Adaptive integration technique for nearly singular integrals in near-field acoustics boundary element analysis

Abstract

The aim of this paper is to present an efficient adaptive integration technique to perform near-field acoustics boundary element analysis, in which nearly singular integrals will be encountered as the source point in integral equations is close to the boundary of the acoustic domain. At this time the integrand varies sharply, so the conventional Gaussian quadrature becomes inefficient or even inaccurate. In this paper, an adaptive integration technique is proposed, which determines required Gauss orders and the number of sub-elements according to the specified integration accuracy and the relative position from the source point in integral equations to the element under integration. Two numerical examples have been presented to demonstrate the efficiency and accuracy of the proposed approach.