NDLI: Regularization and fast solution of large subwavelength problems with imperfectly conducting materials

Content Provider	IEEE Xplore Digital Library
Author	Bleszynski, E.H. Bleszyuski, M. Jaroszewicz, T.
Copyright Year	2007
Description	Author affiliation: Monopole Res., Thousand Oaks (Bleszynski, E.H.; Bleszyuski, M.; Jaroszewicz, T.)
Abstract	We describe an approach to low-frequency regularization of surface integral equations. We consider integral equations modeling general electrically and magnetically conducting sheets characterized by first-order boundary conditions, and parameterized in terms of electric, magnetic, and "cross" resistivities. Special cases of such boundary conditions include perfect conductors, resistive and impedance sheets, and thin penetrable sheets. Our approach constitutes an extension/generalization of the well-established regularization method for problems involving perfect conductors, based on rescaling of solution components in the solenoidal (loop) and remainder (e.g., tree;) subspaces. We demonstrate, on several examples of practical interest, that the proposed method leads to a significant improvement of the integral equation stability for problems with thin surface material sheets, through the use of a rescaling procedure different from that for perfect conductors, and controlled by the frequency dependence of the material parameters. The proposed method significantly improves conditioning of the impedance matrix, and results in correspondingly accelerated convergence ad iterative solutions.We also describe two oilier aspects of our approach: (a) Construction of an efficient algorithm allowing identification of loop and tree solution subspaces, applicable to locally two-dimensional surfaces of general topology (with possible boundaries and handles). The algorithm complexity is approximately O(N), where N is the number of faces of the mesh. (b) Interfacing of the low-frequency regularization with fast FFT-based (ATM) solver, which allows us to treat large problems (of sub-wavelength type) and provides a smooth transition to arbitrarily low frequencies. We show examples of application of the approach to solution to low frequency magnetic shielding problems involving geometrically and topologically complex configurations of high permeability materials.
Starting Page	3456
Ending Page	3459
File Size	930307
Page Count	4
File Format	PDF
ISBN	9781424408771
DOI	10.1109/APS.2007.4396281
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-06-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Conducting materials Integral equations Boundary conditions Surface impedance Sheet materials Iterative algorithms Frequency Magnetic materials Conductivity Stability
Content Type	Text
Resource Type	Article

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