The Multilevel UV Factorization Algorithm Applied In Three Dimensional Random Rough Surface Scattering Problem

The simulation of electromagnetic scattering from three-dimensional random rough surface is playing a more and more important role in Earth Science and microwave remote sensing. With the development of computer science and fast algorithms in computational electromagnetic, the numerical simulation of random rough surface scattering allows people to overcome the restrictions of analytical approximate model to get the numerical solution of Maxwell equations. The Method of Moments(MoM) is an important computational electromagnetic algorithm. It discretizes the continuity equation into whose solution can be obtained by computer.However, the complexity of MoM is O(N2)(N is the number of unknowns). When N becomes very large, the computational load of the MoM increases to an enormous number. The Multilevel Factorization method is not only independent from kernel function, but also can be easily implemented because it directly factorize of sub-matrix in moment method. Meanwhile, it has been proved to be efficient and accurate by many literature. Therefore, the studying of MLUV algorithm and the improvement of it have great theoretical meaning and application prospects.In this paper, we first introduce the background, research significance and the research status of the problem of wave scattering from three-dimensional random rough surface. Then, we introduce the modeling of three-dimensional random rough surface and the derivation of surface integral equation, i.e. PMCHWT integral equation. The chapter III detailed introduction the derivation of the Method of Moments and the details of the Multilevel UV Factorization method. We also compared the results of MLUV algorithm and the Method of Moments in this chapter. In chapter IV, we proposed a new sampling algorithm combined with MLUV algorithm to replace the Coarse-Coarse-Sampling used in conventional MLUV algorithm. We compared the numerical results of the MLUV algorithm combined with new sampling algorithm, the MLUV algorithm combined with Coarse-Coarse-Sampling algorithm.and the MoM method. The numerical results show it significantly improves the accuracy of the matrix Zk whose elements are calculated from K operator. In chapter V, we talking about the parallelization of MLUV algorithm. In this chapter, we first comparing advantages and disadvantages of two typical methods for parallel computing, Open MP and MPI. Considering the situation of our lab. we employ Open MP interface to parallelize the MLUV algorithm. The numerical results have proved that the parallelization of MLUV algorithm can improve the calculating speed. In last chapter, as a conclusion, we summarized our research and looking into the future.