Research On Application Of Meshless Method In Electromagnetic Field

As a new branch of numerical method, meshless method bases on the information of nodes, notmeshes. That is the reason for its overcoming difficulties from mesh distortion, and can handleproblems which traditional mesh method can not work out properly. So it has a bright future in actualapplication.The paper studied application of universe set RBF (Radial Basis Function) Meshless method innumerical analysis of electromagnetic field, solved three kinds of electromagnetic problems—staticfield,1-D and2-D time-domain field problems, verified the feasibility for RBF meshless method.Firstly, the paper introduced a solving plan for static field’s boundary value problem, includescomputational spatial discretization, shape function establishment and approximate functioncalculation. According to the simulation result of an infinite rectangle ground metal slot, we can seethe accuracy of the method and can make a conclusion that shape parameter has a direct influence forthe result.Secondly, we used RBF meshless method to obtain a solution of1-D Maxwell equation, andanalyzed one-dimensional free space, then normal media has been added to expand the method’sserviceable range. After this, the thesis discussed the absorbing boundary conditions. WaveImpedance Matching Boundary Condition (WIMBC) is proved to be applicable to RBF meshlessmethod through the same calculating examples as before, and further simulation of EBG(Electromagnetic Band Gap) structure shows good agreement with the result of FDTD method. At thesame time, the effect of first order MUR boundary condition was also examined, the computationresult was explained by deducing process and algorithm. Besides, unconditionally stable ADImeshless method has been researched in this thesis, the method is proved to be able to shortencalculation time and calculation efficiency while sustaining the calculation precision.At last, RBF meshless method is apply for analyzing2-D time domain field, after comparing theerrors, it can be concluded that RBF meshless method’s precision was higher than FDTD method inthe case of rectangular resonant cavity. But there were some errors in the simulation of cylinderresonator, reasonable explanations have been given by two directions: the nodes distribution andradial basis function selection.