Improvements in the computational efficiency and convergence of the Invariant Imbedding T-matrix method for spheroids and hexagonal prisms

The invariant-imbedding T-matrix (II-TM) method is a numerical method for accurately computing the single-scattering properties of dielectric particles. Because of the linearity of Maxwell’s equations, the incident electric field and the scattered electric field can be related through a transition matrix (T-Matrix). The II-TM method computes the T-matrix through a matrix recurrence formula which stems from an electromagnetic volume integral equation. The recurrence starts with an inscribed sphere within the particle and ends with the circumscribed sphere of the particle. For each iteration, a matrix known as the U-matrix is computed with the Gauss Legendre (GL) quadrature, and matrix inversion is subsequently performed to obtain the T-matrix corresponding to the portion of the particle enclosed by the spherical shell. We modify a commonly used scheme to avoid applying the quadrature scheme to discontinuities. Moreover, we apply a new scheme to generate nodes and weights in conjunction with the GL quadrature. This leads to a considerable improvement on convergence and computational efficiency in the cases of hexagonal prisms and spheroids. The basic shapes of ice crystals in the atmosphere are hexagonal columns and plates. The single-scattering properties of hexagonal ice prisms are important to atmospheric optics, radiative transfer, and remote sensing. We demonstrate that the present approach can significantly accelerate the convergence in simulating light scattering by hexagonal ice crystals.