柱坐标系“分解”思想WLP-FDTD的PML实现

doi:10.19596/j.cnki.1001-246x.8728

计算物理 ›› 2024, Vol. 41 ›› Issue (4): 440-452.DOI: 10.19596/j.cnki.1001-246x.8728

柱坐标系“分解”思想WLP-FDTD的PML实现

朱大伟¹^,²(), 陈海林²^,*(), 徐佳琛¹, 周晓晓¹^,³, 徐博奥⁴

1. 南京工业职业技术大学电气工程学院，江苏南京 210023
2. 陆军工程大学电磁环境效应与光电工程国家级重点实验室，江苏南京 210007
3. 南京理工大学电子工程与光电技术学院，江苏南京 210094
4. 中国人民解放军96901部队，北京 100000

收稿日期:2023-03-15 出版日期:2024-07-25 发布日期:2024-08-24
通讯作者: 陈海林
作者简介:朱大伟，男，博士，高级实验师，研究方向为计算电磁学、电磁兼容等，E-mail：zdw10101216@126.com
基金资助:
国家自然科学基金(61701221);南京工业职业技术大学引进人才科研启动基金(YK21-02-01)

PML Implementation of WLP-FDTD Algorithm Based on "Decomposition" Ideology in Cylindrical Coordinate System

Dawei ZHU¹^,²(), Hailin CHEN²^,*(), Jiachen XU¹, Xiaoxiao ZHOU¹^,³, Boao XU⁴

1. School of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing, Jiangsu 210023, China
2. National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA Army Engineering University, Nanjing, Jiangsu 210007, China
3. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
4. Unit of PLA, Beijing 100000, China

Received:2023-03-15 Online:2024-07-25 Published:2024-08-24
Contact: Hailin CHEN

摘要/Abstract

摘要：

从柱坐标系下传统时域有限差分(FDTD)的基本方程出发，解决传统加权Laguerre多项式(WLP)-FDTD算法在计算上存在内存消耗大和计算效率低的问题。本文的“分解”思想分为两部分，首先，在频域上对电磁场方程进行第一次分解，并代入PML参数，将分解后的时域方程转换至Laguerre域，使原三维双向求解问题转换为二维单向规模来求解，降低计算的内存消耗。其次，通过LU分解对求解规模降低后的Laguerre域系数矩阵实施第二次分解，实现规避大型稀疏矩阵求解的第一步，进而通过追赶法求解三对角电磁场方程，以提高计算效率，带动内存消耗的降低。算例证明: 对比传统WLP-FDTD法，本文算法可在内存消耗上降低57%，计算效率提高49%左右，且在不丢失精度的情况下，具有较好的电磁波吸收效果，误差反射系数可达-70 dB。

关键词: 加权Laguerre-FDTD法, 分解思想, LU分解, 追赶法, 降低求解规模

Abstract:

Based on the basic equations of conventional finite-difference-time-domian(FDTD) algorithm in cylindrical coordinate system, in order to solve the problems of large memory consumption and low computational efficiency in computation of conventional weighted-Laguerre-polynomial(WLP)-FDTD algorithm. The idea of "Decomposition" in this paper is divided into two parts. Firstly, the electromagnetic field equation is decomposed for the first time in the frequency domain, and PML parameters are substituted, and the decomposed time-domain equation is converted to the Laguerre domain, so that the original three-dimensional bidirectional solution problem is converted into two-dimensional one-way scale to solve, reducing the memory consumption of calculation. Secondly, LU decomposition is used to decompose the coefficient matrix of Laguerre domain after solution scale reduction, which realizes the first step of avoiding large sparse matrix, and then the chase after method is used to solve the conventional electromagnetic field equation, so as to improve the computational efficiency and reduce memory consumption. Numerical examples show that comparing with conventional WLP-FDTD, the proposed scheme can reduce the memory consumption by 57% and increase the computing efficiency by 49%, without losing the accuracy, the proposed method has a good electromagnetic wave absorption effect, and the reflection error can reach -70 dB.

Key words: weighted-Laguerre-polynomial-FDTD, decomposition ideology, LU decomposition, chase after method, reduce the scale of solution

中图分类号:

O441

朱大伟, 陈海林, 徐佳琛, 周晓晓, 徐博奥. 柱坐标系“分解”思想WLP-FDTD的PML实现[J]. 计算物理, 2024, 41(4): 440-452.

Dawei ZHU, Hailin CHEN, Jiachen XU, Xiaoxiao ZHOU, Boao XU. PML Implementation of WLP-FDTD Algorithm Based on "Decomposition" Ideology in Cylindrical Coordinate System[J]. Chinese Journal of Computational Physics, 2024, 41(4): 440-452.

图/表 8

图1 伸缩坐标PML中坐标伸缩函数的取值

Fig.1 The value of coordinate scaling function in PML

图2 算法的执行流程及程序设计

Fig.2 Execution flow and programming ideology of the proposed method

图3 降低求解规模示意图

Fig.3 Schematic diagram of reducing the solving scale

图4 柱坐标系的楔形不规则结构

Fig.4 Wedge-shaped irregular structure of cylindrical coordinate system

图5 观察点处本文算法，传统WLP-FDTD算法与参考值波形结果

Fig.5 Waveform results of the proposed method, conventional WLP-FDTD method and reference value at the observation point

表1 本文算法与传统WLP-FDTD法的内存和效率

Table 1 Memory and efficiency of the proposed method and the conventional WLP-FDTD method

	传播时间/ns	效率/s	内存/MB
传统WLP-FDTD(PML)	1.0	592.6	920.6
本文算法(PML)	1.0	298.7	397.7

图6 本文算法与传统WLP-FDTD法的精度

Fig.6 Accuracy results of the proposed method and the conventional WLP-FDTD method

图7 本文算法与传统WLP-FDTD法的相对反射系数

Fig.7 Relative reflection coefficients of the proposed method and the conventional WLP-FDTD method

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柱坐标系“分解”思想WLP-FDTD的PML实现

PML Implementation of WLP-FDTD Algorithm Based on "Decomposition" Ideology in Cylindrical Coordinate System

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