一种简化的时域非连续伽略金阻抗边界算法  

A simplified impedance boundary algorithm in discontinuous Galerkin time-domain

作　　者：杨谦[1] 魏兵[1] 李林茜[1] 邓浩川 Yang Qian;Wei Bing;Li Lin-Qian;Deng Hao-Chuan(School of Physics,Xidian University,Xi’an 710071,China;Science and Technology on Electromagnetic Scattering Laboratory,Beijing Institute of Environmental Features,Beijing 100854,China)

机构地区：[1]西安电子科技大学物理学院,西安710071 [2]北京环境特性研究所,电磁散射重点实验室,北京100854

出　　处：《物理学报》2023年第6期11-20,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61901324,62001345);中国博士后科学基金(批准号:2019M653548,2019M663928XB);电波环境特性及模化技术国防科技重点实验室基金(批准号:201903002);电磁散射重点实验室基金(批准号:61424090111);中央高校基本科研业务费(批准号:XJS200501,XJS200507,JB200501)资助的课题.

摘　　要：针对时域非连续伽略金(discontinuous Galerkin time-domain, DGTD)算法中的阻抗边界条件问题开展研究.阻抗边界条件中的频域算符jω一般在根号内部,其在时域数值算法中的实现有一定难度.另一方面,DGTD算法中数值通量表达式也含有阻抗边界条件,这也进一步增加了频时转换难度.为了能给出简化的DGTD阻抗边界算法,本文首先针对数值通量表达式进行推导,得到一个特定函数Z_(R),该函数包含频域算符jω,函数以外表达式不含频域算符jω,这样就可以仅处理Z_(R)的频时转换问题.由于Z_(R)形式复杂,对Z_(R)进行矢量匹配处理,得到关于jω的一阶有理分式,进而得到其时域迭代式.这一过程简明、易于实施,还可避开矩阵计算.本文方案经一维及三维算例验证,精度很好,针对特定电磁问题如涂覆层问题可大幅降低计算时间.Large-size conductive targets or coated targets are difficult problems in computational electromagnetics.In general,these problems can be classified as multi-scale problems.Multi-scale problems usually consume a large quantity of computational resources.A lot of efforts have been devoted to seeking for fast methods for these problems.When the skin depth is less than the size of a conductive target,the tangential component of the electric field and magnetic field over the surface of the target can be correlated by the surface impedance.The is usually a complex function of the frequency,and it can be used to formulate an impedance boundary condition(IBC)to describe iterative equations in time domain methods,avoiding the volumetric discretization of the target and improving computational efficiency.This condition is commonly known as the surface impedance boundary condition(SIBC).Similarly,for a conductor whose thickness is in the order of skin depth or less,it also has high resource requirements,if the target is of direct volume discretization.The transmission impedance boundary condition(TIBC)can be utilized instead of a coated object to reduce resource requirements.Therefore,there is no need to discretize volume.~Z~ZR There are few studies on the IBC scheme by using the discontinuous Galerkin time-domain(DGTD)method.Li et al.(Li P,Shi Y,Jiang L J,Bağci H 2015 IEEE Trans.Antennas Propag.635686;Li P,Jiang L J,Bağci H 2015 IEEE Trans.Antennas Propag.633065;Li P,Jiang L J,Bağci H 2018 IEEE Trans.Antennas Propag.663590)discussed the IBC scheme by using the DGTD,which involves complex matrix operations in the processing of IBC.In the DGTD method,numerical flux is used to transmit data between neighboring elements,and the key to the IBC scheme in DGTD is how to handle numerical flux.We propose a DGTD method with a simple form and matrix-free IBC scheme.The key to dealing with IBC in DGTD is numerical flux.Unlike the way in the literature,the impedance is not approximated by rational functions in our study.A specfic f

关 键 词：阻抗边界条件 矢量匹配 时域非连续伽略金算法 

分 类 号：O441.4[理学—电磁学]