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2006•Unpublished venueRequires access

2-D Isotropic Finite Difference Time Domain Method

Fei Xiao, Xiaohong Tang, Ling Wang, Haihong Ma

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Abstract

The numerical dispersion inherent in the conventional FDTD method causes the numerical phase speed to become a function of frequency and direction, which is the main source of error. Unlike the convention treatment to use 1-D finite difference scheme to approximate the spatial partial differential operator (PDO) in Maxwell's equations, the use of the high-dimensional isotropic finite difference scheme in the FDTD method will greatly reduce the numerical anisotropy in the FDTD method, which demonstrates its superiority and applicability. In addition, the stability condition is strictly derived.

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What this paper is about

The numerical dispersion inherent in the conventional FDTD method causes the numerical phase speed to become a function of frequency and direction, which is the main source of error. Unlike the convention treatment to use 1-D finite difference scheme to approximate the spatial partial differential operator (PDO) in Maxwell's equations, the use of the high-dimensional isotropic finite difference scheme in the FDTD method will greatly reduce the numerical anisotropy in the FDTD method, which demonstrates its superiority and applicability. In addition, the stability condition is strictly derived.

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Available abstract

The numerical dispersion inherent in the conventional FDTD method causes the numerical phase speed to become a function of frequency and direction, which is the main source of error. Unlike the convention treatment to use 1-D finite difference scheme to approximate the spatial partial differential operator (PDO) in Maxwell's equations, the use of the high-dimensional isotropic finite difference scheme in the FDTD method will greatly reduce the numerical anisotropy in the FDTD method, which demonstrates its superiority and applicability. In addition, the stability condition is strictly derived.

Key concepts: Finite-difference time-domain method, Finite difference method, Isotropy, Mathematics, Mathematical analysis, Finite difference, Numerical stability, Stability (learning theory)

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