CEPS: /builds/xxjFYZX3/0/carmen/ceps/src/pde/finiteElements/LagrangeBasisFunctions.cpp File Reference

#include "pde/finiteElements/LagrangeBasisFunctions.hpp"

Functions
void	buildSimplexUniformPoints (CepsUInt dim, CepsUInt numberOfPoints, CepsVector< CepsReal3D > &points, CepsVector< CepsInt > &geomCellIndex)
	Constructs the list of uniform points of the simplex of given dimension. More...

CepsVector< CepsArray3< CepsInt > >	buildBasisFunctionExponents (CepsUInt dim, CepsUInt numberOfPoints)
	Constructs the list of ordered exponents for a given number of points, typically constructed x^i y^j z^k with i,j,k < numberOfPoints. Beware the list must be resized when used. More...

void	buildPolysBasisFunction (CepsUInt dim, CepsUInt order, CepsVector< CepsReal3D > &points, CepsVector< CepsInt > &geomCellIndex, CepsVector< Polynomial< 3U >> &polys, void(*pointBuilder)(CepsUInt, CepsUInt, CepsVector< CepsReal3D > &, CepsVector< CepsInt > &))
	Constructs the list of base functions in the form of `Polynomials`. More...

Detailed Description

Functions that build basis functions of Lagrange FEs

Definition in file LagrangeBasisFunctions.cpp.

Function Documentation

◆ buildBasisFunctionExponents()

CepsVector<CepsArray3<CepsInt> > buildBasisFunctionExponents	(	CepsUInt	dim,
		CepsUInt	numberOfPoints
	)

Constructs the list of ordered exponents for a given number of points, typically constructed x^i y^j z^k with i,j,k < numberOfPoints. Beware the list must be resized when used.

Parameters

[in]	dim	the simplex dimension
[in]	numberOfPoints	number of points in first dimension

Returns: CepsVector<CepsArray3<CepsInt>> the list of exponents

Definition at line 99 of file LagrangeBasisFunctions.cpp.

◆ buildPolysBasisFunction()

void buildPolysBasisFunction	(	CepsUInt	dim,
		CepsUInt	order,
		CepsVector< CepsReal3D > &	points,
		CepsVector< CepsInt > &	geomCellIndex,
		CepsVector< Polynomial< 3U >> &	polys,
		void(*)(CepsUInt, CepsUInt, CepsVector< CepsReal3D > &, CepsVector< CepsInt > &)	pointsBuilder
	)

Constructs the list of base functions in the form of Polynomials.

See also: Polynomial

Parameters

[in]	dim	the simplex dimension
[in]	order	the order wanted
[out]	points	the list of points used to buid basis function (with phi_i(x_j) = delta_ij)
[in]	geomCellIndex	geom indices of cell points
[out]	polys	the list of `Polynomial`
[in]	pointsBuilder	function which creates the list of points

Definition at line 144 of file LagrangeBasisFunctions.cpp.

◆ buildSimplexUniformPoints()

void buildSimplexUniformPoints	(	CepsUInt	dim,
		CepsUInt	numberOfPoints,
		CepsVector< CepsReal3D > &	points,
		CepsVector< CepsInt > &	geomCellIndex
	)

Constructs the list of uniform points of the simplex of given dimension.

1D: cable (0)-(1) 2D: triangle (0,0)-(1,0)-(0,1) 3D: tetra (0,0,0)-(1,0,0)-(0,1,0)-(0,0,1)

The following conventions are followed for node numbering of P2 elements:

1D:

$\begin{tikzpicture} \begin{scope}[x=2cm] \node (x0) at (0,0) {0}; \node (x2) at (1,0) {2}; \node (x1) at (0.5,0) {1}; \draw (x0) -- (x2); \draw (x1) -- (x2); \end{scope} \end{tikzpicture}$

2D:

$\begin{tikzpicture} \begin{scope}[x=2cm,y=2cm] \node (x0) at (0,0) {0}; \node (x1) at (1,0) {5}; \node (x2) at (0,1) {2}; \node (x3) at (0.5,0.5) {4}; \node (x4) at (0,0.5) {1}; \node (x5) at (0.5,0) {3}; \draw (x0) -- (x5) -- (x1) -- (x3) -- (x2) -- (x4) -- (x0); \end{scope} \end{tikzpicture}$

3D:

$\begin{tikzpicture} \begin{scope}[x=2cm,y=2cm,z=-1.2cm] \node (x0) at (0,0,0) {0}; \node (x1) at (1,0,0) {9}; \node (x2) at (0,1,0) {5}; \node (x3) at (0,0,1) {2}; \node (x4) at (0,0.5,0.5) {4}; \node (x5) at (0.5,0,0.5) {7}; \node (x6) at (0.5,0.5,0) {8}; \node (x7) at (0.5,0,0) {6}; \node (x8) at (0,0.5,0) {3}; \node (x9) at (0,0,0.5) {1}; \draw (x0) -- (x7) -- (x1) -- (x6) -- (x2) -- (x8) -- (x0); \draw (x0) -- (x9) -- (x3) -- (x4) -- (x2); \draw (x1) -- (x5) -- (x3); \end{scope} \end{tikzpicture}$

Parameters

[in]	dim	the simplex dimension
[in]	numberOfPoints	number of points in the first dimension
[out]	points	the list of points
[out]	geomCellIndex	tells if i-th node matches a geometrical node

Definition at line 63 of file LagrangeBasisFunctions.cpp.