T-matrix computations for particles with high-order finite symmetries
Journal article, 2013

The use of group theoretical methods can substantially reduce numerical ill-conditioning problems in T-matrix computations. There are specific problems related to obtaining the irreducible characters of high-order symmetry groups and to the construction of a transformation from the basis of vector spherical wave functions to the irreducible basis of high-order symmetry groups. These problems are addressed, and numerical solutions are discussed and tested. An important application of the method is non-convex particles perturbed with high-order polynomials. Such morphologies can serve as models for particles with small-scale surface roughness, such as mineral aerosols, atmospheric ice particles with rimed surfaces, and various types of cosmic dust particles. The method is tested for high-order 3D-Chebyshev particles, and the performance of the method is gauged by comparing the results to computations based on iteratively solving a Lippmann-Schwinger T-matrix equation. The latter method trades ill-conditioning problems for potential slow-convergence problems, and it is rather specific, as it is tailored to particles with small-scale surface roughness. The group theoretical method is general and not plagued by slow-convergence problems. The comparison of results shows that both methods achieve a comparable numerical stability. This suggests that for particles with high-order symmetries the group-theoretical approach is able to overcome the illconditioning problems. Remaining numerical limitations are likely to be associated with loss-of-precision problems in the numerical evaluation of the surface integrals.


Cosmic dust

electromagnetic scattering

Mineral dust



Ice clouds


Michael Kahnert

Chalmers, Earth and Space Sciences, Global Environmental Measurements and Modelling

Journal of Quantitative Spectroscopy and Radiative Transfer

0022-4073 (ISSN)

Vol. 123 79-91

Aerosol Optics in Global Earth System Modelling (AGES)

Swedish Research Council (VR), 2011-10-26 -- 2014-10-26.

Subject Categories

Analytical Chemistry



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