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.

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.

Authors

G.C. Diwan

J. Trevelyan

G. Coates

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

Conference Name	International Conference on Computational Mechanics : CM13
Conference Location	Durham, UK
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
Publisher URL	https://www.dur.ac.uk/whatson/event/?eventno=14706