Author(s)

Y.J. Liu, D.M. Zhang & F.J. Rizzo

Abstract

Nearly singular and hypersingular integrals in the boundary element method Y.J. Liu, D.M. Zhang, F.J. Rizzo Center for Nondestructive Evaluation and Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, Iowa 50011, USA ABSTRACT Several techniques in dealing with nearly singular and hypersingular integrals which arise in applications of the boundary element method (BEM) are studied in this paper. The approach of using line integrals is emphasized and explored in some detail due to its high efficiency and accuracy. Numerical examples of stress analysis and scattering from an open crack in a 3-D elastic medium are presented to illustrate the ideas. INTRODUCTION Nearly singular integrals or nearly hypersingular integrals will occur in applications of the boundary element method whenever the source point is close to the surface (e.g., for 3-D problems) on which the integrations have to be performed. For example, nearly singular integrals

Keywords