Base type for a set of hierarchical polynomials on space of dimension >= 2. More...

#include <ptems/spaces/hierarchicalpolynomials.hpp>

Inheritance diagram for ptems::HierarchicalPolynomials< OneDPolynomials, DIM >:

Collaboration diagram for ptems::HierarchicalPolynomials< OneDPolynomials, DIM >:

Static Public Member Functions
template<typename T >
static T *	Polynomials (const ReferenceElement< DIM > &refElement, const Vector< DIM > &pt, T *result, std::size_t polydeg)
	Computes the value of the first N hierarchical polynomials on the reference element, where N is the result of NumberDoFs(refElement, polydeg). More...

template<typename T >
static FuncAndGradData< DIM, T > *	Gradient (const ReferenceElement< DIM > &refElement, const Vector< DIM > &pt, FuncAndGradData< DIM, T > *result, std::size_t polydeg)
	Computes the value of the first N hierarchical polynomials, and their first order derivatives, on the reference element, where N is the result of NumberDoFs(refElement, polydeg). More...

template<typename T >
static FuncGradAndHessianData< DIM, T > *	Hessian (const ReferenceElement< DIM > &refElement, const Vector< DIM > &pt, FuncGradAndHessianData< DIM, T > *result, std::size_t polydeg)
	Computes the value of the first N hierarchical polynomials, and their first and second order derivatives, on the reference element, where N is the result of NumberDoFs(refElement, polydeg). More...

static std::vector< std::size_t >	Indices (const ReferenceElement< DIM > &refElement, std::size_t originalPolydeg, std::size_t newPolydeg)
	Gets the indices of the subset of the basis for polynomial degree `originalPolydeg` which form the basis for polynomial degree `newPolydeg`. More...

Detailed Description

template<typename OneDPolynomials, std::size_t DIM>
struct ptems::HierarchicalPolynomials< OneDPolynomials, DIM >

Base type for a set of hierarchical polynomials on space of dimension >= 2.

Most hierarchical polynomials are defined identically on higher dimensions based purely on their one dimensional definition. This class extracts this commonality.

Template Parameters

OneDPolynomials	The type for the one dimensional polynomials
DIM	The dimension of the polynomials

Member Function Documentation

◆ Gradient()

template<typename OneDPolynomials , std::size_t DIM>

template<typename T >

static FuncAndGradData<DIM,T>* ptems::HierarchicalPolynomials< OneDPolynomials, DIM >::Gradient	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		FuncAndGradData< DIM, T > *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the first N hierarchical polynomials, and their first order derivatives, on the reference element, where N is the result of NumberDoFs(refElement, polydeg).

Template Parameters

T	The type of the result

Parameters

refElement	Reference element - either the reference square or triangle
pt	The point to compute the values of the hierarchical polynomial at
result	Array of at least NumberDoFs(refElement, polydeg) entries, to store the result into
polydeg	The polynomial degree of the hierarchical basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+N where N is the number of basis functions depending on the reference element)

◆ Hessian()

template<typename OneDPolynomials , std::size_t DIM>

template<typename T >

static FuncGradAndHessianData<DIM,T>* ptems::HierarchicalPolynomials< OneDPolynomials, DIM >::Hessian	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		FuncGradAndHessianData< DIM, T > *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the first N hierarchical polynomials, and their first and second order derivatives, on the reference element, where N is the result of NumberDoFs(refElement, polydeg).

Template Parameters

T	The type of the result

Parameters

refElement	Reference element - either the reference square or triangle
pt	The point to compute the values of the hierarchical polynomial at
result	Array of at least NumberDoFs(refElement, polydeg) entries, to store the result into
polydeg	The polynomial degree of the hierarchical basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+N where N is the number of basis functions depending on the reference element)

◆ Indices()

template<typename OneDPolynomials , std::size_t DIM>

static std::vector<std::size_t> ptems::HierarchicalPolynomials< OneDPolynomials, DIM >::Indices	(	const ReferenceElement< DIM > &	refElement,
		std::size_t	originalPolydeg,
		std::size_t	newPolydeg
	)

inlinestatic

Gets the indices of the subset of the basis for polynomial degree originalPolydeg which form the basis for polynomial degree newPolydeg.

Note: For hierarchical polynomials the polynomials of order newPolydeg are contained within the set of polynomials of order originalPolydeg

Exceptions

std::invalid_argument If newPolydeg > originalPolydeg

Parameters

refElement	The reference element the bases are defined on
originalPolydeg	The polynomial degree of the original basis
newPolydeg	The polynomial degree of the smaller basis to get the indices of

Returns: Map of indices for the smaller basis to the original larger basis index

◆ Polynomials()

template<typename OneDPolynomials , std::size_t DIM>

template<typename T >

static T* ptems::HierarchicalPolynomials< OneDPolynomials, DIM >::Polynomials	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		T *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the first N hierarchical polynomials on the reference element, where N is the result of NumberDoFs(refElement, polydeg).

Template Parameters

T	The type of the result

Parameters

refElement	Reference element
pt	The point to compute the values of the hierarchical polynomial at
result	Array of at least NumberDoFs(refElement, polydeg) entries, to store the result into
polydeg	The polynomial degree of the hierarchical basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+N where N is the number of basis functions depending on the reference element)

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

ptems/spaces/hierarchicalpolynomials.hpp

Static Public Member Functions

Detailed Description

template<typename OneDPolynomials, std::size_t DIM> struct ptems::HierarchicalPolynomials< OneDPolynomials, DIM >

Member Function Documentation

◆ Gradient()

◆ Hessian()

◆ Indices()

◆ Polynomials()

template<typename OneDPolynomials, std::size_t DIM>
struct ptems::HierarchicalPolynomials< OneDPolynomials, DIM >