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A comparison of techniques for overcoming non‐uniqueness of boundary integral equations for the collocation partition of unity method in two‐dimensional acoustic scattering
Author(s) -
Diwan G.C.,
Trevelyan J.,
Coates G.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4583
Subject(s) - partition of unity , mathematics , uniqueness , boundary element method , helmholtz equation , helmholtz free energy , piecewise , integral equation , mathematical analysis , collocation (remote sensing) , collocation method , boundary value problem , boundary (topology) , polynomial , partition (number theory) , finite element method , differential equation , computer science , physics , ordinary differential equation , quantum mechanics , combinatorics , machine learning , thermodynamics
SUMMARY The Partition of Unity Method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements. The non‐uniqueness of solution obtained from the conventional boundary integral equation (CBIE) is well known. The CBIE derived through Green's identities suffers from a problem of non‐uniqueness at certain characteristic frequencies. Two of the standard methods of overcoming this problem are the so‐called Combined Helmholtz Integral Equation Formulation (CHIEF) method and that of Burton and Miller. The latter method introduces a hypersingular integral, which may be treated in various ways. In this paper, we present the collocation partition of unity boundary element method (PUBEM) for the Helmholtz problem and compare the performance of CHIEF against a Burton–Miller formulation regularised using the approach of Li and Huang. Copyright © 2013 John Wiley & Sons, Ltd.