Parallel H-matrix Algorithm And Hierarchical Basis H-matrix Algorithm For Solving Electromagnetic Scattering Problems

The method of Moments has a significant effect in the field of computational electromagnetics.However,as the electrical size of the target increases,the requirement on computer performance is getting higher.a variety of fast algorithms have emerged with lower storage and calculation.In order to reduce computational time,parallel schemes have been used to solve electromagnetic problems.The parallel H and H~2 matrix algorithm are implemented in this thesis.Firstly,this thesis analyzes the iterative procedure of H and H~2 algorithm and the parallel computing model.According to the calculation of matrix elements and iterative solution,the row mode parallel scheme is realized.All the processes store basic data of physical model and construct cluster tree.The iterative solution needs a label,which is used to distinguish the job of calculating elements to different processes.The row number of matrix is used for label.The calculations are assigned to different processes by label.The parallel efficiency of iterative solution is close to 1,which indicates that parallel scheme has high computational efficiency.Secondly,this thesis presents a block-mode parallel scheme,which is based on block cluster tree.The impedance matrix element calculation and the equation iteration process are allocated to different processes.In the elements of impedance matrix calculation phase,the nodes of the cluster tree are evenly distributed to different processes.Each process calculates the corresponding elements of the nodes.During the iterative solution phase,the process calculates the corresponding impedance matrix and vector multiplication and gets the complete results.The scheme further reduces the repetitive calculation of the impedance matrix elements.In the block mode,the memory reduction ratio the five processes is close to 0.2.Based on the parallel scheme of H matrix algorithm,this thesis realize parallel H~2 matrix algorithm.In addition,intermediate result is been double counted in the calculation process,the parallel scheme reduces the amount of computation and storage,and optimizes the computation process.