Browsing by Subject "Multiscale electromagnetic problems"

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Open Access
Broadband analysis of multiscale electromagnetic problems: Novel incomplete-leaf MLFMA for potential integral equations
(IEEE, 2021-06-24) Khalichi, Bahram; Ergül, Ö.; Takrimi, Manouchehr; Ertürk, Vakur B.
Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy resulting in an improved efficiency and a significant reduction for the memory requirements (order of magnitudes), while the error is controllable. The superiority of the algorithm is demonstrated in several canonical and real-life multiscale geometries.
Open Access
Fast and efficient solutions of multiscale electromagnetic problems
(2020-09) Khalichi, Bahram
Frequency-domain surface integral equations (SIEs) used together with the method of moments (MoM), and/or its accelerated versions, such as the multilevel fast multipole algorithm (MLFMA), are usually the most promising choices in solving electromagnetic problems including perfect electric conductors (PEC). However, the electric-ﬁeld integral equation (EFIE) (as one of the most popular SIEs) is susceptible to the well-known low-frequency (LF) breakdown problem, which prohibits its use at low frequencies and/or dense discretizations. Although the magnetic-ﬁeld integral equation (MFIE) is less aﬀected from the LF-breakdown, it is usually criticized for being less accurate, and being applicable only to closed surfaces. In addition, the conventional MLFMA which enables the solution of electrically large problems with an extremely large number of unknowns by reducing the computational complexity for memory requirements and CPU time suﬀers from the LF breakdown when applied to the geometries with electrically small features. We proposed a mixed-form MLFMA and incorporated it with the recently introduced potential integral equations (PIEs), which are immune to the LF-breakdown problem, to obtain an eﬃcient and accurate broadband solver to analyze electromagnetic scattering/radiation problems from PEC surfaces over a wide frequency range. The mixed-form MLFMA uses the conventional MLFMA at middle/high frequencies and the nondirective stable plane wave MLFMA (NSPWMLFMA) at low frequencies (i.e., electrically small boxes). We demonstrated that the proposed algorithm is accurate enough to be applied for both open and closed surfaces. In addition, we modiﬁed and utilized incomplete tree structures in conjunction with the mixed-form MLFMA to have a novel broadband incomplete-leaf (IL) MLFMA (IL-MLFMA) for the fast and accurate solution of multiscale scattering/radiation problems using PIEs. The proposed method is capable of handling multiscale electromagnetic problems containing ﬁne geometrical details in their structures. The algorithm is population based and deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy, and hence the error is controllable. As a result, by using the proposed IL-MLFMA for PIEs (i) the eﬃciency is improved and (ii) the memory requirements are signiﬁcantly reduced (order of magnitude) while the accuracy is maintained.