A comparison of techniques for overcoming non-uniqueness of boundary integral equations for collocation Partition of Unity methods in acoustics.

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