Functions | Variables
oomph::Orthpoly Namespace Reference

Functions

void gll_nodes (const unsigned &Nnode, Vector< double > &x)
 Calculates the Gauss Lobatto Legendre abscissas for degree p = NNode-1. More...
 
void gll_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)
 
void gl_nodes (const unsigned &Nnode, Vector< double > &x)
 
void gl_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)
 
double legendre (const unsigned &p, const double &x)
 Calculates Legendre polynomial of degree p at x using the three term recurrence relation $ (n+1) P_{n+1} = (2n+1)xP_{n} - nP_{n-1} $. More...
 
void legendre_vector (const unsigned &p, const double &x, Vector< double > &polys)
 Calculates Legendre polynomial of degree p at x using three term recursive formula. Returns all polynomials up to order p in the vector. More...
 
double dlegendre (const unsigned &p, const double &x)
 Calculates first derivative of Legendre polynomial of degree p at x using three term recursive formula. $ nP_{n+1}^{'} = (2n+1)xP_{n}^{'} - (n+1)P_{n-1}^{'} $. More...
 
double ddlegendre (const unsigned &p, const double &x)
 Calculates second derivative of Legendre polynomial of degree p at x using three term recursive formula. More...
 
double jacobi (const int &alpha, const int &beta, const unsigned &p, const double &x)
 Calculate the Jacobi polnomials. More...
 
void jacobi (const int &alpha, const int &beta, const unsigned &p, const double &x, Vector< double > &polys)
 Calculate the Jacobi polnomials all in one goe. More...
 

Variables

const double eps = 1.0e-15
 

Function Documentation

◆ ddlegendre()

double oomph::Orthpoly::ddlegendre ( const unsigned &  p,
const double &  x 
)
inline

Calculates second derivative of Legendre polynomial of degree p at x using three term recursive formula.

Definition at line 144 of file orthpoly.h.

References i.

Referenced by gll_nodes(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::oc_hang_helper(), oomph::OneDimensionalLegendreDShape< NNODE_1D >::OneDimensionalLegendreDShape(), oomph::OneDLegendreDShapeParam::OneDLegendreDShapeParam(), and oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::quad_hang_helper().

◆ dlegendre()

double oomph::Orthpoly::dlegendre ( const unsigned &  p,
const double &  x 
)
inline

Calculates first derivative of Legendre polynomial of degree p at x using three term recursive formula. $ nP_{n+1}^{'} = (2n+1)xP_{n}^{'} - (n+1)P_{n-1}^{'} $.

Definition at line 121 of file orthpoly.h.

Referenced by gl_nodes(), gll_nodes(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::oc_hang_helper(), oomph::OneDimensionalLegendreDShape< NNODE_1D >::OneDimensionalLegendreDShape(), oomph::OneDimensionalLegendreShape< NNODE_1D >::OneDimensionalLegendreShape(), oomph::OneDimensionalModalDShape::OneDimensionalModalDShape(), oomph::OneDLegendreDShapeParam::OneDLegendreDShapeParam(), oomph::OneDLegendreShapeParam::OneDLegendreShapeParam(), and oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::quad_hang_helper().

◆ gl_nodes() [1/2]

void oomph::Orthpoly::gl_nodes ( const unsigned &  Nnode,
Vector< double > &  x 
)

Definition at line 105 of file orthpoly.cc.

References dlegendre(), eps, legendre(), and oomph::MathematicalConstants::Pi.

Referenced by oomph::GaussLegendre< 1, NPTS_1D >::GaussLegendre(), oomph::GaussLegendre< 2, NPTS_1D >::GaussLegendre(), oomph::GaussLegendre< 3, NPTS_1D >::GaussLegendre(), and gl_nodes().

◆ gl_nodes() [2/2]

void oomph::Orthpoly::gl_nodes ( const unsigned &  Nnode,
Vector< double > &  x,
Vector< double > &  w 
)

Definition at line 148 of file orthpoly.cc.

