The study of the effective methods dealing with problems with thin domains is an important and a difficult issue in boundary element method (BEM). For the special structures of thin bodies, the singular and nearly singular integrals often occur simultaneously in boundary integral equations (BIEs). Therefore, the conventional boundary element method (CBEM) is invalid to obtain accurate results. This paper based on the indirect variable regularized BIEs of plane potential problems, and a nonlinear variable transformation is introduced in order to improve the rapid variations of nearly singular integrals. By doing these, the boundary singular and nearly singular integrals can all be evaluated effectively. Numerical examples demonstrate that the present method can deal with thin-body problems with the thickness-to-length ratios range from 1.0E-01 to 1.0E-10
Zhang, Yao-Ming and Gu, Yan
"AN EFFECTIVE METHOD IN BEM FOR POTENTIAL PROBLEMS OF THIN BODIES,"
Journal of Marine Science and Technology: Vol. 18:
1, Article 17.
Available at: https://jmstt.ntou.edu.tw/journal/vol18/iss1/17