeg	Point into an array to store the polynomial degree. The array will have enough space to store CodomainDimensionSize() values

Returns: std::size_t* The pointer to the array entry AFTER the last polynomial degree entered. Must be equal to nextPolydeg+CodomainDimensionSize()

Implemented in ptems::DiscreteFunctionSpace< DIM, X, N >, and ptems::DiscreteFunctionSpace< DIM, double, 1 >.

◆ ID()

template<std::size_t DIM, typename X >

std::uintptr_t ptems::DiscreteFunctionSpaceInterface< DIM, X >::ID ( ) const

inline

Gets a unique ID for the space (actually just the pointer address)

Returns: The unique ID

◆ Interpolate() [1/2]

template<std::size_t DIM, typename X >

virtual std::vector<X>::iterator ptems::DiscreteFunctionSpaceInterface< DIM, X >::Interpolate	(	[[maybe_unused] ] typename std::vector< X >::iterator	dofsBegin,
		[[maybe_unused] ] typename std::vector< X >::iterator	dofsEnd,
		[[maybe_unused] ] const std::function< X(const Vector< DIM > &, std::size_t)> &	func
	)		const

inlineprotectedvirtual

Fill the degrees of freedom for this space by interpolating the specified function.

Exceptions

std::logic_error If dofsEnd-dofsBegin is less than the number of degrees of freedom to be populated

Warning: Note that dofsEnd-dofsBegin may be larger than the number of degrees of freedom in the space. Implementations of this function MUST ONLY populate the same number degrees of degrees of freedom as NumberGlobalDoFs() and return the iterator to dofsBegin+NumberGlobalDoFs()

Parameters

dofsBegin	Iterator pointing to the start of the degrees of freedom to fill
dofsEnd	Iterator pointing to the end of the degrees of freedom to fill
func	The function to interpolate. Functional which takes two arguments: global coordinate and component of the vector space

Returns: Iterator pointing to past the last degree of freedom populated by the interpolation. Must be dofsBegin+NumberGlobalDoFs().

◆ Interpolate() [2/2]

template<std::size_t DIM, typename X >

virtual std::vector<X>::iterator ptems::DiscreteFunctionSpaceInterface< DIM, X >::Interpolate	(	typename std::vector< X >::iterator	dofsBegin,
		typename std::vector< X >::iterator	dofsEnd,
		const X *	value
	)		const

protectedpure virtual

Fill the degrees of freedom for this space by interpolating the specified constant function.

Exceptions

std::logic_error If dofsEnd-dofsBegin is less than the number of degrees of freedom to be populated

Warning: Note that dofsEnd-dofsBegin may be larger than the number of degrees of freedom in the space. Implementations of this function MUST ONLY populate the same number degrees of degrees of freedom as NumberGlobalDoFs() and return the iterator to dofsBegin+NumberGlobalDoFs()

Parameters

dofsBegin	Iterator pointing to the start of the degrees of freedom to fill
dofsEnd	Iterator pointing to the end of the degrees of freedom to fill
value	Pointer to array containing the constants for each component

Returns: Iterator pointing to past the last degree of freedom populated by the interpolation. Must be dofsBegin+NumberGlobalDoFs().

Implemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ IsContinuous()

template<std::size_t DIM, typename X >

virtual bool ptems::DiscreteFunctionSpaceInterface< DIM, X >::IsContinuous ( ) const

pure virtual

Gets if the functions space is continuous over element boundaries.

Returns: true If continuous, false otherwise

Implemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::PiecewiseConstant< DIM, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::DiscontinuousSpace< LegendrePolynomials< DIM >, DIM, double, 1 >, ptems::DiscontinuousSpace< LagrangePolynomials< DIM >, DIM, double, 1 >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ NumberGlobalDoFs()

template<std::size_t DIM, typename X >

virtual std::size_t ptems::DiscreteFunctionSpaceInterface< DIM, X >::NumberGlobalDoFs ( ) const

pure virtual

Gets the global number of degrees of freedom for the space.

