Adaptive Integration Method Based on Sub-Division 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 equation close to the boundary of 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 the 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 equation to the element under integration. By introducing the Jacobian of the sub-element, nearly singular integrals can be calculated numerically without the nodal values of sub-elements. Two numerical examples are presented to demonstrate the efficiency and accuracy of the proposed approach.