oomph::OneDimensionalLegendreShape< NNODE_1D > Class Template Reference

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

#include <shape.h>

Inheritance diagram for oomph::OneDimensionalLegendreShape< NNODE_1D >:

Public Member Functions
	OneDimensionalLegendreShape (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 ()
	Static function used to populate the stored positions. More...
static double	nodal_position (const unsigned &n)

Static Public Attributes
static Vector< double >	z

Static Private Attributes
static bool	Nodes_calculated = false

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

template<unsigned NNODE_1D>
class oomph::OneDimensionalLegendreShape< NNODE_1D >

Class that returns the shape functions associated with legendre.

Constructor & Destructor Documentation

OneDimensionalLegendreShape()

template<unsigned NNODE_1D>

oomph::OneDimensionalLegendreShape< NNODE_1D >::OneDimensionalLegendreShape ( const double &  s )

inline

Constructor.

                                                 : Shape(NNODE_1D)
    {
      using namespace Orthpoly;
 
      unsigned p = NNODE_1D - 1;
      // Now populate the shape function
      for (unsigned i = 0; i < NNODE_1D; i++)
      {
        // If we're at one of the nodes, the value must be 1.0
        if (std::fabs(s - z[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[i]) * (z[i] - s));
        }
      }
    }

References oomph::Orthpoly::dlegendre(), oomph::Orthpoly::eps, boost::multiprecision::fabs(), i, oomph::Orthpoly::legendre(), p, s, and oomph::OneDimensionalLegendreShape< NNODE_1D >::z.

Member Function Documentation

calculate_nodal_positions()

template<unsigned NNODE_1D>

static void oomph::OneDimensionalLegendreShape< NNODE_1D >::calculate_nodal_positions ( )

inlinestatic

Static function used to populate the stored positions.

    {
      if (!Nodes_calculated)
      {
        Orthpoly::gll_nodes(NNODE_1D, z);
        Nodes_calculated = true;
      }
    }

References oomph::Orthpoly::gll_nodes(), oomph::OneDimensionalLegendreShape< NNODE_1D >::Nodes_calculated, and oomph::OneDimensionalLegendreShape< NNODE_1D >::z.

Referenced by oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::dshape_local(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::dshape_local(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::dshape_local(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::QSpectralElement< 1, NNODE_1D >::QSpectralElement(), oomph::QSpectralElement< 2, NNODE_1D >::QSpectralElement(), oomph::QSpectralElement< 3, NNODE_1D >::QSpectralElement(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::shape(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::shape(), and oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::shape().

nodal_position()

template<unsigned NNODE_1D>

static double oomph::OneDimensionalLegendreShape< NNODE_1D >::nodal_position ( const unsigned &  n )

inlinestatic

    {
      return z[n];
    }

References n, and oomph::OneDimensionalLegendreShape< NNODE_1D >::z.

Referenced by oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::local_coordinate_of_node(), oomph::QSpectralElement< 1, NNODE_1D >::local_coordinate_of_node(), oomph::QSpectralElement< 2, NNODE_1D >::local_coordinate_of_node(), oomph::QSpectralElement< 3, NNODE_1D >::local_coordinate_of_node(), oomph::PRefineableQElement< 1, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::PRefineableQElement< 2, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::PRefineableQElement< 3, INITIAL_NNODE_1D >::local_one_d_fraction_of_node(), oomph::QSpectralElement< 1, NNODE_1D >::local_one_d_fraction_of_node(), oomph::QSpectralElement< 2, NNODE_1D >::local_one_d_fraction_of_node(), and oomph::QSpectralElement< 3, NNODE_1D >::local_one_d_fraction_of_node().

Member Data Documentation

Nodes_calculated

template<unsigned NNODE_1D>

bool oomph::OneDimensionalLegendreShape< NNODE_1D >::Nodes_calculated = false

staticprivate

Referenced by oomph::OneDimensionalLegendreShape< NNODE_1D >::calculate_nodal_positions().

z

template<unsigned NNODE_1D>

Vector< double > oomph::OneDimensionalLegendreShape< NNODE_1D >::z

static

Referenced by oomph::OneDimensionalLegendreShape< NNODE_1D >::calculate_nodal_positions(), oomph::OneDimensionalLegendreShape< NNODE_1D >::nodal_position(), oomph::OneDimensionalLegendreDShape< NNODE_1D >::OneDimensionalLegendreDShape(), and oomph::OneDimensionalLegendreShape< NNODE_1D >::OneDimensionalLegendreShape().

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

• shape.h