Regularisation of the equivalent source method for robust numerical modelling of acoustic scattering

Abstract

The equivalent source method can be used to model acoustic scattering, by representing the scattering object with a set of equivalent sources that satisfy a boundary condition. The equivalent source strengths are optimised by a least-squares method. When the equivalent sources are positioned further from the boundary to reduce the boundary condition error, the optimisation becomes ill-conditioned. This limits the application of the equivalent source method in irregularly-shaped objects as boundary condition error is highly sensitive to equivalent source placement. To overcome the problem of ill-conditioning, a regularisation parameter is introduced, which increases the robustness to errors in the modelled acoustic field by limiting the power of overdriven equivalent sources. Simulations of a rigid infinite wall with an equivalent dipole line-array, reveal that regularisation reduces boundary condition error in all ill-conditioned cases. Good trade-offs between boundary condition error and regularisation are achieved for a wide range of regularisation parameter values. This allows the results to be calculated for varying frequencies and distances between the equivalent sources and the boundary. Regularisation reduces the sensitivity of boundary condition error to equivalent source placement, thereby increasing the flexibility of the equivalent source method for irregularly-shaped scattering objects.