NDLI: Finite-Element Time-Domain Solution of the Vector Wave Equation in Doubly Dispersive Media Using Möbius Transformation Technique

Content Provider	IEEE Xplore Digital Library
Author	Akbarzadeh-Sharbaf, A. Giannacopoulos, D.D.
Copyright Year	1963
Abstract	Several finite-element time-domain (FETD) formulations to model inhomogeneous and electrically/magnetically/doubly dispersive materials based on the second-order vector wave equation discretized by the Newmark-β scheme are developed. In contrast to the existing formulations, which employ recursive convolution (RC) approaches, we use a Möbius transformation method to derive our new formulations. Hence, the obtained equations are not only simpler in form and easier to derive and implement, but also do not suffer from the intrinsic limitations of the RC methods in modeling arbitrary high-order media. To obtain the formulations, we first demonstrate that the update equation for the electric field strength {e} in the mixed Crank-Nicolson (CN) FETD formulation, which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first-order differential equations using Crank-Nicolson scheme in time, is equivalent to the unconditionally stable (US) second-order vector wave equation for the same variable ( {e}) discretized by the Newmark- β method with β = 1/4. In addition, we show that the update equation for the magnetic flux density {b} in CN-FETD is the same as the second-order vector wave equation for {b} on the dual grid discretized again by a similar Newmark-β method. Subsequently, thanks to the mixed FETD formulation properties, we derive update equations for the constitutive relations using a Möbius transformation method separately. In addition, we use the shown equivalence to derive formulations based on the vector wave equation. Finally, several numerical examples are solved to validate the developed formulations.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	4158
Ending Page	4166
Page Count	9
File Size	2398147
File Format	PDF
ISSN	0018926X
Volume Number	61
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	finite-element time-domain method Dispersive media
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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