Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for s...Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations.This is fulfilled by considering time variable as normal space variable.Under this scheme,there is no need to remove time-dependent variable during the whole solution process.Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method.We propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix easily.Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.展开更多
在计算大规模介质-金属复合周期结构的电磁散射时,传统积分方程方法存在未知量大、存储占用多和计算时间长等问题。本文采用广义PMCHWT(Poggio-Miller-Chang-Harrington-Wu-Tsai)-电场积分方程(electric field integral equation,EFIE)...在计算大规模介质-金属复合周期结构的电磁散射时,传统积分方程方法存在未知量大、存储占用多和计算时间长等问题。本文采用广义PMCHWT(Poggio-Miller-Chang-Harrington-Wu-Tsai)-电场积分方程(electric field integral equation,EFIE)方法计算均匀介质-金属复合结构的电磁响应。该方法通过在分界面处设置区域连接模型(contact-region modeling,CRM)来保证边界处的连续性。为加速子阵列阻抗矩阵填充,采用快速偶极子方法(fast dipole method,FDM)来提高计算效率并降低内存占用。结合子全域(sub-entire-domain,SED)基函数方法,子阵列的电流分布特征可被推广到大规模介质-金属复合周期结构的电磁场计算中。数值算例表明,本文方法能够在保证计算精度的同时大幅度降低计算代价,内存占用降低至商业软件Altair FEKO(使用多层快速多极子方法)的1/10,计算误差在2.6 dB以内。展开更多
Accurate simulations of ultra-wideband （UWB） electromagnetic radiation from an antenna were developed based on a time-domain finite element method （TDFEM） based on p-step Lagrange interpolation for the temporal ex...Accurate simulations of ultra-wideband （UWB） electromagnetic radiation from an antenna were developed based on a time-domain finite element method （TDFEM） based on p-step Lagrange interpolation for the temporal expansion. The motivation was to utilize the good interpolation features and straightforward computations for UWB antenna simulations. Numerical results were obtained from the cases of the cavity resonance problem, a bowtie and a Sierpinski bowtie antenna. Comparisons with an existing TDFEM approach employed linear temporal basis functions show good agreement to demonstrate the validity of the present schemes. The TDFEM with 2-step Lagrange interpolation as the temporal basis functions achieves better numerical results with only a small increase to run time and memory use in terms of the relative errors of the resonant frequency in the cavity for the transverse electric mode and the radiation patterns of the bowtie antenna.展开更多
基金The first author is supported by the Natural Science Foundation of Anhui Province(Project No.1908085QA09)the University Natural Science Research Project of Anhui Province(Project Nos.KJ2019A0591&KJ2020B06)。
文摘Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations.This is fulfilled by considering time variable as normal space variable.Under this scheme,there is no need to remove time-dependent variable during the whole solution process.Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method.We propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix easily.Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.
文摘在计算大规模介质-金属复合周期结构的电磁散射时,传统积分方程方法存在未知量大、存储占用多和计算时间长等问题。本文采用广义PMCHWT(Poggio-Miller-Chang-Harrington-Wu-Tsai)-电场积分方程(electric field integral equation,EFIE)方法计算均匀介质-金属复合结构的电磁响应。该方法通过在分界面处设置区域连接模型(contact-region modeling,CRM)来保证边界处的连续性。为加速子阵列阻抗矩阵填充,采用快速偶极子方法(fast dipole method,FDM)来提高计算效率并降低内存占用。结合子全域(sub-entire-domain,SED)基函数方法,子阵列的电流分布特征可被推广到大规模介质-金属复合周期结构的电磁场计算中。数值算例表明,本文方法能够在保证计算精度的同时大幅度降低计算代价,内存占用降低至商业软件Altair FEKO(使用多层快速多极子方法)的1/10,计算误差在2.6 dB以内。
文摘Accurate simulations of ultra-wideband （UWB） electromagnetic radiation from an antenna were developed based on a time-domain finite element method （TDFEM） based on p-step Lagrange interpolation for the temporal expansion. The motivation was to utilize the good interpolation features and straightforward computations for UWB antenna simulations. Numerical results were obtained from the cases of the cavity resonance problem, a bowtie and a Sierpinski bowtie antenna. Comparisons with an existing TDFEM approach employed linear temporal basis functions show good agreement to demonstrate the validity of the present schemes. The TDFEM with 2-step Lagrange interpolation as the temporal basis functions achieves better numerical results with only a small increase to run time and memory use in terms of the relative errors of the resonant frequency in the cavity for the transverse electric mode and the radiation patterns of the bowtie antenna.
