Study Of Time Domain Integral Equation Based Method And Its Application In Simulation With High Electromagnetic Field At Low Frequency

Simulation,experiment and analysis are three generally used methods in industy with high electromagnetic filed with low frequency.In this dissertation,simulation methods are studied based on national defense projects.While simulating electromagnetic problems at low frequency,methods based on time-domain integral equation(TDIE)are very efficient.Computational complexity and memory cost are insensitive because the low frequency.However,incident field with long duration and the resonant structure may trigger the instability which is the key problem of TDIE-based methods.Three instable phenomenons:initial condition problem,inner resonant modes and linear loop modes are studied.The original and derivative forms are two common forms of TDIE.The initial condition problem only occurs in the marching-on-in-time(MOT)solvers based on the derivative form of TDIE(DF-TDIE),and caused by the inappropriate settings of the initial conditions.A constraint condition for temporal basis functions is proposed to avoid this problem,and its efficiency is demonstrated by numerial experiments.The unusual high reponse at inner resonant frequency in MOT solver is called inner resonant mode.In this dissertation,the inner resonant mode in DF-TDIE is studied.The impact of inner resonant mode in the DF-TDIE and original TDIE are quite similar,and both of them can be cancelled by accurate calculations of impedance matrices and matrix equations.Linear loop modes are loop currents with their amplitude increasing as time.The modes are the main reason of the divergent of the current solution.After the theoretical anlysis,it's proved that the machine error makes the linear loop modes belong to the null space of DF-TDIE which,as a result,can not be avoid.The study also reveals that errors dure to currents' space-time discretization and calculation of matrices elements have no discernible impact on spurious linear loop modes.Specifically,the magnitudes of linear loop modes are approximately proportional to the incident field at the initial time and the reciprocal of time step size,as will be demonstrated by several numerical experiments.It should be noted that the static loop modes in the original TDIE are special cases of linear loop modes.The efficient evaluation of double surface integrals not only improves the stability of MOT solver,but also accelerates the filling of impedance matrices.A general integration scheme which can efficiently evaluate the integrals with different,complicated and singular kernals are proposed.In the proposed integration scheme,the inner 2-D integrals are calculated by angular integration(AI)scheme and improved radial integration(IRI)scheme;the outer integrals are evaluated by Duffy-PT.The AI and IRI schemes are very general because they calculate the inner integrals half-analytically-half-numerially.Moreover,appropriate integration strategy and efficient smoothing technique are applied to ensure the fast convergence of results.The order of integration in AI and IRI schemes are opposite,which gives them different properties.The AI scheme is more efficient for evaluating the complicated kernals,while the IRI scheme is more suitable for the piecewise temporal basis functions.Both two integration schemes are very general,fast and accurate.The smoothing technique is redesigned,after that,the Duffy-PT method is expanded and can be used for more singular integrals.Nevertheless,the original Duffy-PT's efficiency drops quickly when calculating integrals over obtuse triangles.To solve this problem,two different improving methods-adaptive redistribution method for integration points and triangle division method-are proposed.In the last part of this dissertation,the electromagnetic compatibility of armored vehicle is studied through simulation and experiment using MOT solver,commercial softwares and specifically designed testing system.The study shows that the low-frequency magnetic shielding effect of the power box is insufficient.One proper solution is changing the material of power box.After comparisions among five different metals,the power box is recreated by a cheap metal with sufficient magnetic shielding effect.