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On the computation of nearly singular integrals in 3D BEM collocation
Author(s) -
Scuderi Letizia
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2229
Subject(s) - gravitational singularity , collocation (remote sensing) , boundary element method , computation , planar , boundary (topology) , domain (mathematical analysis) , mathematics , point (geometry) , singular integral , element (criminal law) , singular point of a curve , mathematical analysis , geometry , computer science , finite element method , algorithm , integral equation , physics , law , computer graphics (images) , machine learning , political science , thermodynamics
In this paper, we propose an efficient strategy to compute nearly singular integrals over planar triangles in R 3 arising in boundary element method collocation. The strategy is based on a proper use of various non‐linear transformations, which smooth or move away or quite eliminate all the singularities close to the domain of integration. We will deal with near singularities of the form 1/ r , 1/ r 2 and 1/ r 3 , r =∥ x − y ∥ being the distance between a fixed near observation point x and a generic point y of a triangular element. Extensive numerical tests and comparisons with some already existing methods show that the approach proposed here is highly efficient and competitive. Copyright © 2007 John Wiley & Sons, Ltd.