Electromagnetic Problems Mmol And Applied Research

Method of Line(MoL) is an effective numerical method in solving electromagnetic problems. MoL uses finite difference technique to discretize the problem into a system of ordinary differential equations with nodal line functions as unknowns, and allows a fast analytical solution in one dimension. MoL has been applied in solving kinds of electromagnetic problems and has proved to be a versatile and effective numerical method.However, conventional MoL will face difficulties and complexity when it is applied to open space electromagnetic problems. For solving open space electromagnetic problems, MoL may one way combine with Electric Walls or Magnetic Walls or the other combine with absorbing boundary conditions(ABC). For the first case, radiation has to been taken into account. For the later case, it's necessary to keep the calculation space as small as possible by truncate the finite differential mesh as close to the object as possible. All these two case will aggravate MoL's complexity and decrease MoL's efficiency.To overcome these shortages, a Modified Method of Lines(MMoL) is proposed in this thesis, based on the conventional MoL. The basic ideal of MMoL is: by discretizing with radial lines, the two-dimensional or three-dimensional Helmholtz equation reduces to a set of ordinary one-dimensional differential equations, which can be solved analytically in radial direction after an orthogonal transformation applied, and no Electric/magnetic Wall or ABC are need anymore. MMoL has two advantages: first, it's a fast and accurate semi-analytical method, and second, it can be applied to deal electromagnetic problems of objects in open space without using any artificial or absorbing boundary conditions.The works carried out in this thesis are as follows:(1) MMoL is studied in detail theoretically. The MMoL analyses of electromagnetic scattering problems of any two or three dimensional objects in open space are presented.(2) Numerical results are obtained by MMoL for scattering problems of arbitrary 2D cylinders. These results agree very well with those by analytical solutions.(3) Propagation properties of the dielectric waveguide structures with arbitrary cross-sections are also studied numerically by MMoL. And the numerical results are in excellent agreement with those published in literature.MMoL is simple in concept and easy to apply. The validity of MMoL has been tested. Several cases of 2D or 3D scattering problems have been successfully solved. The results agree well with analytical solutions or those published in literature.The work in this thesis may used as a base for farther research of MMoL.