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.