Note: Implementations of this function can cache this value for performance IF the number only changes when the mesh changes. The implementation must then invalidate the cached value when OnMeshChanged is called.

Exceptions

std::logic_error If the underlying mesh is invalid for the type of space; e.g., nonconforming mesh for a conforming space.

Returns: Global number of degrees of freedom

Implemented in ptems::VirtualElementSpace< HBasis, 2, X, N >, ptems::PiecewiseConstant< DIM, X, N >, ptems::DiscontinuousSpace< Polynomials, DIM, X, N >, ptems::DiscontinuousSpace< LegendrePolynomials< DIM >, DIM, double, 1 >, ptems::DiscontinuousSpace< LagrangePolynomials< DIM >, DIM, double, 1 >, ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, and ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ OnMeshChanged()

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::OnMeshChanged	(	const PFEMesh< DIM > &	previousMesh,
		DiscreteFunctionSpaceInterface< DIM, X > *	previousSpace,
		const typename FEMesh< DIM >::Modifications &	changes,
		const DoFChangeList< X > &	dofs
	)

protectedpure virtual

Event notification from mesh that the mesh has been changed.

The space should perform any necessary changes to conform to the new mesh.

The m_mesh variable will contain the new mesh.

Warning: The target vector in dofs may already contain values, this MUST NOT be overwritten, new values should instead be appended.

Exceptions

std::logic_error If the new mesh is invalid for the type of space; e.g., nonconforming mesh for a conforming space.

Parameters

previousMesh	The mesh before refinement
previousSpace	The space for the previous mesh
changes	A FEMesh<DIM>::Modifications structure defining the change to the mesh
dofs	Map (actually array of pairs) of the degree of freedom from a function which is part of this space before the change, to a (reference to a) vector to APPEND with the new degrees of freedom after mesh change

Implemented in ptems::DiscreteCartesianProductSpace< DIM, X, N >.

◆ SetPolynomialDegree() [1/2]

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::SetPolynomialDegree	(	[[maybe_unused] ] const std::map< std::size_t, const std::size_t * > &	elementPolydegs,
		const DoFChangeList< X > &	dofs
	)

inlineprotectedvirtual

Set the polynomial degree of the specified elements and update the DoFs of the specified functions.

Warning: The target vector in dofs may already contain values, this MUST NOT be overwritten, new values should instead be appended.

Parameters

elementPolydegs	(Ordered) map of element number to array (of length N) of new polynomial degrees for each component
dofs	Map (actually array of pairs) of the degree of freedom from a function which is part of this space before the change, to a (reference to a) vector to APPEND with the new degrees of freedom after mesh change

◆ SetPolynomialDegree() [2/2]

template<std::size_t DIM, typename X >

virtual void ptems::DiscreteFunctionSpaceInterface< DIM, X >::SetPolynomialDegree	(	[[maybe_unused] ] const std::size_t *	polydeg,
		const DoFChangeList< X > &	dofs
	)

inlineprotectedvirtual

Set the polynomial degree of the all elements and update the DoFs of the specified functions.

Warning: The target vector in dofs may already contain values, this MUST NOT be overwritten, new values should instead be appended.

Parameters

polydeg	Array (of length N) of new polynomial degrees for each component
dofs	Map (actually array of pairs) of the degree of freedom from a function which is part of this space before the change, to a (reference to a) vector to APPEND with the new degrees of freedom after mesh change

◆ StronglyImposedDofMapping()

template<std::size_t DIM, typename X >

std::vector<std::size_t> ptems::DiscreteFunctionSpaceInterface< DIM, X >::StronglyImposedDofMapping ( std::size_t & size ) const

inline

Create mapping from global dof number to DoF number of the reduced set of dofs with strongly imposed boundary conditions Dofs removed (Dirichlet)

See also: StronglyImposedDoFs; IndexStronglyImposedDof; NumberGlobalDoFs

Parameters

size	Index of first dof of reduced set of dofs. Updated to index of last dof+1.

