| Fast solution of electromagnetic field problems is the one of the keys on many applications, there are many fast algorithms based on Method of Moments in the frequency domain. Hierarchical-Matrix-Based(H-Matrix-Based) method, which is similar to Fast Multi-pole Method, can be used to solve integral equations fast. In essence, H-Matrix-Based method is separating the source variable and field variable in the degenerated kernel, storing the partial elements of the coefficient matrix implicitly, and then reducing the computation of iteration solution.In this thesis, H-Matrix-Based method on fast solving the low complexity electromagnetic field problems is studied, and some improvements are presented. Firstly, the method of using Lagrange interpolation polynomial to decompose the MoM matrix is studied, and some related calculation procedures are implemented. Secondly, a method of controlling the coefficient matrix's approximation precision is presented for dynamic electromagnetic field problems through analyzing the error of the Lagrange interpolation polynomial, this method can increase the coefficient matrix's approximation precision combined with Chebyshev interpolation polynomial. Some numerical examples show that improved H-Matrix-Based method needs less memory requirement and the CPU time, which are proportional to O ? Nlog ? N ??. Lastly, improved H-Matrix-Based method combined with ILU precondition technique is analyzed, the results of the analysis show that this method can reduce the number of iterations with maintaining the CPU time of once iteration proportional to O ? Nlog ? N ??. |
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