Hybrid Method Of Finite Element Method And Mode Matched Method

Transient finite element method hybridization with mode matched method is constructed for modeling discontinuous problem in waveguide. Within this context, four specific areas are addressed: (1) By means of finite integration technique, a new kind of the first order partial difference equation is derived from the original disperse transmission line equation of the uniform waveguide's. As it is the kind of one dimension Dirichlet's boundary problem, it is convenient for us to solve this equation from the leapfrog scheme.Because computation is carried out in one dimension, both high calculation efficiency and precision have been obtained in this method. Meanwhile, this method provide us a different selection to simulate the transient response of waveguide with non-simplical, for examples cylinder and elliptic waveguide, and avoid solving the second order equation, or using finite difference time domain to simulate a three dimension problem, sometimes the latter precision is not satisfied with the need, or low efficiency. (2) Basing on known method, the kernel function of one dimension dispersive transmission line system is expanded in the form of a finite series, and then the original convolution computation is replaced by a recurrence iterative procedure. It's so-called local method of computing convolution. (3) From the symmetric ideal in mathematics, a new model of fictitious loss transmission line(FLTL) is deduced in this dissertation. The loss in this model does not concern the real loss in the real transmission line, and disturbed the orthogonal condition of the transmission line modes. Both transmission and loss characteristics of the line have been carefully investigated in this dissertation, and then both so-called the perfect absorbing condition and the optimum parameters of the line are obtained. It can produce a little of loss to absorb the return wave from the non-ideal terminated boundary condition's yielded from the convolution computing. Our method can depress the fictitious return wave loss below to –50dB level. (4) As the result of the aforementioned studies', a transient finite element method hybridization with mode matched method has been developed to find the solution of complicated waveguide junction problems that are modeled by three dimension unstructured tetrahedron mesh. In this method, Field vector are first sampled on the certain plane, and then the existed scattering modal voltages are obtain by means of orthogonal expanding integration. Those scattering modal voltages are used as sources to calculate the boundary condition at the porter plane of the waveguide, thus the finite element method time domain can carry out for every time iterative step. For investigating the performance of our method, it has been evaluated to simulate a uniform segment of rectangular waveguide. The more lower fictitious return wave loss, which is lower –10 dB than the one yielded from the first order absorbing boundary condition, is illustrated in our method.