SOME MORE ON LOGARITHMIC SINGULARITY INTEGRATION IN BOUNDARY ELEMENT METOD

Tomasz Rymarczyk

1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics (Poland)
https://orcid.org/0000-0002-3524-9151

Jan Sikora

sik59@wp.pl
1Research & Development Centre Netrix S.A., Lublin, Poland, 2University of Economics and Innovation in Lublin, Faculty of Transport and Informatics (Poland)
https://orcid.org/0000-0002-9492-5818

Abstract

The accuracy of calculations of integrals with logarithmic singularities for two methods, namely the method of ignoring singularities and the method of subtraction (consisting in separating the singular part from the remaining non-singular), are presented in this paper. Only two-dimensional problems, like Dirichlet's problems, as well as acoustic problems formulated in the frequency domain are considered. Problems related to the accuracy of calculations are discussed and the influence of frequency, as well as the influence of the geometry of the analysed area on the accuracy of calculations, are indicated. When we talk about the influence of geometry, we mean not only discretization, but also the configuration of the area, such as the sharp edges of the boundary line, assuming the use of the classic, without any modifications, Boundary Element Method.

Keywords:

singular integral calculating, ignoring singularity method, singularity subtraction technique, acoustic wave propagation, Boundary Element Method (BEM)