A comparison of techniques for overcoming nonuniqueness of boundary integral equations for collocation Partition of Unity methods in acoustics

Diwan, G.C.; Trevelyan, J.; Coates, G.

Abstract

In the last decade the Partition of Unity Method has become attractive as one approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements. It is well known that the conventional boundary integral equation obtained through Green’s representation theorem suers from a problem of nonuniqueness at certain frequencies. The standard methods of overcoming this problem are the so-called CHIEF method and that of Burton and Miller. The latter method introduces a hypersingular operator which may be treated in various ways. In this paper we present the collocation Partition of Unity BEM for Helmholtz problems and compare the performance of CHIEF against a Burton-Miller formulation regularised using the approach of Li and Huang.

Citation

Diwan, G., Trevelyan, J., & Coates, G. (2013, March). A comparison of techniques for overcoming nonuniqueness of boundary integral equations for collocation Partition of Unity methods in acoustics. Presented at International Conference on Computational Mechanics : CM13, Durham, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: International Conference on Computational Mechanics : CM13
• Start Date: Mar 25, 2013
• End Date: Mar 27, 2013
• Publication Date: Mar 1, 2013
• Deposit Date: Jan 5, 2016
• Publicly Available Date: Jan 28, 2016
• Keywords: Nonuniqueness, CHIEF, Burton - Miller formulation, Partition of Unity BEM
• Public URL: https://durham-repository.worktribe.com/output/1152151
• Publisher URL: https://www.dur.ac.uk/whatson/event/?eventno=14706