Research On Key Techniques Of Solving Electrically Large Electromagnetic Problems Based On Hierarchical Basis H-Matrix Method

Solving electrically large scale electromagnetic problems is one of the main research directions in the field of computational electromagnetics. Reducing the computing time and memory requirement is the key to these problems. The Method of Moments(MoM) has a pivotal position in the field, and it can solve the electromagnetic problems of electrically moderate targets well. However, its memory requirement and compute complexity will increase dramatically with the increase of target objects’ electric size. The emergence of a variety of fast algorithms makes it possible to solve electromagnetic problems of electrically large targets.Based on MoM, Hierarchical matrix method partitions the impedance matrix into near zone blocks and far zone blocks, while the elements of near parts are calculated directly using MoM and the far parts by means of low rank approximation. Thus the memory requirement and compute complexity are both reduced. On the base of Hierarchical matrix method, Hierarchical Basis H-Matrix Method introduces transfer matrix to reuse the information of base cluster, and further to reduce the amount of storage. The memory requirement and compute complexity are both approximatelly proportional to the number of unknowns and the H~2-Matrix method is suitable to solve electromagnetic radiation and scattering problems of electrically large targets.In this thesis, linear algebraic equations in the frame of H~2-Matrix method are solved by using conjugate gradient method. The amount of count in single step iteration is analyzed and the acceleration techniques are proposed. The techniques are used to solve the scattering problems of electrically large perfect electric conductors(PEC). Firstly, according to the nested property of the H~2 algorithm and the characteristic that overlapping nodes exist among nodes in the same block tree layer, a portion of matrix-vector products are stored temporarily to avoid double-count. This skill significantly accelerates calculation speed with little memory increase. Secondly, the degenerated kernel function matrices are stored in a compression format according to its Toeplitz property. And the fast Fourier transform(FFT) is applied to speed up the product of matrix and vector. Finally, bistatic Radar Cross Section(RCS) of PEC in different electric sizes are solved. They show the acceleration methods can solve electrically large electromagnetic problems effectively and accurately, and have advantages both in reducing the memory requirement and significantly shorten the single iteration time.