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

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。

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.