Returns: Vector of length NumberGlobalDoFs containing either IndexStronglyImposedDof if the Dof is strongly imposed, or a new index in the reduced set

◆ StronglyImposedDoFs()

template<std::size_t DIM, typename X >

std::unordered_map<std::size_t, X> ptems::DiscreteFunctionSpaceInterface< DIM, X >::StronglyImposedDoFs ( ) const

inline

Computes the set of global DoFs with strongly imposed Dirichlet boundary conditions.

Returns: dofs Set of global dof number and value for strongly imposed Dirichlet BC

◆ SupportsVariablePolynomialDegree() [1/2]

template<std::size_t DIM, typename X >

virtual bool ptems::DiscreteFunctionSpaceInterface< DIM, X >::SupportsVariablePolynomialDegree ( ) const

inlinevirtual

Gets whether the space can be modified with varying polynomial degree for each element for any component.

Note: If this returns true then CanIncrementPolynomialDegree must also return true

Returns: true if the polynomial degree can be different on different elements; false otherwise

Reimplemented in ptems::ContinuousLagrangeSpace< 2, X, N >, ptems::ContinuousLagrangeSpace< 1, X, N >, ptems::DiscreteCartesianProductSpace< DIM, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< DIM, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< 1, X, N >, ptems::VariableDegreeDiscreteFunctionSpace< 2, X, N >, and ptems::VariableDegreeDiscreteFunctionSpace< DIM, double, 1 >.

◆ SupportsVariablePolynomialDegree() [2/2]

template<std::size_t DIM, typename X >

virtual bool ptems::DiscreteFunctionSpaceInterface< DIM, X >::SupportsVariablePolynomialDegree ( [[maybe_unused] ] std::size_t component ) const

inlinevirtual

Gets whether the space can be modified with varying polynomial degree for each element for the specified codomain component.

Parameters

component Index of component to check

Returns: true if the polynomial degree of the specified component can be different on different elements; false otherwise

Reimplemented in ptems::DiscreteCartesianProductSpace< DIM, X, N >.

Member Data Documentation

◆ IndexStronglyImposedDof

template<std::size_t DIM, typename X >

constexpr std::size_t ptems::DiscreteFunctionSpaceInterface< DIM, X >::IndexStronglyImposedDof = -1

staticconstexpr

Index in the mapping returned by StronglyImposedDofMapping if the dof is strongly imposed.

See also: StronglyImposedDofMapping

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

ptems/space.hpp

Public Member Functions

Static Public Attributes

Protected Member Functions

Friends

Detailed Description

template<std::size_t DIM, typename X> class ptems::DiscreteFunctionSpaceInterface< DIM, X >

Member Function Documentation

◆ CanIncrementPolynomialDegree() [1/2]

◆ CanIncrementPolynomialDegree() [2/2]

◆ CodomainDimensionSize()

◆ ComputeBasisFunctions()

◆ ComputeDoFAtBasis()

◆ ComputeDoFAtBasisProjection()

◆ ComputeDoFMapping()

◆ ComputeFourthOrderBasisFunctions()

◆ ComputeGlobalDoFOffset()

◆ ComputeGradBasisFunctions()

◆ ComputeGradValueBasisFunctions()

◆ ComputeHessianBasisFunctions()

◆ ComputeLocalAnalyticityEstimate()

◆ ComputeNumberLocalDoFs()

◆ ComputeStronglyImposedDoFs()

◆ ComputeThirdOrderBasisFunctions()

◆ CreateClone()

◆ FillPolynomialDegree()

◆ ID()

◆ Interpolate() [1/2]

◆ Interpolate() [2/2]

◆ IsContinuous()

◆ NumberGlobalDoFs()

◆ OnMeshChanged()

◆ SetPolynomialDegree() [1/2]

◆ SetPolynomialDegree() [2/2]

◆ StronglyImposedDofMapping()

◆ StronglyImposedDoFs()

◆ SupportsVariablePolynomialDegree() [1/2]

◆ SupportsVariablePolynomialDegree() [2/2]

Member Data Documentation

◆ IndexStronglyImposedDof

template<std::size_t DIM, typename X>
class ptems::DiscreteFunctionSpaceInterface< DIM, X >