A Study On Degenerate Kernels Of Electronmagnetic Field Integral Equation

A large amount of storage space and computational time are required for solving problemswith the conventional method of moments (MOM). For more computational efficiency, some fastalgorithms have been presented including the method based on the Fast Fourier Transform, the FastMultipole Method and so on. The storage and computational complexities for solving problems canbe obviously decreased by using the degenerated kernel approximation, which has implicitlyinvolved in the fast multipole method. It can be regarded as one method of the degenerated kernelapproximation. That means there are many other methods which can also approach the kernel withsome techniques, such as the Taylor expansion, the polynomial interpolation, etc. By means of thesemethods, the source and filed variables can also be separated similar to the multipole expansion.Thus the requirements of storage and computational time can be reduced.In this thesis, firstly, based on the H-Matrix theory, an improved technique to approach thekernel function with phase compensation of electromagnetic integral equations with the radial basisfunction is presented. The domain of the piecewise basis functions of the moment of method (MoM)is divided into the near blocks and far blocks. The far blocks can be approximated with radial basisfunction interpolations with phase compensation. The approximation accuracy and efficiency can beimproved while the required storage space and the computational time are decreased.Secondly, conductors such as sphere, cone sphere and NASA almond are analyzed using theproposed methods. Finally, the numerical results validates the correctness and validity of thealgorithm raised. The numerical examples show that the required memory space and the CPU timeare proportional toΟ N logN by using the H-matrix-based method. H-matrix-based methodwith proper degenerated kernel may be more explored for algorithms with higher efficiency.