Application Of High-Order FDTD Method To Electromagnetic Scattering Problem

The problem of electromagnetic scattering is an important research domain incomputational electromagnetics. It is very important and practical to analyze theelectromagnetic scattering characteristics of complex objects quickly and efficiently.There are a large number of methods, including analytic and numerical methods, forsolving electromagnetic scattering problems, but for complex objects the analyticmethods will be restricted. So it is important to pay more attentions to the numericalmethods. In this thesis, mainly contents are expanded around the High-Order FDTDmethod, which is one of the electromagnetic numerical methods. Concretely, themainly work in this thesis may be divided into three parts:Firstly, the two-dimensional and three-dimensional difference equations have beenpresented in detail, and then the stability conditions and numerical dispersion erroranalysis of High-Order FDTD method have been compared with the traditional FDTDmethod. High-Order formulae, including two-dimensional and three-dimensional, ofthe anisotropic perfectly matched layer absorbing boundary conditions, are introducedin this thesis and the absorbing effect has been tested and analyzed through numericalexperiments.Secondly, the High-Order FDTD method has been applied to electromagneticscattering problems and the numerical results shown that High-Order FDTD methodwas more efficient than FDTD method. Some key techniques were also included inthis part, which were shown as follows. One is that ray theory based on 3-D DirectXtechnique was applied to the three- dimensional targets modeling problem, throughwhich Yee mesh model of arbitrarily shaped targets can be constructed. The other oneis that the total field and scattering filed technique was introduced successfully inHigh method and some improved formulae are also given. And finally, an improvednear to far field transforms method, which is based on polynomial interpolation theory and traditional transform method, was presented.At last, to increase the computational accuracy in the curving surfaces scatteringproblems, a High-Order subgridding algorithm based on forward and backwarddifference equations and time-domain and space-domain interpolation technique ispresented. For conduct objects, an expanding mesh method is proposed to reduce thereflection of field values in those meshes near to the surface by avoiding orminimizing the discontinuity of field variables. Some numerical experiments werealso included to test the efficiency of the two methods, and the results confirmed theanalysis.In a word, the research in this thesis not only provides good theory basis and technicalsupport for the application of High-Order FDTD method in electromagnetic scatteringproblems, but also plays an important role in expanding the application scope of finitedifference time-domain method.