Eliminating the fictitious frequency problem in BEM solutions of the external Helmholtz equation
Evert Klaseboer, Florian DE Charlet, Boo-Cheong Khoo, Qiang Sun, Derek YC Chan
Engineering Analysis with Boundary Elements | Elsevier | Published : 2019
The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green’s function is replaced by a modified Green’s function, it is shown that these fictitious frequencies do not necessarily have to correspond to the internal resonance frequency of the object. Together with a recently developed fully desingularized boundary element method that confers superior numerical accuracy, a simple and practical way is proposed for detecting and avoiding these fictitious solutions. The concepts are illustrated with examples of a scattering wave on a rigid sphere.
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Awarded by Australian Research Council
This work is supported in part by the Australian Research Council grants, DE150100169 & CE140100003, to QS and a Discovery Project Grant DP170100376 to DYCC.