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

• Published in: Journal of the Chinese Institute of Engineers Vol. 30; no. 2; pp. 219 - 230
• Main Authors: Shiah, Yui-Chuin, Shih, Yi-Shiau
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.03.2007
• Subjects: anisotropic thermal field; interior thermal fields; nearly singular integrals
• ISSN: 0253-3839; 2158-7299
• DOI: 10.1080/02533839.2007.9671248

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 hyper-singular 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.