×

Adaptive integration technique for nearly singular integrals in near-field acoustics boundary element analysis. (English) Zbl 1302.76122

Gao, X. W. (ed.) et al., Boundary elements and other mesh reduction methods XXXVI. Selected papers based on the presentations at the 36th international conference (BEM/MRM), New Forest, UK, June 8–11, 2014. Southampton: WIT Press (ISBN 978-1-84564-841-1/hbk; 978-1-84564-842-8/ebook). WIT Transactions on Modelling and Simulation 56, 353-363 (2014).
Summary: 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.
For the entire collection see [Zbl 1279.65006].

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI