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

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