Extended Foldy–Lax Approximation on Multiple Scattering

Abstract

The 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.

Keywords:

• multiple scattering
• extended Foldy–Lax approximation
• Lippmann–Schwinger integral equation
• dipole effect
• self-interacting effect

AMS Subject Classification:

• 35C15
• 47A40
• 45E10