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A Meshless Method for the Helmholtz Eigenvalue Problem Based on the Taylor Series of the 3-D Green's Function

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The solution of the Helmholtz eigenvalue problem is considered through the use of the method of the fundamental solutions. Taylor series of these solutions are employed to form a polynomial eigenvalue problem. The presented method diff ers from other methods such as the multiple reciprocity method. Here, the Green's function itself is expanded and no integration is performed. Results on classical geometries (sphere, parallelepiped box and finite cylinder) demonstrate the accuracy of the method for the determination of the eigenvalues with Neumann, Dirichlet and Robin boundary conditions. Furthermore, the center of the Taylor approximation is shown to be adjustable, allowing the method to be theoretically eff ective for any arbitrarily part of the eigenvalue spectra.
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Document Type: Research Article

Publication date: September 1, 2013

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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