Improved acoustical analysis method using the normal derivative form of a Helmholtz boundary integral equation

Nonuniqueness problem suffered by the normal derivative form (NDF) of a Helmholtz boundary integral equation (HBIE) applied to external Neumann problems is investigated. The NDF equation is useful in solving sound field around open surfaces, but it suffers from nonuniqueness when it is used for solving surface velocity potential at eigenvalues of corresponding internal Neumann problems of a closed surface. We have found that Schenck's CHIEF method reduces the error in the exterior sound field for some eigenvalues of the NDF equation. But the velocity potential on the surface is nonunique by the CHIEF method. Results show that, at internal eigenvalues, the NDF equation is not suitable for calculating sound field in the exterior domain. Whereas, Burton and Miller's equation (BM equation) is effective in estimating the unique surface velocity potential and gives accurate results for both the internal and external sound fields of a closed surface. In this research, a modified NDF equation (MNDF) is developed as a combination of NDF and BM equations. This MNDF is expected to give unique solutions for all wavenumbers for the sound field around open and closed surfaces combined.