PML Implementation of WLP-FDTD Algorithm Based on

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

Abstract

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

CLC Number:

O441

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.

Figures/Tables 8

Fig.1 The value of coordinate scaling function in PML

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

Fig.3 Schematic diagram of reducing the solving scale

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

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

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

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

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

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