Jie Liao

Extended Foldy–Lax Approximation on Multiple Scattering

AbstractThe Foldy–Lax self-consistent system has been widely used as an efficient numerical approximation of multiple scattering of time harmonic wave through a medium with many scatterers when the relative radius of each scatterer is small and the distribution of scatterers is sparse. In this paper, an “extended” Foldy–Lax self-consistent system including both source and dipole effects as well as corrections due to the self-interacting effects will be introduced, in which the scattering amplitudes and the corrections are determined as powers of the small scaled radius. This new approach substantially improves the accuracy of the approximation of the original Foldy–Lax approach.

Foldy–Lax approximation on multiple scattering by many small scatterers

The multiple scattering of time harmonic wave emitted by a localized source through a medium with many scatterers can be approximated by an Foldy–Lax self-consistent system when the relative radius of each scatterer is small and the distribution of scatterers is sparse. The scattering amplitude in the Foldy–Lax self-consistent system will be specified in terms of scatterer volume and scattering strength. By neglecting the self-interaction effect, the difference from the exciting field in the Foldy–Lax formula to the analytic wave field given implicitly by the Lippmann–Schwinger integral equation is compared. An upper bound of the difference is obtained in terms of scaled radius and sparsity of the distribution of the scatterers.