Singular Boundary Method for Three-Dimensional Low and Middle Frequency Acoustic Problems

Abstract

As an extension of the methods presented in Chapter 2, this chapter takes acoustic problems as the physical background to apply the singular boundary method to the three-dimensional Helmholtz equation. Based on the Burton-Miller formulations, the Burton-Miller singular boundary method is constructed to deal with the non-uniqueness difficulties at resonance frequency. Two seta of origin intensity factors based on the subtraction and adding-back technique are derived. In addition, for efficient evaluation of near-boundary and boundary solutions of the Helmholtz equation with wideband wavenumbers, this chapter proposes a regularized singular boundary method and derives a set of near intensity factors based on the subtraction and adding-back technique.

Keywords: Singular boundary method, Sound wave propagation, Origin intensity factor, Near intensity factor.

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