Astudy On Hierarchical-matrix-based Algorithm For Solving Electromagnetic Scattering From Conducting Bodies

A large amount of storage space and computational time are required for solving problems with the conventional method of moments (MOM). For more computational efficiency, some fast algorithms have been presented including the method based on the Fast Fourier Transform, the Fast Multipole Method and so on. The storage and computational complexities for solving problems can be obviously decreased by using the degenerated kernel approximation, which has implicitly involved in the fast multipole method. It can be regarded as one method of the degenerated kernel approximation. That means there are many other methods which can also approach the kernel with some techniques, such as the Taylor expansion, the Lagrange interpolation, etc. By means of these methods, 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, based on the H-Matrix theory, the Lagrange interpolation is used to get the degenerated kernel for the fast calculations. Firstly, the triangular facets are employed to discrete the surface of the three-dimensional conducting scatterers, Then, the common edges of triangular elements can be obtained by the fundamental relationships between nodes, edges and facets. By using the MOM, the surface current of target can be calculated. Secondly, The circumscribed cube of the scatterer is decomposed in different layers by using octree technique. Then, the common edges of the elements are reordered in the finest layer. Thirdly, the block obtained can be divided into so-called near blocks and far blocks. The near blocks which dose not satisfy the admissibility condition are directly calculated with MOM; the far blocks which satisfy the admissibility condition are approximated using the Lagrange interpolations. And then the conjugate gradient method is used for solving the matrix-vector equation. Finally, the current obtained from the H-matrix method and the current of MOM are compared to verify the correctness of the H-matrix method. The amount of storage space and computational time of the H-matrix method are also analyzed. The results show that H-matrix-based method with proper degenerated kernel maybe more explored for algorithms with more efficiency for solving electromagnetic scattering from conducting bodies.