An improved form of the hypersingular boundary integral equation for exterior acoustic problems

An improved form of the hypersingular boundary integral equation (BIE) for acoustic problems is developed in this paper. One popular method for overcoming non-unique problems that occur at characteristic frequencies is the well-known Burton and Miller (1971) method [7], which consists of a linear combination of the Helmholtz equation and its normal derivative equation. The crucial part in implementing this formulation is dealing with the hypersingular integrals. This paper proposes an improved reformulation of the Burton–Miller method and is used to regularize the hypersingular integrals using a new singularity subtraction technique and properties from the associated Laplace equations. It contains only weakly singular integrals and is directly valid for acoustic problems with arbitrary boundary conditions. This work is expected to lead to considerable progress in subsequent developments of the fast multipole boundary element method (FMBEM) for acoustic problems. Numerical examples of both radiation and scattering problems clearly demonstrate that the improved BIE can provide efficient, accurate, and reliable results for 3-D acoustics.