FD-TD Method with PMLs ABC Based on the Principles of Multidimensional Wave Digital Filters for Discrete-Time Modelling of Maxwell's Equations

Yoshihiro NAKA; Hiroyoshi IKUNO; Masahiko NISHIMOTO; Akira YATA

FD-TD Method with PMLs ABC Based on the Principles of Multidimensional Wave Digital Filters for Discrete-Time Modelling of Maxwell's Equations

Yoshihiro NAKA, Hiroyoshi IKUNO, Masahiko NISHIMOTO, Akira YATA

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We present a finite-difference time-domain (FD-TD) method with the perfectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-time modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and its MD-WDFs' representation by using the current-controlled voltage sources. In order to estimate the lower bound of numerical errors which come from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD method based on the MD-WDFs over the Yee algorithm. Simultaneously, we estimate numerical errors in practical problems as a function of grid cell size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we analyze several typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method based on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.

Publication: IEICE TRANSACTIONS on Electronics Vol.E81-C No.2 pp.305-314

Publication Date: 1998/02/25

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Category: Electromagnetic Theory

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Yoshihiro NAKA, Hiroyoshi IKUNO, Masahiko NISHIMOTO, Akira YATA, "FD-TD Method with PMLs ABC Based on the Principles of Multidimensional Wave Digital Filters for Discrete-Time Modelling of Maxwell's Equations" in IEICE TRANSACTIONS on Electronics, vol. E81-C, no. 2, pp. 305-314, February 1998, doi: .
Abstract: We present a finite-difference time-domain (FD-TD) method with the perfectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-time modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and its MD-WDFs' representation by using the current-controlled voltage sources. In order to estimate the lower bound of numerical errors which come from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD method based on the MD-WDFs over the Yee algorithm. Simultaneously, we estimate numerical errors in practical problems as a function of grid cell size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we analyze several typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method based on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e81-c_2_305/_p

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@ARTICLE{e81-c_2_305,
author={Yoshihiro NAKA, Hiroyoshi IKUNO, Masahiko NISHIMOTO, Akira YATA, },
journal={IEICE TRANSACTIONS on Electronics},
title={FD-TD Method with PMLs ABC Based on the Principles of Multidimensional Wave Digital Filters for Discrete-Time Modelling of Maxwell's Equations},
year={1998},
volume={E81-C},
number={2},
pages={305-314},
abstract={We present a finite-difference time-domain (FD-TD) method with the perfectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-time modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and its MD-WDFs' representation by using the current-controlled voltage sources. In order to estimate the lower bound of numerical errors which come from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD method based on the MD-WDFs over the Yee algorithm. Simultaneously, we estimate numerical errors in practical problems as a function of grid cell size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we analyze several typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method based on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - FD-TD Method with PMLs ABC Based on the Principles of Multidimensional Wave Digital Filters for Discrete-Time Modelling of Maxwell's Equations
T2 - IEICE TRANSACTIONS on Electronics
SP - 305
EP - 314
AU - Yoshihiro NAKA
AU - Hiroyoshi IKUNO
AU - Masahiko NISHIMOTO
AU - Akira YATA
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E81-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 1998
AB - We present a finite-difference time-domain (FD-TD) method with the perfectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-time modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and its MD-WDFs' representation by using the current-controlled voltage sources. In order to estimate the lower bound of numerical errors which come from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD method based on the MD-WDFs over the Yee algorithm. Simultaneously, we estimate numerical errors in practical problems as a function of grid cell size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we analyze several typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method based on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.
ER -