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Innovative mimetic discretizations for electromagnetic problems. (English) Zbl 1191.78056
Summary: We introduce a discretization methodology for Maxwell equations based on Mimetic Finite Differences (MFD). Following the lines of the recent advances in MFD techniques [see {\it F. Brezzi} et al., Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3682--3692 (2007; Zbl 1173.76370)] and the references therein) and using some of the results of [{\it F. Brezzi} and {\it A. Buffa}, Scalar products of discrete differential forms, in preparation], we propose mimetic discretizations for several formulations of electromagnetic problems both at low and high frequency in the time-harmonic regime. The numerical analysis for some of the proposed discretizations has already been developed, whereas for others the convergence study is an object of ongoing research.

78M20Finite difference methods (optics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
78A25General electromagnetic theory
Full Text: DOI
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