NDLI: Optimal error estimates and modified energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell’s equations

Content Provider	Springer Nature Link
Author	Gao, LiPing Zhang, Bo
Copyright Year	2013
Abstract	This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell’s equations. Precisely, for the case with a perfectly electric conducting (PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete H $^{1}$-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L $^{2}$-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell’s equations introduced in this paper. Furthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.
Starting Page	1705
Ending Page	1726
Page Count	22
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	56
Issue Number	8
e-ISSN	18691862
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-03-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	alternating direction implicit method finite-difference time-domain method Maxwell’s equations optimal error estimate superconvergence unconditional stability energy conservation divergence preserving property Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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OPTIMAL ERROR ESTIMATES AND ENERGY CONSERVATION IDENTITIES OF THE ADI-FDTD SCHEME ON STAGGERED GRIDS FOR 3D MAXWELL’S EQUATIONS

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