Special Issue on Wave Based Numerical Methods; Guest Editors: B. Nolte and St. MarburgNo Access

NUMERICAL ANALYSIS OF LARGE-SCALE SOUND FIELDS USING ITERATIVE METHODS PART I: APPLICATION OF KRYLOV SUBSPACE METHODS TO BOUNDARY ELEMENT ANALYSIS

Y. YASUDA

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

JSPS Research Fellow.

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S. SAKAMOTO

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

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Y. KOSAKA

Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8563, Japan

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T. SAKUMA

Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8563, Japan

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N. OKAMOTO

Venture Business Laboratory, Oita University, 700 Dannoharu, Oita-city, Oita 870-1192, Japan

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, and

T. OSHIMA

Faculty of Engineering, Niigata University, 8050 Ninomachi, Igarashi, Niigata-city, Niigata 950-2181, Japan

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https://doi.org/10.1142/S0218396X07003470Cited by:9 (Source: Crossref)

Abstract

The convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3D acoustical BEM is investigated through numerical experiments. The fast multipole BEM, which is an efficient BEM based on the fast multipole method, is used for solving problems with up to about 100,000 DOF. It is verified that the convergence behavior of solvers is much affected by the formulation of the BEM (singular, hypersingular, and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCGStab2 have more stable convergence than others, and these solvers are useful when solving interior problems in basic singular formulation. When solving exterior problems with greatly complex shape in Burton-Miller formulation, all solvers hardly converge without preconditioning, whereas the convergence behavior is much improved with ILU-type preconditioning. In these cases GMRes is the fastest, whereas CGS is one of the good choices, when taken into account the difficulty of determining the timing of restart for GMRes. As for calculation for rigid thin objects in hypersingular formulation, much more rapid convergence is observed than ordinary interior/exterior problems, especially using BiCG-like solvers.

Revised version of the previous publication in Journal of Environmental Engineering (Transactions of Architectural Institute of Japan), No. 605, pp. 15–22, 2006 (in Japanese).

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