TY - JOUR
T1 - A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations
AU - Yefet, Amir
AU - Petropoulos, Peter G.
N1 - Funding Information:
This effort was sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.
PY - 2001/4/10
Y1 - 2001/4/10
N2 - We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates long-time stability. Numerical results verify both the stability analysis, and the scheme's fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the application of such high-order schemes are also discussed.
AB - We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates long-time stability. Numerical results verify both the stability analysis, and the scheme's fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the application of such high-order schemes are also discussed.
KW - Maxwell's equations, staggered finite-difference schemes, fourth-order schemes, FD-TD scheme
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U2 - 10.1006/jcph.2001.6691
DO - 10.1006/jcph.2001.6691
M3 - Article
AN - SCOPUS:0000522244
SN - 0021-9991
VL - 168
SP - 286
EP - 315
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -