The Rayleigh-Gans Approximation (RGA) is a computationally cheap method capable of producing accurate scattering results for particles with refractive index close to 1. It has been shown that the RGA tends to underestimate the scattering from ice particles. More accurate techniques can be used to estimate the scattering properties of non-spherical particles (e.g. the Discrete Dipole Approximation, DDA), but they are computationally expensive. Hence there is a demand for alternative methods to calculate scattering properties in a more efficient way, improving speed and ease of calculations, and decreasing computational load. This is particularly important for integrating over particle size distributions.
A logical extension of RGA is to use an iterative scheme, referred to in the literature as a scattering order formulation of the DDA (SOF-DDA). Using this method, the RGA solution is obtained on the first iteration. The technique is an implementation of the classical Jacobi iterative method on the DDA linear system. However, similarly to RGA, the values of size parameter and refractive index for which this method converges is limited. To improve convergence for larger size parameters, a relaxation technique can be used. This method is sensitive to the choice of relaxation parameter, and the optimal choice of this parameter is unclear.
It is interesting to explore techniques that have been used to choose the relaxation parameter for other applications to see how they perform for microwave scattering by ice crystals. Here we examine methods used in Helmholtz scattering problems, and determine the analogous specification for our Maxwell problem. The resulting convergence improvements are presented. These improvements could be beneficial to the development of new computationally efficient microwave scattering methods.
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