A Study On Degenerate Kernel Functions For Solving Integral Equations Of Electromagnetic Field Problems

Solving large scale objects problems is very necessary in computational electromagnetic research. A large amount of storage space and computational time are required for solving problems with the conventional method of moments(MoM). To improve the efficiency, some fast algorithms have been presented including the fast multipole method(FMM) which can be regarded as a material method of the degenerate kernel approximation. The source and filed variables can be separated and the storage and computational complexities for solving problems can be obviously decreased by using the degenerate kernel approximation, which has implicitly involved in the fast multipole method.Firstly, this dissertation introduces the concept of H-matrix method and deduces the storage and computational complexity which are proportional to O(Nlog N) in theory. Then, base in the thought of degenerate kernel function and consider the research and realization of the fast multipole method, further use the least squares method in complex domain to approximate the kernel function. A new kind of degenerate kernel functions produces by selecting fitting functions with the same exponential form of fast multipole method, the precision can be controlled by the count of the fit points and the direction vector of the exponential function. Finally, conductors such as conducting sphere, conducting cube and NASA almond are analyzed by using the proposed methods,the numerical results validate the correctness and validity of the algorithm and show that H-matrix-based method with exponential degenerate kernel may be more explored for algorithms with higher efficiency.