Numerical errors of superposition solutions to the acoustic radiation of a vibrating structure

The superposition method is a newly developed method for computing the acoustic field radiated or scattered from a structure. By this method, a solution to the acoustic field is obtained by superposing the waves from a number of equivalent point sources interior to the surface of the structure. The strengths of the sources are determined such that they give the same velocity at each mode on the surface of the structure as prescribed. This paper presents an analysis of the numerical error of the superposition solution. It has been shown that the maximum error of the superposition solution can be estimated by the surface velocity reconstruction error. The surface velocity reconstruction error, which can be computed directly, depends on the surface velocity distribution and velocity interpolation functions associated with the surface nodes. A spherical radiator with different surface velocity distributions is chosen to demonstrate how acoustic wavenumbers, the number of the surface nodes, and locations of the sources affect the surface velocity reconstruction error and, consequently, the accuracy of the superposition solution.