Class that returns the shape functions associated with legendre. More...

#include <Qspectral_elements.h>

Inheritance diagram for oomph::OneDLegendreShapeParam:

Public Member Functions
	OneDLegendreShapeParam (const unsigned &order, const double &s)
	Constructor. More...

Public Member Functions inherited from oomph::Shape
	Shape (const unsigned &N)
	Constructor for a single-index set of shape functions. More...

	Shape (const unsigned &N, const unsigned &M)
	Constructor for a two-index set of shape functions. More...

	Shape (const Shape &shape)=delete
	Broken copy constructor. More...

	Shape ()

void	operator= (const Shape &shape)

void	operator= (Shape *const &shape_pt)

	~Shape ()
	Destructor, clear up the memory allocated by the object. More...

void	resize (const unsigned &N, const unsigned &M=1)
	Change the size of the storage. More...

double &	operator[] (const unsigned &i)
	Overload the bracket operator to provide access to values. More...

const double &	operator[] (const unsigned &i) const
	Overload the bracket operator (const version) More...

double &	operator() (const unsigned &i)
	Overload the round bracket operator to provide access to values. More...

const double &	operator() (const unsigned &i) const
	Overload the round bracket operator (const version) More...

double &	operator() (const unsigned &i, const unsigned &j)
	Overload the round bracket operator, allowing for two indices. More...

const double &	operator() (const unsigned &i, const unsigned &j) const

unsigned	nindex1 () const
	Return the range of index 1 of the shape function object. More...

unsigned	nindex2 () const
	Return the range of index 2 of the shape function object. More...

Static Public Member Functions
static void	calculate_nodal_positions (const unsigned &order)
	Static function used to populate the stored positions. More...

static double	nodal_position (const unsigned &order, const unsigned &n)

Static Public Attributes
static std::map< unsigned, Vector< double > >	z

Additional Inherited Members
Protected Member Functions inherited from oomph::Shape
void	range_check (const unsigned &i, const unsigned &j) const
	Private function that checks whether the index is in range. More...

Protected Attributes inherited from oomph::Shape
double *	Psi

double *	Allocated_storage

unsigned	Index1
	Size of the first index of the shape function. More...

unsigned	Index2
	Size of the second index of the shape function. More...

Detailed Description

Class that returns the shape functions associated with legendre.

Constructor & Destructor Documentation

◆ OneDLegendreShapeParam()

oomph::OneDLegendreShapeParam::OneDLegendreShapeParam	(	const unsigned &	order,
		const double &	s
	)

inline

Constructor.

       : Shape(order)
     {
       using namespace Orthpoly;
  
       unsigned p = order - 1;
       // Now populate the shape function
       for (unsigned i = 0; i < order; i++)
       {
         // If we're at one of the nodes, the value must be 1.0
         if (std::fabs(s - z[order][i]) < Orthpoly::eps)
         {
           (*this)[i] = 1.0;
         }
         // Otherwise use the lagrangian interpolant
         else
         {
           (*this)[i] =
             (1.0 - s * s) * dlegendre(p, s) /
             (p * (p + 1) * legendre(p, z[order][i]) * (z[order][i] - s));
         }
       }
     }

References oomph::Orthpoly::dlegendre(), oomph::Orthpoly::eps, boost::multiprecision::fabs(), i, oomph::Orthpoly::legendre(), p, s, and z.

Member Function Documentation

◆ calculate_nodal_positions()

static void oomph::OneDLegendreShapeParam::calculate_nodal_positions ( const unsigned & order )

inlinestatic

Static function used to populate the stored positions.

     {
       // If we haven't already calculated these
       if (z.find(order) == z.end())
       {
         Orthpoly::gll_nodes(order, z[order]);
       }
     }

References oomph::Orthpoly::gll_nodes(), and z.

◆ nodal_position()

static double oomph::OneDLegendreShapeParam::nodal_position	(	const unsigned &	order,
		const unsigned &	n
	)

inlinestatic

     {
       return z[order][n];
     }

References n, and z.

Member Data Documentation

◆ z

std::map< unsigned, Vector< double > > oomph::OneDLegendreShapeParam::z

static

Referenced by calculate_nodal_positions(), nodal_position(), oomph::OneDLegendreDShapeParam::OneDLegendreDShapeParam(), and OneDLegendreShapeParam().

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Additional Inherited Members