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Development and analysis of Crank‐Nicolson scheme for metamaterial Maxwell's equations on nonuniform rectangular grids
Author(s) -
Wang Xiang,
Li Jichun,
Fang Zhiwei
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22275
Subject(s) - metamaterial , mathematics , scheme (mathematics) , maxwell's equations , crank–nicolson method , stability (learning theory) , mathematical analysis , physics , computer science , optics , machine learning
In this paper, we develop a fully implicit scheme on staggered grids to solve the Maxwell's equations when Drude metamaterial is involved. Unconditional stability and optimal error estimate of the scheme are proved. Numerical results are provided to support the theoretical analysis, and used to demonstrate the applicability of the scheme to simulate the complicated backward wave propagation phenomenon occurring in metamaterials.