Combined Helmholtz equation–least squares (CHELS) method for reconstructing radiated acoustic pressure fields

Abstract

A combined Helmholtz equation–least squares (CHELS) method is developed for reconstructing acoustic pressures radiated from an arbitrary object. This method combines the HELS method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); Wu and Yu, ibid. 104, 2054–2060 (1998)] and boundary element method (BEM)-based Helmholtz integral formulation. The main advantage of the HELS method is its simplicity in expressing the radiated acoustic pressure in terms of an expansion of orthonormal basis functions. However, the accuracy of reconstruction may deteriorate with the increase of complexity of source geometry. This is because the convergence of the basis functions becomes poorer for an irregular surface than for a smooth surface. The BEM-based integral formulation allows for reconstruction of the radiated acoustic pressures on an arbitrarily shaped object. However, the number of measurements required for reconstruction is often too large to make the process practical. In the CHELS method, only a finite number of measurements are taken to establish the HELS method. Once this is done, enough field pressures are generated using the HELS method, which are then taken as input to the BEM-based integral formulation to reconstruct acoustic pressures everywhere. [Work supported by NSF Grant No. CMS-9802847.]