Regularization of nearly singular integrals in the boundary element analysis for interior anisotropic thermal field near the boundary

Abstract

In this paper the previously developed scheme of integration by parts to treat the boundary thermal field is applied to calculate the interior thermal field. Also, the scheme is extended further to regularize the strongly singular integral appearing in the boundary integral equation for interior calculations of the heat fluxes. Moreover, the present work develops a semi-analytical integration scheme to regularize the hypersingular integral for the interior heat-flux calculations. All formulations are derived for elements of arbitrary orders with general interpolation. At the end, the veracity of the scheme is illustrated by numerical examples.

Evaluation of Singular and Nearly Singular Integrals in the BEM with Exact Geometrical Representation

“…However, it is popular as well that the standard BEM formulations include singular and nearly singular integrals, and thus the integrations should be performed very carefully. In the past decades, many direct and indirect algorithms for singular integral have been developed and used successfully [1][2][3][4][5][6][7][8][9][10][11]. The nearly singular integrals, however, need to be further studied, although great progresses have been achieved for each of the existing methods.…”

“…These proposed methods can be divided on the whole into two categories: "indirect algorithms" and "irect algorithms". The indirect algorithms [4,[9][10][11], which benefit from the regularization ideas and techniques for the singular integrals, are mainly to calculate indirectly or avoid calculating the nearly singular integrals by establishing new regularized boundary integral equations (BIEs). However, the accuracy of their calculated results is not very satisfactory.…”