On the behavior of solutions obtained by the HELS method inside the minimum sphere

Abstract

Previous experimental and numerical studies have shown that the Helmholtz equation least-squares (HELS) method [Wu, J. Acoust. Soc. Am. 107, 2511–2522 (2000)] can be an effective methodology for nearfield acoustical holography. However, results also demonstrated that the accuracy of reconstruction on a highly nonspherical surface might be unsatisfactory. The validity of the HELS method on these highly nonspherical surfaces has become a controversial topic, just like the Rayleigh hypothesis for acoustic scattering on a corrugated surface. In this paper, the validity of solutions obtained by the HELS method will be examined for acoustic radiation from an infinite column with a rectangular cross section. The acoustic field inside the minimal circle that encircles the column will be reconstructed. The convergence of solutions both on the surface and inside the minimum circle will be checked. Moreover, a modified HELS formulation will be used, which describes the acoustic pressure as a superposition of both out-going and in-coming spherical waves. The nature of the solutions thus obtained will be examined, and the dependence of convergence of the HELS solution on the validity of the Rayleigh hypothesis and on the measurement locations will be investigated. [Work supported by NSF.]