Convolutional CFS-PML for the 2-D Crank–Nicolson FDTD Scheme and Its Application in Simulation of Ultralow Frequency Electromagnetic Problems

IF 4.6 1区计算机科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Antennas and Propagation Pub Date : 2025-01-13 DOI:10.1109/TAP.2025.3526905

Mohammadreza Roohie;Afshin Rezaei-Zare

{"title":"Convolutional CFS-PML for the 2-D Crank–Nicolson FDTD Scheme and Its Application in Simulation of Ultralow Frequency Electromagnetic Problems","authors":"Mohammadreza Roohie;Afshin Rezaei-Zare","doi":"10.1109/TAP.2025.3526905","DOIUrl":null,"url":null,"abstract":"A convolutional implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) with complex frequency-shifted (CFS) constitutive parameters is developed for the original 2-D Crank-Nicolson (CN) scheme of the finite-difference time-domain (FDTD) method. The proposed CN-FDTD method leverages the benefits of both CFS-PML and the unconditionally stable CN scheme, overcoming the stability limits of the conventional FDTD method and decreasing the numerical reflection of evanescent waves. The effectiveness of the proposed scheme is validated by conducting an analysis of the absorbing boundary reflection error and the simulation speed. For an ultralow frequency and small-scale problem with an extremely fine spatial mesh size (<inline-formula> <tex-math>$2\\times 10^{7}$ </tex-math></inline-formula> times smaller than the minimum exited wavelength) and using time steps <inline-formula> <tex-math>$4\\times 10^{6}$ </tex-math></inline-formula> times larger than those in conventional FDTD, we achieved a CPU time improvement of up to <inline-formula> <tex-math>$2.9360\\times 10^{4}$ </tex-math></inline-formula> times compared to the conventional FDTD method, with less than 3% numerical error.","PeriodicalId":13102,"journal":{"name":"IEEE Transactions on Antennas and Propagation","volume":"73 5","pages":"3095-3107"},"PeriodicalIF":4.6000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Antennas and Propagation","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10839276/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}

引用次数: 0

Abstract

A convolutional implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) with complex frequency-shifted (CFS) constitutive parameters is developed for the original 2-D Crank-Nicolson (CN) scheme of the finite-difference time-domain (FDTD) method. The proposed CN-FDTD method leverages the benefits of both CFS-PML and the unconditionally stable CN scheme, overcoming the stability limits of the conventional FDTD method and decreasing the numerical reflection of evanescent waves. The effectiveness of the proposed scheme is validated by conducting an analysis of the absorbing boundary reflection error and the simulation speed. For an ultralow frequency and small-scale problem with an extremely fine spatial mesh size (

$2\times 10^{7}$

times smaller than the minimum exited wavelength) and using time steps

$4\times 10^{6}$

times larger than those in conventional FDTD, we achieved a CPU time improvement of up to

$2.9360\times 10^{4}$

times compared to the conventional FDTD method, with less than 3% numerical error.

查看原文本刊更多论文

二维Crank-Nicolson时域有限差分格式的卷积CFS-PML及其在超低频电磁问题仿真中的应用

针对有限差分时域（FDTD）方法的原始二维Crank-Nicolson （CN）格式，提出了具有复频移（CFS）本构参数的完全匹配层（PML）吸收边界条件（ABC）的卷积实现。本文提出的CN-FDTD方法综合了CFS-PML和无条件稳定CN格式的优点，克服了传统FDTD方法的稳定性限制，降低了倏逝波的数值反射。通过对吸收边界反射误差和仿真速度的分析，验证了该方案的有效性。对于极细空间网格尺寸（比最小输出波长小2倍10^{7}美元）的超低频率和小规模问题，使用比传统FDTD大4倍10^{6}美元的时间步长，与传统FDTD方法相比，我们实现了高达2.9360倍10^{4}美元的CPU时间改进，数值误差小于3%。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

IEEE Transactions on Antennas and Propagation 工程技术-电信学

CiteScore

10.40

自引率

28.10%

发文量

968

审稿时长

4.7 months

期刊介绍： IEEE Transactions on Antennas and Propagation includes theoretical and experimental advances in antennas, including design and development, and in the propagation of electromagnetic waves, including scattering, diffraction, and interaction with continuous media; and applications pertaining to antennas and propagation, such as remote sensing, applied optics, and millimeter and submillimeter wave techniques