Note: this is documentation for an old release. View the latest documentation at docs.fenicsproject.org/basix/v0.8.0/cpp/namespacebasix_1_1moments.html

Basix 0.4.1

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Functions
basix::moments Namespace Reference

Functions to create integral moment DOFs. More...

Functions

std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > make_integral_moments (const FiniteElement &moment_space, cell::type celltype, std::size_t value_size, int q_deg)
 
std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > make_dot_integral_moments (const FiniteElement &V, cell::type celltype, std::size_t value_size, int q_deg)
 
std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > make_tangent_integral_moments (const FiniteElement &V, cell::type celltype, std::size_t value_size, int q_deg)
 
std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > make_normal_integral_moments (const FiniteElement &V, cell::type celltype, std::size_t value_size, int q_deg)
 

Detailed Description

Functions to create integral moment DOFs.

Function Documentation

◆ make_dot_integral_moments()

std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > basix::moments::make_dot_integral_moments ( const FiniteElement V,
cell::type  celltype,
std::size_t  value_size,
int  q_deg 
)

Make interpolation points and weights for dot product integral moments

These will represent the integral of each function in the moment space over each sub entity of the moment space's cell type in a cell with the given type. For example, if the input cell type is a triangle and the moment space is a P1 space on an edge, this will perform two integrals for each of the 3 edges of the triangle.

Todo:
Clarify what happens value size of the moment space is less than value_size.
Parameters
VThe space to compute the integral moments against
celltypeThe cell type of the cell on which the space is being defined
value_sizeThe value size of the space being defined
q_degThe quadrature degree used for the integrals
Returns
(interpolation points, interpolation matrix)

◆ make_integral_moments()

std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > basix::moments::make_integral_moments ( const FiniteElement moment_space,
cell::type  celltype,
std::size_t  value_size,
int  q_deg 
)

Make interpolation points and weights for simple integral moments

These will represent the integral of each function in the moment space over each sub entity of the moment space's cell type in a cell with the given type. For example, if the input cell type is a triangle, and the moment space is a P1 space on an edge, this will perform two integrals for each of the 3 edges of the triangle.

Parameters
moment_spaceThe space to compute the integral moments against
celltypeThe cell type of the cell on which the space is being defined
value_sizeThe value size of the space being defined
q_degThe quadrature degree used for the integrals
Returns
(interpolation points, interpolation matrix)

◆ make_normal_integral_moments()

std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > basix::moments::make_normal_integral_moments ( const FiniteElement V,
cell::type  celltype,
std::size_t  value_size,
int  q_deg 
)

Compute interpolation points and weights for normal integral moments

These can only be used when the moment space is defined on facets of the cell

Parameters
[in]VThe space to compute the integral moments against
[in]celltypeThe cell type of the cell on which the space is being defined
[in]value_sizeThe value size of the space being defined
[in]q_degThe quadrature degree used for the integrals
Returns
(interpolation points, interpolation matrix)

◆ make_tangent_integral_moments()

std::pair< std::vector< xt::xtensor< double, 2 > >, std::vector< xt::xtensor< double, 3 > > > basix::moments::make_tangent_integral_moments ( const FiniteElement V,
cell::type  celltype,
std::size_t  value_size,
int  q_deg 
)

Make interpolation points and weights for tangent integral moments

These can only be used when the moment space is defined on edges of the cell

Parameters
VThe space to compute the integral moments against
celltypeThe cell type of the cell on which the space is being defined
value_sizeThe value size of the space being defined the space
q_degThe quadrature degree used for the integrals
Returns
(interpolation points, interpolation matrix)