optimalerrorestimatesandmodifiedenergyconservationidentitiesoftheadifdtdschemeonstaggeredgridsfor3dmaxwellsequations

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	optimalerrorestimatesandmodifiedenergyconservationidentitiesoftheadifdtdschemeonstaggeredgridsfor3dmaxwellsequations
	Gao Liping 1; Zhang Bo2
	2013
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	56 期号:8 页码:1705
摘要	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.
语种	英语
资助项目	[Natural Science Foundation of Shandong Province] ; [Research Reward for Excellent Young Scientists from Shandong Province] ; [National Natural Science Foundation of China]
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/39171
专题	应用数学研究所
作者单位	1.School of Sciences,China University of Petroleum 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Gao Liping,Zhang Bo. optimalerrorestimatesandmodifiedenergyconservationidentitiesoftheadifdtdschemeonstaggeredgridsfor3dmaxwellsequations[J]. sciencechinamathematics,2013,56(8):1705.
APA	Gao Liping,&Zhang Bo.(2013).optimalerrorestimatesandmodifiedenergyconservationidentitiesoftheadifdtdschemeonstaggeredgridsfor3dmaxwellsequations.sciencechinamathematics,56(8),1705.
MLA	Gao Liping,et al."optimalerrorestimatesandmodifiedenergyconservationidentitiesoftheadifdtdschemeonstaggeredgridsfor3dmaxwellsequations".sciencechinamathematics 56.8(2013):1705.