Abstract
This paper extends the Helmholtz equation least squares (HELS) method previously developed by Wang et aL [1995] and Wang and Wu [1997] to reconstruction of acoustic pressure fields in an interior region. In this methodology, the acoustic pressures are reconstructed through an expansion of acoustic modes, or a set of independent functions generated via an orthonormalization with respect to the particular solutions to the Helmholtz equation on the particular surface under consideration. The coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points. The errors incurred in this process are minimized by the least squares method. Numerical examples of partially vibrating cylinders with two spherical endcaps at various half-length to radius aspect ratios and frequencies are demonstrated. The reconstructed acoustic pressures are compared with numerical solutions obtained by using a direct boundary element method.
