Application Of Unconditionally Stable Finite Difference Time Domain Method In Ground Penetrating Radar System

Computational electromagnetics methods have received attention in the electromagnetic field in recent years,and the Finite-Difference Time-Domain Method(FDTD),as an efficient and accurate numerical method,has been widely used in various fields.Ground Penetrating Radar(GPR),as one of the important geophysical methods,includes a long transmission line responsible for transmitting signals,a ground penetrating radar array and a computer responsible for issuing commands and solving signals.The simulation of the ground penetrating radar system is used in the research to verify the overall system design and to compare the data after the experiment.Therefore,the simulation of the ground penetrating radar system based on the computational electromagnetic method has always been one of the main research objects in the ground penetrating radar system.And comprehensive ease of use and effectiveness,as a mature computational electromagnetics method,FDTD is widely used in the simulation of ground penetrating radar systems,but FDTD is limited by stability conditions and is used in simulation of ground penetrating radars.For various problems such as large-scale detection and dispersive media,the calculation will become extremely slow.On this issue,this thesis uses the domain transform unconditionally stable FDTD method and the explicit implicit unconditionally stable FDTD method to study the long transmission line,waveform forward modeling and dispersive medium simulation in the ground penetrating radar system.The specific research content is as follows:1.The basic principle of the finite difference time domain method is analyzed and explained,and two specific unconditionally stable finite difference time domain method formats based on domain transform unconditionally stable and explicit implicit unconditionally stable are derived.These two formats are respectively carried out Analysis and stability proof.2.With the introduction of Maxwell's wave equation,this paper divides the long transmission line in the ground penetrating radar system into unit structure and analyzes it.On this basis,the transmission line equation and the parameter calculation method of the transmission line unit are derived,and the FDTD for the transmission line equation is given.Analysis process: Based on the FDTD analysis of the transmission line equation,this paper gives two unconditionally stable transmission line unconditionally stable FDTD algorithms and performs simulation verification.3.Aiming at the waveform forward modeling of ground penetrating radar,this paper analyzes the excitation source setting in the forward modeling model of ground penetrating radar based on FDTD theory,presents a medium interface processing method based on two types of loop integration paths and studies the simulated boundary conditions;Two types of ground penetrating radar forward models under unconditionally stable FDTD are deduced and simulated and verified;for the dispersive medium in the ground penetrating radar forward modeling,several dispersive medium models are analyzed separately,and the auxiliary differential equations are given.The unconditionally stable FDTD method has been verified by simulation.In this paper,through the in-depth study of the unconditionally stable finite difference time domain method,the unconditionally stable FDTD algorithm and the ground penetrating radar system are combined,and the calculation and application of the ground penetrating radar system have achieved unconditional stability.The effectiveness of the unconditional stability method in the ground penetrating radar system is proved.