An Exponential Time Differencing Algorithm for the FDTD-PML Analysis of Nonlinear Photonic Bandgap Structures

Zhao, Xu; Ma, Xikui; Liu, Qi

doi:10.1109/tmag.2013.2283227

Cited by 6 publications

(2 citation statements)

References 10 publications

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“…Later on, they received attention in , but the most comprehensive treatment, and in particular the ETD with Runge‐Kutta time stepping, is in the article by Cox and Matthews and its modification by Kassam and Trefethen . Since then, a great number of papers covering a wide range of natural sciences have used it (see, e.g., and references therein).…”

Section: Introductionmentioning

confidence: 99%

An exponential time differencing method of lines for the Burgers and the modified Burgers equations

Bratsos¹

2018

Numerical Methods Partial

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A second–order exponential time differencing scheme using the method of lines is developed in this article for the numerical solution of the Burgers and the modified Burgers equations. For each case, the resulting nonlinear system is solved explicitly using a modified predictor‐corrector method. The efficiency of the method introduced is tested by comparing experimental results with others selected from the available literature.

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Section: Introductionmentioning

confidence: 99%

An exponential time differencing method of lines for the Burgers and the modified Burgers equations

Bratsos¹

2018

Numerical Methods Partial

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“…These techniques include the recursive convolution (RC) [2], piecewise linear recursive convolution (PLRC) [3]and auxiliary differential equation (ADE) [4]. By mapping the frequency-domain relation is to Z-domain, then the Z transform (ZT) technique is developed [5,6].Recently, exponential time differential (ETD) algorithm is proposed to raise the accuracy [7,8]. The RC approaches have typically been faster and have required fewer computer memory resources than the ADE and ZT approaches, but the latter two have usually been more accurate.…”

Section: Introductionmentioning

confidence: 99%

Microwave reflection and transmission characteristics through plasma slab based on PLRC

Ji¹,

Ma²

2015

Proceedings of the 2015 International Power, Electronics and Materials Engineering Conference

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Abstract. he piecewise linear recursive convolution (PLRC)is proposed for cold plasma medium using finite-difference time-domain (FDTD) method. In PLRC algorithm, the electric field with time is piecewise interpolated and the recursive convolution was introduced. The reflection and transmission coefficients were calculated by the electromagnetic response of a differential Gaussian pulse. The calculation results are validated with analytic values and the results agree well with each other. The calculation results show that higher frequency microwave can transmit through the plasma and lower frequency is forbidden.

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An exponential time differencing method of lines for Burgers–Fisher and coupled Burgers equations

Bratsos

2019

Journal of Computational and Applied Mathematics

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An Exponential Time Differencing Algorithm for the FDTD-PML Analysis of Nonlinear Photonic Bandgap Structures

Cited by 6 publications

References 10 publications

An exponential time differencing method of lines for the Burgers and the modified Burgers equations

An exponential time differencing method of lines for the Burgers and the modified Burgers equations

Microwave reflection and transmission characteristics through plasma slab based on PLRC

An exponential time differencing method of lines for Burgers–Fisher and coupled Burgers equations

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