An overview of the methods for deriving recurrence relations for T-matrix calculation. (February 2019) - Doicu, Adrian; Wriedt, Thomas; Khebbache, Naima
Highlights: We review the recurrence relations for T-matrix calculation. It is proved that the recurrence relations of the invariant embedding T-matrix method and the superposition T-matrix method are analytically equivalent. It is shown that the recurrence schemes of the superposition T-matrix method are morestable than that of the invariant embedding T-matrix method. Abstract: In this paper, we present a consistent analysis of the methods dealing with the derivation of recurrence relations for calculation of the T -matrix. Central and forward recurrence relations are obtained in the framework of the invariant embedding T -matrix method, the matrix Riccati equation method, and the superposition T -matrix method. The accuracies and efficiencies of the central and forward recurrence schemes are analyzed, and some implementation issues related to the improvement of the numerical accuracy and to the problem of overcoming of overflow errors are discussed.