研究目的
Investigating the methods for deriving recurrence relations for T-matrix calculation in electromagnetic scattering by large and highly non-spherical particles.
研究成果
The paper concludes that the recurrence relations derived from the invariant embedding T-matrix method, the matrix Riccati equation method, and the superposition T-matrix method are analytically equivalent. The central recurrence schemes provide slightly better accuracy than the forward schemes, and the superposition T-matrix method is more stable. The study also highlights the importance of a scaling procedure for computing spherical Bessel and Neumann functions to extend the applicability of the methods.
研究不足
The study is limited to axisymmetric particles and does not address the full range of particle shapes and sizes. The numerical simulations are performed with double-precision floating-point variables, which may limit the range of applicability for very large particles or high expansion orders.
1：Experimental Design and Method Selection:
The study involves the analysis of three methods for deriving recurrence relations for T-matrix calculation: the invariant embedding T-matrix method, the matrix Riccati equation method, and the superposition T-matrix method. Theoretical models and algorithms are employed to derive central and forward recurrence relations.
2：Sample Selection and Data Sources:
The analysis is based on theoretical foundations and numerical simulations, with a focus on axisymmetric particles.
3：List of Experimental Equipment and Materials:
The study utilizes computational methods and numerical simulations, with specific mention of a Fortran computer program for implementing the recurrence schemes.
4：Experimental Procedures and Operational Workflow:
The methodology includes deriving recurrence relations, implementing them in a computational program, and analyzing their accuracies and efficiencies through numerical simulations.
5：Data Analysis Methods:
The analysis involves comparing the accuracies and efficiencies of different recurrence schemes and discussing implementation issues related to numerical accuracy and overflow errors.
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