Iterative Methods For Solving Complex Linear Algebraic Systems

Complex valued linear algebraic systems arise in many fields of science and engineering computing,such as in electromagnetism,structural dynamics,wave propagation,time-dependent Schr¨odinger equations and inverse scattering problems and many others.Therefore,it is special significant for solving the complex valued linear algebraic systems in a fast and efficient way.In this paper,we focus on the iteration methods for solving the problem,especially for such a class of linear systems arising from the finite element approximation of the hybrid formulations of the time-harmonic eddy current problems.The main work of this paper is divided into two parts: Firstly,We establish a class of preconditioned block alternating splitting implicit iteration methods and demonstrate its convergence.Secondly,we accelerate the block alternating splitting implicit iteration scheme by Seidel technique.Experimental results show the feasibility and efficientiveness of the new iteration schemes in this paper.And the Seidel technique play a more significant role in promoting the calculation of the problem,especially for the more large scaled coefficient matrix.