【理工研セミナー】Method of Analytical Regularization in Computational Electromagnetics (計算電磁気学における解析的正則化法)-国際交流・公開研究セミナー
Alexander I. Nosich教授(ウクライナ国立科学アカデミー電波物理学・電子工学研究所)が来日されるのを機会に,電磁波問題に対する厳密解法として注目されている解析的正則化法に関し,その歴史的背景と最近の進展に関してご講演をお願いしました.是非ご参集ください.
題目 :Method of Analytical Regularization in Computational Electromagnetics(計算電磁気学における解析的正則化法)
講演者 :Dr. Alexander I. Nosich, Professor and Leading Scientist(Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine)
講演の概要:
We review a general approach to overcome the difficulties in the method-of-moments (MoM) numerical solutions of electromagnetics problems. It consists in obtaining the second kind integral equations (IE) of the Fredholm type, with smoother kernels, from the first kind equations. Discretization of these new equations, either by collocation or by a Galerkin-type projection on a set of basis functions, generates matrix equations, whose condition numbers remain small when the number of mesh points or “impedance-matrix” size is progressively increased. The approach mentioned is collectively called the Method of Analytical Regularization (MAR); sometimes semi-inversion is used as a synonym. It is based on the identification and analytical inversion of the whole singular part of the original IE or its most singular component.
As has been emphasized, MAR has guaranteed point-wise convergence, and thus a controlled accuracy of numerical results. Provided that all intermediate computations necessary for filling in the matrix and the right-hand part have been done with superior accuracy, the parameter controlling the final accuracy is just the size of the matrix, i.e., the order of its truncation. Depending on the nature of the inverted part, the number of equations needed for practical 3-4 digit accuracy is usually slightly greater than, respectively, the electrical dimension of the scatterer, or its inverse value, or the normalized deviation of the surface from the canonical shape, in terms of both distance and curvature.
By using MAR it is possible to overcome many difficulties encountered in conventional MoM treatments. Theoretical merits of the MAR are numerous: exact solution existence is established, convergence is guaranteed, and rigorous asymptotic formulas can be derived. Computationally, the MAR results in a small matrix size for practical 3-4 digit accuracy and sometimes no numerical integrations are at all needed for filling in the matrix. Thus, the cost of MAR algorithms is record low in terms of both CPU memory and time. A frequent feature is that both power conservation and reciprocity are satisfied at the machine-precision level, independently of the number of equations, whatever it is. As resolvent operator is bounded, the condition number is small and stable, not growing with mesh refinement or increasing with the number of basis functions.
連絡先:中央大学理工学部電気電子情報通信工学科
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