کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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5428827 | 1508692 | 2013 | 13 صفحه PDF | دانلود رایگان |
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 ill-conditioning problems. Remaining numerical limitations are likely to be associated with loss-of-precision problems in the numerical evaluation of the surface integrals.
⺠Group theoretical methods in T-matrix method extended to high-order symmetry groups. ⺠GAP software for computational group theory coupled to T-matrix code Tsym. ⺠The method can overcome numerical ill-conditioning problems. ⺠Important applications are particles with small-scale surface roughness.
Journal: Journal of Quantitative Spectroscopy and Radiative Transfer - Volume 123, July 2013, Pages 79-91