NiHu  2.0
Functions
telles_1987.hpp File Reference
Libraries for specific fields of application » Specialised singular and nearly singular integration methods

Implementation of Telles' quadrature transform method. More...

#include "core/quadrature.hpp"
#include <cmath>
Include dependency graph for telles_1987.hpp:
This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Functions

template<class QuadDerived >
QuadDerived NiHu::telles_transform (quadrature_base< QuadDerived > const &q, typename quadrature_traits< QuadDerived >::domain_t::xi_t const &eta_bar, typename quadrature_traits< QuadDerived >::domain_t::scalar_t const &d=typename quadrature_traits< QuadDerived >::domain_t::scalar_t())
 Telles third order polynomial transform. More...
 

Detailed Description

Implementation of Telles' quadrature transform method.

Definition in file telles_1987.hpp.

Function Documentation

◆ telles_transform()

template<class QuadDerived >
QuadDerived NiHu::telles_transform ( quadrature_base< QuadDerived > const &  q,
typename quadrature_traits< QuadDerived >::domain_t::xi_t const &  eta_bar,
typename quadrature_traits< QuadDerived >::domain_t::scalar_t const &  d = typename quadrature_traits<QuadDerived>::domain_t::scalar_t() 
)

Telles third order polynomial transform.

Template Parameters
QuadDerivedDerived quadrature type
Parameters
[in]qQuadrature to transform
[in]eta_barThe singular location in the element coordinate system
[in]dDistance of the singular point in the other direction
Returns
Transformed quadrature with new base points and weights

Performs the third order polynomial transform on a quadrature to cancel singularities or calculate nearly singular integrals more accurately. The method is implemented as given in Ref. [1].

References:
[1] J.C.F. Telles: A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. International Journal for numerical methods in engineering. Vol. 24, pp. 959-973 (1987) DOI: 10.1002/nme.1620240509
Todo:
MSVC refuses typename in parameter instantiation GCC needs typename in parameter instantiation -> conflict resolved by #ifdef _MSC_VER

Definition at line 44 of file telles_1987.hpp.