The Time Domain Numerical Calculation of an Integro-Differential Equation for Ultrashort Electromagnetic Pulse Propagation in Layered Media

2005 ◽  
pp. 647-653
Author(s):  
Igor V. Scherbatko ◽  
Stavros Iezekiel ◽  
Alexander G. Nerukh
Keyword(s):  
Differential Equation ◽  
Numerical Calculation ◽  
Time Domain ◽  
Electromagnetic Pulse ◽  
Pulse Propagation ◽  
Layered Media ◽  
Integro Differential Equation ◽  
Ultrashort Electromagnetic Pulse ◽  
The Time Domain

scholarly journals Time domain solution of electromagnetic radiation model of the grounding system excited by pulse current

2020 ◽  
Vol 35 (1) ◽  
pp. 74-81
Author(s):  
Nedis Dautbasic ◽  
Adnan Mujezinovic
Keyword(s):  
Differential Equation ◽  
Electromagnetic Radiation ◽  
Time Domain ◽  
Gauge Condition ◽  
Pulse Excitation ◽  
Solution Technique ◽  
Grounding System ◽  
Integro Differential Equation ◽  
Transient Voltage ◽  
The Time Domain

This paper deals with an advanced electromagnetic radiation approach for analyzing the time-domain performance of grounding systems under pulse excitation currents. The model of the grounding systems presented within this paper is based on the homogeneous Pocklington integro-differential equation for the calculation of the current distribution on the grounding system and Lorentz gauge condition which is used for the grounding system transient voltage calculation. For the solution of the Pocklington integro-differential equation, the indirect boundary element method and marching on-in time method are used. Fur- thermore, the solution technique for the calculation of the grounding system transient voltage is presented. The numerical model for the calculation of the grounding system transients was verified by comparing it with onsite measurement results.

Unified integro-differential equation for efficient dispersive FDTD simulations

2017 ◽  
Vol 36 (4) ◽  
pp. 1089-1105 ◽  
Author(s):  
Omar Ramadan
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Stability Limit ◽  
Model Parameters ◽  
Time Step ◽  
Content Type ◽  
Integro Differential Equation ◽  
Dispersive Model ◽  
Fdtd Simulations ◽  
Dispersive Models

Purpose The purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations. Design/methodology/approach In this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed. Findings It is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation. Research limitations/implications The stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit. Practical implications Based on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function. Originality/value The proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

scholarly journals Introduction to the method of estimating time-domain response based on amplitude-frequency characteristics

2021 ◽  
Vol 2087 (1) ◽  
pp. 012061
Author(s):  
Mingrui Wang ◽  
Mei Xu ◽  
Jiangfeng Wang ◽  
Yingying Guo
Keyword(s):  
Research And Development ◽  
Time Domain ◽  
Electromagnetic Pulse ◽  
Parametric Modeling ◽  
Frequency Characteristics ◽  
Practical Applications ◽  
Time Domain Response ◽  
The Time Domain ◽  
Non Parametric

Abstract How to use the amplitude-frequency characteristics to reconstruct the signal to obtain the time-domain response has always been a concern in the field of nuclear electromagnetic protection. So far, in practical applications, parametric modeling and non-parametric modeling have been used to solve related problems. This article summarizes the research and development of using amplitude-frequency characteristics to recover time-domain signals in the field of nuclear electromagnetic pulse protection, and briefly introduces the shortcomings of the two methods in combination with specific experiments.

Uncertain Circuit Equation

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Yang Liu
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Time Domain ◽  
Electrical Circuit ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Liu Process ◽  
The Time Domain ◽  
Steady State Solutions ◽  
Transient And Steady State

Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.

Symmetric Arc Solutions of ζ¨ = ζn

1968 ◽  
Vol 35 (3) ◽  
pp. 565-570
Author(s):  
C. P. Atkinson ◽  
B. L. Dhoopar
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Complex Variable ◽  
Digital Computer ◽  
Nonlinear Differential Equations ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Complex Variables ◽  
Complex Modes ◽  
The Time Domain

This paper, “Symmetric Arc Solutions of ζ¨ = ζn,” presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ¨ The solutions are called symmetric arc solutions since they form such arcs on the ζ = u + iv-plane. The solutions, ζ(t), are “complex modes” of coupled nonlinear differential equations in the complex variables z1 and z2. Symmetric arc solutions are presented for a range of n from n = 3 to n = 101. Approximate solutions are presented and compared with solutions generated by digital computer. Solutions are presented on the ζ-plane and in the time domain as u(t) and v(t).

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