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Efficient Implementation of InnerOuter Flexible GMRES for the Method of Moments Based on a VolumeSurface Integral Equation
Hidetoshi CHIBA Toru FUKASAWA Hiroaki MIYASHITA Yoshihiko KONISHI
Publication
IEICE TRANSACTIONS on Electronics
Vol.E94C
No.1
pp.2431 Publication Date: 2011/01/01 Online ISSN: 17451353
DOI: 10.1587/transele.E94.C.24 Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application) Category: Numerical Techniques Keyword: flexible GMRES, integral equation methods, method of moments, multilevel fast multipole algorithm, Krylov subspace methods,
Full Text: FreePDF(1.5MB)
Summary:
This paper presents flexible innerouter Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To obtain the maximum efficiency of the innerouter methods, it is desirable to compute the inner iterations with the least possible effort. Hence, generally, inaccurate matrixvector multiplication (MVM) is performed in the inner solver within a short computation time. This is realized by using a particular feature of the multipole techniques. The accuracy and computational cost of the FMM can be controlled by appropriately selecting the truncation number, which indicates the number of multipoles used to express farfield interactions. On the basis of the abovementioned fact, we construct a lessaccurate but much cheaper version of the FMM by intentionally setting the truncation number to a sufficiently low value, and then use it for the computation of inaccurate MVM in the inner solver. However, there exists no definite rule for determining the suitable level of accuracy for the FMM within the inner solver. The main focus of this study is to clarify the relationship between the overall efficiency of the flexible innerouter Krylov solver and the accuracy of the FMM within the inner solver. Numerical experiments reveal that there exits an optimal accuracy level for the FMM within the inner solver, and that a moderately accurate FMM operator serves as the optimal preconditioner.

