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.
Highlights
The multiple scattering by finite-size inhomogeneities has attracted interests of many researchers and the finite-size effect has been treated in different aspects
An “extended” Foldy–Lax selfconsistent 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
The multiple scattering problem can be written by standard inhomogeneous Helmholtz equation and the solution is represented by the well-known Lippmann–Schwinger integral equation [3], which can be solved exactly by separation of variables and using spherical harmonics, or, high-accuracy numerical techniques have been developed to address this problem, for example [1]
Summary
The multiple scattering by finite-size inhomogeneities has attracted interests of many researchers and the finite-size effect has been treated in different aspects. The multiple scattering problem can be written by standard inhomogeneous Helmholtz equation and the solution is represented by the well-known Lippmann–Schwinger integral equation [3], which can be solved exactly by separation of variables and using spherical harmonics, or, high-accuracy numerical techniques have been developed to address this problem, for example [1]. The extended Foldy–Lax system (1.2) is an extension of Foldy–Lax system (1.1), since (1.1) can be derived by taken ηl’s and βj’s be zeros in the first equation of (1.2) With both the self-interaction effect and dipole effect being included in this new approach, the accuracy of the approximation is substantially improved.
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