oomph::OneDimensionalLegendreDShape< NNODE_1D > Class Template Reference

#include <shape.h>

Inheritance diagram for oomph::OneDimensionalLegendreDShape< NNODE_1D >:

Public Member Functions
	OneDimensionalLegendreDShape (const double &s)
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...

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...

Constructor & Destructor Documentation

OneDimensionalLegendreDShape()

template<unsigned NNODE_1D>

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

inline

                                                  : Shape(NNODE_1D)
    {
      unsigned p = NNODE_1D - 1;
      Vector<double> z = OneDimensionalLegendreShape<NNODE_1D>::z;
 
 
      bool root = false;
 
      for (unsigned i = 0; i < NNODE_1D; i++)
      {
        unsigned rootnum = 0;
        for (unsigned j = 0; j < NNODE_1D; j++)
        { // Loop over roots to check if
          if (std::fabs(s - z[j]) < 10 * Orthpoly::eps)
          { // s happens to be a root.
            root = true;
            break;
          }
          rootnum += 1;
        }
        if (root == true)
        {
          if (i == rootnum && i == 0)
          {
            (*this)[i] = -(1.0 + p) * p / 4.0;
          }
          else if (i == rootnum && i == p)
          {
            (*this)[i] = (1.0 + p) * p / 4.0;
          }
          else if (i == rootnum)
          {
            (*this)[i] = 0.0;
          }
          else
          {
            (*this)[i] = Orthpoly::legendre(p, z[rootnum]) /
                         Orthpoly::legendre(p, z[i]) / (z[rootnum] - z[i]);
          }
        }
        else
        {
          (*this)[i] =
            ((1 + s * (s - 2 * z[i])) / (s - z[i]) * Orthpoly::dlegendre(p, s) -
             (1 - s * s) * Orthpoly::ddlegendre(p, s)) /
            p / (p + 1.0) / Orthpoly::legendre(p, z[i]) / (s - z[i]);
        }
        root = false;
      }
    }

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

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

• shape.h