The fast multipole boundary element method (FMBEM), which is an efficient BEM that uses the fast multipole method (FMM), is known to suffer from instability at low frequencies when the well-known high-frequency diagonal form is employed. In the present paper, various formulations for a low-frequency FMBEM (LF-FMBEM), which is based on the original multipole expansion theory, are discussed; the LF-FMBEM can be used to prevent the low-frequency instability. Concrete computational procedures for singular, hypersingular, Burton-Miller, indirect (dual BEM), and mixed formulations are described in detail. The computational accuracy and efficiency of the LF-FMBEM are validated by performing numerical experiments and carrying out a formal estimation of the efficiency. Moreover, practically appropriate settings for numerical items such as truncation numbers for multipole/local expansion coefficients and the lowest level of the hierarchical cell structure used in the FMM are investigated; the differences in the efficiency of the LF-FMBEM when different types of formulations are used are also discussed.

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Heat exchangers and boilers are widely used in various plants such as power plants and chemical plants. In heat exchangers and boilers, tube banks are set in a duct such that water passes through inside the tubes and warm gas outside the tubes. Due to the external flow around tube banks, the resonance phenomenon called the self-sustained tone occurs at a certain velocity. The self-sustained tone might cause noise problems in the surroundings, cause losses due to plant shutdown, etc. The self-sustained tone has been studied, and the generation mechanism has been experimentally and numerically clarified. In this paper, we have performed numerical simulations of high level sound generated in boiler tube bank duct with the flow and an acoustic simulation without the flow for a practical generation prediction of a self-sustained tone. The results show a good agreement with measurement data, and that acoustic resonance phenomenon has been numerically captured and clarified. There is the slight difference in the resonance frequencies obtained from the acoustic simulation (without the flow) by means of BEM and the CFD simulation or the experiments due to the absence or presence of the flow.

Karman vortex shedding occurs when the gas passes through the duct with tube bank of the heat exchangers, such as gas heaters and boilers. Very high level sound in called "self-sustained tones" occurs due to the interference of the vortex and the sound field in the duct. In general, baffle plates are used to suppress the self-sustained tone. However, it is difficult to use them effectively, because insertion conditions have not been established. Then, perforated plates are installed in both sides of the duct to suppress the self-sustained tones. As a result, it was clarified that the perforated plate could suppress the self-sustained tone as expected. The perforated plates are generally used with a cavity to obtain the suppression effect effectively. However the perforated plates change the acoustic natural frequency of the sound field of the duct. In previous paper, this was not referred. This paper aims to clarify the role of the perforated plates when it changes the acoustic natural frequency of the duct. In this study, one dimensional duct will be used for simplicity and the relationship between the aperture ratio and the acoustic natural frequency will be obtained analytically and experimentally. As a result, it was clarified that the analytical results are in good agreement with the experimental ones and the plates with holes had a role of acoustic damping in calculation of the acoustic natural frequency of the one dimensional sound field like a duct with plates with holes. 熱交換器のダクト内には管群(熱交換を行うため，温水や蒸気などを通す管の集合部)が存在する．この管群と

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