Eliminating the fictitious frequency problem in BEM solutions of the external Helmholtz equation. (December 2019)

• Record Type: Journal Article
• Authors: Klaseboer, Evert; Charlet, Florian D.E.; Khoo, Boo-Cheong; Sun, Qiang; Chan, Derek Y.C.
• Is Part Of: Engineering analysis with boundary elements. Volume 109(2019)
• Page Start: 106
• Page End: 116
• Publication Date: 2019-12
• Subjects: Internal resonance -- Desingularized boundary element method -- Frequency shift -- Modified Green's function; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2019.06.021
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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.