References dlegendre(), gl_nodes(), and i.

◆ gll_nodes() [1/2]

void oomph::Orthpoly::gll_nodes ( const unsigned &  Nnode,
Vector< double > &  x 
)

Calculates the Gauss Lobatto Legendre abscissas for degree p = NNode-1.

Definition at line 33 of file orthpoly.cc.

References ddlegendre(), dlegendre(), eps, and oomph::MathematicalConstants::Pi.

Referenced by oomph::OneDimensionalLegendreShape< NNODE_1D >::calculate_nodal_positions(), oomph::OneDLegendreShapeParam::calculate_nodal_positions(), oomph::GaussLobattoLegendre< 1, NPTS_1D >::GaussLobattoLegendre(), oomph::GaussLobattoLegendre< 2, NPTS_1D >::GaussLobattoLegendre(), oomph::GaussLobattoLegendre< 3, NPTS_1D >::GaussLobattoLegendre(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::get_node_at_local_coordinate(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::get_node_at_local_coordinate(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::get_node_at_local_coordinate(), gll_nodes(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::oc_hang_helper(), and oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::quad_hang_helper().

◆ gll_nodes() [2/2]

void oomph::Orthpoly::gll_nodes ( const unsigned &  Nnode,
Vector< double > &  x,
Vector< double > &  w 
)

Definition at line 90 of file orthpoly.cc.

References gll_nodes(), i, and legendre().

◆ jacobi() [1/2]

double oomph::Orthpoly::jacobi ( const int &  alpha,
const int &  beta,
const unsigned &  p,
const double &  x 
)
inline

Calculate the Jacobi polnomials.

Definition at line 168 of file orthpoly.h.

◆ jacobi() [2/2]

void oomph::Orthpoly::jacobi ( const int &  alpha,
const int &  beta,
const unsigned &  p,
const double &  x,
Vector< double > &  polys 
)
inline

Calculate the Jacobi polnomials all in one goe.

Definition at line 200 of file orthpoly.h.

◆ legendre()

double oomph::Orthpoly::legendre ( const unsigned &  p,
const double &  x 
)
inline

Calculates Legendre polynomial of degree p at x using the three term recurrence relation $ (n+1) P_{n+1} = (2n+1)xP_{n} - nP_{n-1} $.

Definition at line 57 of file orthpoly.h.

Referenced by gl_nodes(), gll_nodes(), oomph::OneDimensionalLegendreDShape< NNODE_1D >::OneDimensionalLegendreDShape(), oomph::OneDimensionalLegendreShape< NNODE_1D >::OneDimensionalLegendreShape(), oomph::OneDimensionalModalDShape::OneDimensionalModalDShape(), oomph::OneDimensionalModalShape::OneDimensionalModalShape(), oomph::OneDLegendreDShapeParam::OneDLegendreDShapeParam(), and oomph::OneDLegendreShapeParam::OneDLegendreShapeParam().

◆ legendre_vector()

void oomph::Orthpoly::legendre_vector ( const unsigned &  p,
const double &  x,
Vector< double > &  polys 
)
inline

Calculates Legendre polynomial of degree p at x using three term recursive formula. Returns all polynomials up to order p in the vector.

Definition at line 88 of file orthpoly.h.

Variable Documentation

◆ eps

const double oomph::Orthpoly::eps = 1.0e-15

Definition at line 52 of file orthpoly.h.

Referenced by oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::dviscosity_dinvariant(), gl_nodes(), gll_nodes(), oomph::OneDimensionalLegendreDShape< NNODE_1D >::OneDimensionalLegendreDShape(), oomph::OneDimensionalLegendreShape< NNODE_1D >::OneDimensionalLegendreShape(), oomph::OneDLegendreDShapeParam::OneDLegendreDShapeParam(), oomph::OneDLegendreShapeParam::OneDLegendreShapeParam(), and oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::viscosity().