NDLI: An Efficient Algorithm for Implementing the Crank–Nicolson Scheme in the Mixed Finite-Element Time-Domain Method

Content Provider	IEEE Xplore Digital Library
Author	Ru-Shan Chen Lei Du Zhenbao Ye Yang Yang
Copyright Year	1963
Abstract	In this paper, an efficient algorithm for implementing Crank-Nicolson scheme in the finite-element time-domain (FETD) method is presented. Based on a direct discretization of the first-order coupled Maxwell curl equations, this algorithm employs edge elements (Whitney 1-form) to expand the electric field and face elements (Whitney 2-form) for the magnetic field. Since the curl of an edge-element is the linear combination of those face elements whose faces contain the given edge, only the Maxwell-Ampere equation composes a sparse linear matrix equation for the electric field update; the Maxwell-Faraday equation is explicit. The Crank-Nicolson scheme is implemented leading to an unconditionally stable vector FETD method and the matrix inverse is not required to be computed explicitly. Therefore, only one matrix equation is required to be solved at each time step. Numerical results demonstrate that the proposed method is efficient when compared with the conventional leap-frog mixed FETD method and the Crank-Nicolson FDTD method.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	3216
Ending Page	3222
Page Count	7
File Size	645840
File Format	PDF
ISSN	0018926X
Volume Number	57
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-10-01
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 methods Time domain analysis Maxwell equations Finite difference methods Magnetic fields Sparse matrices Partial differential equations Space technology Nonlinear equations Electromagnetic modeling unconditionally stable Crank–Nicolson scheme finite-element time-domain (FETD) method first-order coupled Maxwell curl equations
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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