A NOTE ON THE CONVERGENCE OF THE DIRECT COLLOCATION BOUNDARY ELEMENT METHOD

✍ Scribed by P. Juhl

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 236 KB
• Volume: 212
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1456

✦ Synopsis

Convergence results for acoustic boundary element formulations have mainly been presented in the mathematical and numerical literature, and the results do not seem to be widely known among acoustic engineers. In this paper, an overview of some of the literature dealing with convergence of boundary element formulations is presented, and an intuitive account of the results is given. The convergence of an axisymmetric boundary element formulation is studied by using linear, quadratic or superparametric elements. It is demonstrated how the rate of convergence of these formulations is reduced for calculations involving bodies with edges (geometric singularities). Two methods for improving the rate of convergence are suggested and examined. First, elements modelling the singular behaviour of the sound field are used, and then a novel technique of replacing the mid-element node is presented. The latter approach is a generalization of the well-known quarter point technique in which the mid-element node is displaced better to model the singularity.