MFEM  v4.3.0
Finite element discretization library
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mfem::Poly_1D Class Reference

#include <fe.hpp>

Classes

class  Basis
 

Public Types

enum  EvalType {
  ChangeOfBasis = 0, Barycentric = 1, Positive = 2, Integrated = 3,
  NumEvalTypes = 4
}
 

Public Member Functions

 Poly_1D ()
 
const double * GetPoints (const int p, const int btype)
 Get the coordinates of the points of the given BasisType, btype. More...
 
const double * OpenPoints (const int p, const int btype=BasisType::GaussLegendre)
 Get coordinates of an open (GaussLegendre) set of points if degree p. More...
 
const double * ClosedPoints (const int p, const int btype=BasisType::GaussLobatto)
 Get coordinates of a closed (GaussLegendre) set of points if degree p. More...
 
BasisGetBasis (const int p, const int btype)
 Get a Poly_1D::Basis object of the given degree and BasisType, btype. More...
 
 ~Poly_1D ()
 

Static Public Member Functions

static const int * Binom (const int p)
 Get a pointer to an array containing the binomial coefficients "p choose k" for k=0,...,p for the given p. More...
 
static void CalcBasis (const int p, const double x, double *u)
 Evaluate the values of a hierarchical 1D basis at point x hierarchical = k-th basis function is degree k polynomial. More...
 
static void CalcBasis (const int p, const double x, double *u, double *d)
 Evaluate the values and derivatives of a hierarchical 1D basis at point x. More...
 
static void CalcBasis (const int p, const double x, double *u, double *d, double *dd)
 Evaluate the values, derivatives and second derivatives of a hierarchical 1D basis at point x. More...
 
static double CalcDelta (const int p, const double x)
 Evaluate a representation of a Delta function at point x. More...
 
static void ChebyshevPoints (const int p, double *x)
 Compute the points for the Chebyshev polynomials of order p and place them in the already allocated x array. More...
 
static void CalcBinomTerms (const int p, const double x, const double y, double *u)
 Compute the p terms in the expansion of the binomial (x + y)^p and store them in the already allocated u array. More...
 
static void CalcBinomTerms (const int p, const double x, const double y, double *u, double *d)
 Compute the terms in the expansion of the binomial (x + y)^p and their derivatives with respect to x assuming that dy/dx = -1. Store the results in the already allocated u and d arrays. More...
 
static void CalcDBinomTerms (const int p, const double x, const double y, double *d)
 Compute the derivatives (w.r.t. x) of the terms in the expansion of the binomial (x + y)^p assuming that dy/dx = -1. Store the results in the already allocated d array. More...
 
static void CalcBernstein (const int p, const double x, double *u)
 Compute the values of the Bernstein basis functions of order p at coordinate x and store the results in the already allocated u array. More...
 
static void CalcBernstein (const int p, const double x, double *u, double *d)
 Compute the values and derivatives of the Bernstein basis functions of order p at coordinate x and store the results in the already allocated u and d arrays. More...
 
static void CalcLegendre (const int p, const double x, double *u)
 
static void CalcLegendre (const int p, const double x, double *u, double *d)
 

Detailed Description

Class for computing 1D special polynomials and their associated basis functions

Definition at line 1961 of file fe.hpp.

Member Enumeration Documentation

Enumerator
ChangeOfBasis 
Barycentric 
Positive 
Integrated 
NumEvalTypes 

Definition at line 1964 of file fe.hpp.

Constructor & Destructor Documentation

mfem::Poly_1D::Poly_1D ( )
inline

Definition at line 2019 of file fe.hpp.

mfem::Poly_1D::~Poly_1D ( )

Definition at line 7692 of file fe.cpp.

Member Function Documentation

const int * mfem::Poly_1D::Binom ( const int  p)
static

Get a pointer to an array containing the binomial coefficients "p choose k" for k=0,...,p for the given p.

Definition at line 7401 of file fe.cpp.

static void mfem::Poly_1D::CalcBasis ( const int  p,
const double  x,
double *  u 
)
inlinestatic

Evaluate the values of a hierarchical 1D basis at point x hierarchical = k-th basis function is degree k polynomial.

Definition at line 2058 of file fe.hpp.

static void mfem::Poly_1D::CalcBasis ( const int  p,
const double  x,
double *  u,
double *  d 
)
inlinestatic

Evaluate the values and derivatives of a hierarchical 1D basis at point x.

Definition at line 2067 of file fe.hpp.

static void mfem::Poly_1D::CalcBasis ( const int  p,
const double  x,
double *  u,
double *  d,
double *  dd 
)
inlinestatic

Evaluate the values, derivatives and second derivatives of a hierarchical 1D basis at point x.

Definition at line 2074 of file fe.hpp.

static void mfem::Poly_1D::CalcBernstein ( const int  p,
const double  x,
double *  u 
)
inlinestatic

Compute the values of the Bernstein basis functions of order p at coordinate x and store the results in the already allocated u array.

Definition at line 2107 of file fe.hpp.

static void mfem::Poly_1D::CalcBernstein ( const int  p,
const double  x,
double *  u,
double *  d 
)
inlinestatic

Compute the values and derivatives of the Bernstein basis functions of order p at coordinate x and store the results in the already allocated u and d arrays.

Definition at line 2113 of file fe.hpp.

void mfem::Poly_1D::CalcBinomTerms ( const int  p,
const double  x,
const double  y,
double *  u 
)
static

Compute the p terms in the expansion of the binomial (x + y)^p and store them in the already allocated u array.

Definition at line 7450 of file fe.cpp.

void mfem::Poly_1D::CalcBinomTerms ( const int  p,
const double  x,
const double  y,
double *  u,
double *  d 
)
static

Compute the terms in the expansion of the binomial (x + y)^p and their derivatives with respect to x assuming that dy/dx = -1. Store the results in the already allocated u and d arrays.

Definition at line 7479 of file fe.cpp.

void mfem::Poly_1D::CalcDBinomTerms ( const int  p,
const double  x,
const double  y,
double *  d 
)
static

Compute the derivatives (w.r.t. x) of the terms in the expansion of the binomial (x + y)^p assuming that dy/dx = -1. Store the results in the already allocated d array.

Definition at line 7514 of file fe.cpp.

static double mfem::Poly_1D::CalcDelta ( const int  p,
const double  x 
)
inlinestatic

Evaluate a representation of a Delta function at point x.

Definition at line 2082 of file fe.hpp.

void mfem::Poly_1D::CalcLegendre ( const int  p,
const double  x,
double *  u 
)
static

Definition at line 7544 of file fe.cpp.

void mfem::Poly_1D::CalcLegendre ( const int  p,
const double  x,
double *  u,
double *  d 
)
static

Definition at line 7558 of file fe.cpp.

void mfem::Poly_1D::ChebyshevPoints ( const int  p,
double *  x 
)
static

Compute the points for the Chebyshev polynomials of order p and place them in the already allocated x array.

Definition at line 7418 of file fe.cpp.

const double* mfem::Poly_1D::ClosedPoints ( const int  p,
const int  btype = BasisType::GaussLobatto 
)
inline

Get coordinates of a closed (GaussLegendre) set of points if degree p.

Definition at line 2042 of file fe.hpp.

Poly_1D::Basis & mfem::Poly_1D::GetBasis ( const int  p,
const int  btype 
)

Get a Poly_1D::Basis object of the given degree and BasisType, btype.

Parameters
[in]pThe polynomial degree of the basis.
[in]btypeThe BasisType.
Returns
A reference to an object of type Poly_1D::Basis that represents the requested basis type.

Definition at line 7667 of file fe.cpp.

const double * mfem::Poly_1D::GetPoints ( const int  p,
const int  btype 
)

Get the coordinates of the points of the given BasisType, btype.

Parameters
[in]pThe polynomial degree; the number of points is p+1.
[in]btypeThe BasisType.
Returns
A pointer to an array containing the p+1 coordinates of the points. Returns NULL if the BasisType has no associated set of points.

Definition at line 7643 of file fe.cpp.

const double* mfem::Poly_1D::OpenPoints ( const int  p,
const int  btype = BasisType::GaussLegendre 
)
inline

Get coordinates of an open (GaussLegendre) set of points if degree p.

Definition at line 2037 of file fe.hpp.


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