Investigation of invariant-imbedding T-Matrix method computational efficiency for particles with complicated geometries

Abstract:

The single-scattering properties of aerosol particles and ice crystals in the atmosphere have long been studied, and it is well known that numerical calculations become more difficult as wider classes of particle shapes are considered. To compute the single scattering properties of particles with arbitrary shape and morphology, a method called the invariant-imbedding T-Matrix (II-TM) method has been developed. This method applies an invariant-imbedding technique to solve the electromagnetic volume integral equation: the equation is first solved for a sphere inscribed within the particle and, by iteratively considering additions of concentric shells, ends with a solution for the sphere circumscribing the particle. As shown in previous studies, the method is accurate and computationally efficient in computing single scattering properties of symmetric particles, a variety of irregular particles, and a few complicated concave particles. However, the computational cost can rise significantly in cases like irregular dust particles with concave structures or aggregate particles with many monomers, because achieving acceptable accuracy requires an increase of the dimension of the T-matrix beyond the dimension needed for simpler particles. The critical step in the II-TM method that involves a particle’s shape is the computation of a matrix called the ‘U-Matrix’. In this study we quantify the relation between T-matrix dimension, the U-Matrix, and particle complexity, and we show how the relation can be used to guide improvement of the II-TM computational efficiency.