The Research On Improving Accuracy Of Multilevel Fast Multipole Algorithm

The tranditional Mo M is not suitable for solving large electromagnetic scattering or radiation problem for the computational complexity and memory requirements. A lot of fast algorithms have been proposed for solving the electromagnetic scattering from electrically large objects. The multilevel fast multipole algorithm(MLFMA) which is based on Fast multiple method(FMM) is one of these algorithms. Comparing with the MoM, the MLFMA introduces extra error sources because it use the addition theorem on Green function and the interpolation matrix for improving the computational efficiency.In this thesis, the FORTRAN code of the FMM and the MLFMA are accomplished with the theory of the FMM and MLFMA. Firstly, the error sources of the FMM which are the truncation error of the infinite series and numerical integtration error on the unit sphere are researched. The selection method of the truncation number is determined and numerical examples can demonstrate the accuracy of the code of the FMM. Secondly, the change of the interpolation accuracy and accumulation error of multilevels are researched with adding the poles as the sampling points. By comparison, the interpolation error is reduced with adding the poles. Finally, the accuracy of the MLFMA is improved significantly with employing the poles as the sampling points from the Radar Cross Section(RCS) of the numerical examples.