Open Access

ARTICLE

Calculation of Potential Second Derivatives by Means of a Regularized Indirect Algorithm in the Boundary Element Method

H.B. Chen¹, Masa. Tanaka²

1 CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: hbchen@ustc.edu.cn
2 Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan

Computer Modeling in Engineering & Sciences 2010, 69(1), 19-42. https://doi.org/10.3970/cmes.2010.069.019

Abstract

Highly accurate calculation of derivative values to the field variable is a key issue in numerical analysis of engineering problems. The boundary integral equations (BIEs) of potential second derivatives are of third order singularities and obviously the direct calculation of these high order singular integrals is rather cumbersome. The idea of the present paper is to use an indirect algorithm which is based on the regularized BIE formulations of the potential second derivatives, following the work of the present first author and his coworkers. The regularized formulations, numerical strategies and example tests are given for both potential first and second derivatives to make this work systematic and easier to observe the error sources. Numerical results show the validity of the newly proposed algorithm in the calculation of potential second derivatives at the boundary in two dimensional potential problems.

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Keywords

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