Defines Legendre polynomials in the specified dimension on reference elements. More...

#include <ptems/spaces/monomials.hpp>

Inheritance diagram for ptems::Monomials< DIM >:

Collaboration diagram for ptems::Monomials< DIM >:

Static Public Member Functions
template<typename T = double>
static Vector< DIM >	EstimateAnalyticity ([[maybe_unused]] const ReferenceElement< DIM > &refElement, [[maybe_unused]] std::size_t polydeg, [[maybe_unused]] T *coefficients)
	Estimates the analyticity of a function with the current basis and specified coefficients. More...

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...

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...

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<std::size_t DIM>
struct ptems::Monomials< DIM >

Defines Legendre polynomials in the specified dimension on reference elements.

Defines the set of hierarchical monomials in the reference element of the form \(\prod_{i=1}^{DIM} x_i^\alpha_i\), for the multi-index \(\alpha\).

Template Parameters

DIM	The dimension the Legendre polynomials are in

The properties of the multi-index depend on the type of reference element; e.g.,

for simplicial reference elements \(\sum_{i=1}^DIM \alpha_i \leq p+1\), and
for hypercube reference elements \(\alpha_i \leq p+1\) for \(i=1,\dots,DIM\)

Member Function Documentation

◆ EstimateAnalyticity()

template<std::size_t DIM>

template<typename T = double>

static Vector<DIM> ptems::Monomials< DIM >::EstimateAnalyticity	(	[[maybe_unused] ] const ReferenceElement< DIM > &	refElement,
		[[maybe_unused] ] std::size_t	polydeg,
		[[maybe_unused] ] T *	coefficients
	)

inlinestatic

Estimates the analyticity of a function with the current basis and specified coefficients.

Template Parameters

T	The type of the coefficients (default=double)

Parameters

refElement	The reference element
polydeg	The polynomial degree of the function
coefficients	Array of coefficients for each basis. Must be length of NumberDoFs

Returns: Vector of analyticity for each dimension in range [0,1], or -1 if analyticity computation invalid

◆ Gradient()

static FuncAndGradData<DIM,T>* ptems::HierarchicalPolynomials< Monomials< 1 > , DIM >::Gradient	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		FuncAndGradData< DIM, T > *	result,
		std::size_t	polydeg
	)

inlinestaticinherited

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()

static FuncGradAndHessianData<DIM,T>* ptems::HierarchicalPolynomials< Monomials< 1 > , DIM >::Hessian	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		FuncGradAndHessianData< DIM, T > *	result,
		std::size_t	polydeg
	)

inlinestaticinherited

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()

static std::vector<std::size_t> ptems::HierarchicalPolynomials< Monomials< 1 > , DIM >::Indices	(	const ReferenceElement< DIM > &	refElement,
		std::size_t	originalPolydeg,
		std::size_t	newPolydeg
	)

inlinestaticinherited

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()

static T* ptems::HierarchicalPolynomials< Monomials< 1 > , DIM >::Polynomials	(	const ReferenceElement< DIM > &	refElement,
		const Vector< DIM > &	pt,
		T *	result,
		std::size_t	polydeg
	)

inlinestaticinherited

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/monomials.hpp

Static Public Member Functions

Detailed Description

template<std::size_t DIM> struct ptems::Monomials< DIM >

Member Function Documentation

◆ EstimateAnalyticity()

◆ Gradient()

◆ Hessian()

◆ Indices()

◆ Polynomials()

template<std::size_t DIM>
struct ptems::Monomials< DIM >