Abstract
Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.
Highlights
A Compact Unconditionally Stable Method for Time-Domain Maxwell’s EquationsHigher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions
Over the past few decades, finite-difference time-domain (FDTD) method has been widely applied to a variety of electromagnetic problems
Unlike conventional split-step FDTD method which is based on the exponential evolution operator, this method simultaneously utilizes symmetric operator and uniform splitting to decompose Maxwell’s matrix into four matrices, the time step is divided into four substeps
Summary
Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. Analyses of stability and numerical dispersion are carried out. The proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionallystable methods
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