oiseau::dg::nodal::RefLine Class Reference

Represents a reference line element used in nodal Discontinuous Galerkin methods. More...

#include <ref_line.hpp>

Inheritance diagram for oiseau::dg::nodal::RefLine:

Public Member Functions
	RefLine (unsigned order)
	Constructs a RefLine element of the given polynomial order.
Public Member Functions inherited from oiseau::dg::nodal::RefElement
const xt::xarray< double > &	v () const
const xt::xarray< double > &	gv () const
const xt::xarray< double > &	d () const
const xt::xarray< double > &	r () const
unsigned	order () const
unsigned	number_of_nodes () const
unsigned	number_of_face_nodes () const

Static Public Member Functions
static xt::xarray< double >	basis_function (const xt::xarray< double > &r, int i)
	Evaluates the i-th Lagrange basis function at the given reference points.
static xt::xarray< double >	grad_basis_function (const xt::xarray< double > &r, int i)
	Evaluates the gradient of the i-th Lagrange basis function at the given reference points.

Additional Inherited Members
Protected Member Functions inherited from oiseau::dg::nodal::RefElement
	RefElement (unsigned order)
Protected Attributes inherited from oiseau::dg::nodal::RefElement
unsigned	m_order
unsigned	m_np {}
unsigned	m_nfp {}
xt::xarray< double >	m_v
xt::xarray< double >	m_gv
xt::xarray< double >	m_d
xt::xarray< double >	m_r

Detailed Description

Represents a reference line element used in nodal Discontinuous Galerkin methods.

This class implements the necessary basis functions, their gradients, and supporting operators for a 1D reference element (line) of arbitrary polynomial order.

ASCII representation of the reference line node numbering (order = 4):

(0) (1) (2) (3) (4) |--—|--—|--—|--—| -1 1

The line spans the reference interval [-1, 1]. Nodes are placed at Gauss, Gauss–Lobatto, or Jacobi–Gauss points depending on the implementation in generate_line_nodes.

Constructor & Destructor Documentation

RefLine()

oiseau::dg::nodal::RefLine::RefLine ( unsigned order )

explicit

Constructs a RefLine element of the given polynomial order.

Parameters

order

The polynomial order of the reference element.

Member Function Documentation

basis_function()

xt::xarray< double > oiseau::dg::nodal::RefLine::basis_function ( const xt::xarray< double > & r, int i )

static

Evaluates the i-th Lagrange basis function at the given reference points.

Parameters

r	Reference coordinates where the basis function is evaluated.
i	Index of the basis function to evaluate.

Returns

The value of the i-th basis function at each point in r.

grad_basis_function()

xt::xarray< double > oiseau::dg::nodal::RefLine::grad_basis_function ( const xt::xarray< double > & r, int i )

static

Evaluates the gradient of the i-th Lagrange basis function at the given reference points.

Parameters

r	Reference coordinates where the gradient is evaluated.
i	Index of the basis function.

Returns

The gradient of the i-th basis function at each point in r.

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

• /__w/oiseau/oiseau/src/oiseau/dg/nodal/ref_line.hpp
• /__w/oiseau/oiseau/src/oiseau/dg/nodal/ref_line.cpp