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Fast Multipole Boundary Element Method for Large-Scale Steady-State Sound Field Analysis. Part I: Setup and Validation

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In order to reduce computational complexity and memory requirements for three-dimensional acoustical analysis, using the boundary element method (BEM), a new method for steady-state sound fields is developed based on the fast multipole algorithm. This method, called the Fast Multipole BEM (FMBEM), drastically accelerates an iterative solution of large-scale linear systems, without composing the dense influence coefficient matrices used for the conventional BEM. An efficient computational scheme is presented for the boundary integral equations in the basic form and in the normal derivative form, where the fast multipole algorithm is introduced over the multiple levels, by employing a concept of cells clustering boundary elements and hierarchical cell structure. Theoretical analysis shows how efficiently the FMBEM can reduce the computational complexity and the memory requirements compared with the BEM, in two typical problems assuming uniform distributions of nodes within a space and on its surface, respectively. A numerical test solving an acoustic tube problem confirms the validity of this method with respect to computational accuracy and efficiency.
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Document Type: Research Article

Publication date: July 1, 2002

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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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