A Study On Discrete Method For Solving Electromagnetic Scattering Problems Of The Volume Integral Equation

The fast analysis of the electromagnetic scattering problems of large size has always been intensive researched in computational methods for electromagnetics. Some algorithms have been presented, including the Fast Multipole Method(FMM), the Multilevel Fast Multipole Method (MLFMM),the fast algorithm based on Hierarchical Matrix and so on. The overall algorithm computational complexity is not only related to the performance of the core solution calculation, but also including the pre-procedure and after-procedure complexity. The fast algorithm presented in this thesis for finding the common and non-common facets of hexahedrons mesh can be employed for the preprocess of the moment method and the other fast algorithms solving electromagnetic problems. The fast algorithm is based on the concepts of adjacency matrix and incidence matrix in the graph theory and the algorithm of sparse matrix transpose and product. Thus the requirements of storage and computational time can be reduced.In this thesis, based on the algorithm for finding the common and non-common facets of tetrahedrons mesh, the hexahedrons are employed to discrete the three-dimensional object. Then, the fast algorithms for finding the common and non-common facets of hexahedrons mesh can be obtained by the adjacency and incidence relationships between nodes, edges, facets and volumes. Several different models are analyzed using the proposed methods,and give the time required to find common and non-common facets. The computational and storage complexity for finding the common and non-common facets in the algorithm is linear order. Then select Roof-top function as the basis function and weight function.The bistatic RCS of target can be calculated by applying the fast algorithm for finding the common and non-common facets to the method of moments. Lastly, the bistatic RCS of dielectric cube,cylinder with a finite length and dielectric cuboid are analyzed using the proposed methods.And the results are compared with the commercial software results. The results show that the fast algorithms for finding the common and non-common facets in hexahedrons element mesh are efficient for solving electromagnetic scattering.