Decomposition Projective Method Based On Orthogonal Complement Space And Its Applications

With the wide application of Computational Electromagnetics in the civilian and military fields,such as radar,communication,electromagnetic compatibility,medical diagnosis,etc,the calculation scale of electromagnetic problems becomes larger and larger,and the structures become more and more complicated,which lead to the research focus on the algorithm of large multi-scale and complicated electromagnetic problems.For large multi-scale electromagnetic problems,a huge amount of unknown nodes will be produced after the numerical discretization,and the size of linear algebraic equations will be rather large,bringing the problem that computing resource can not satisfy its requirement.At this point,the partition algorithm becomes a better choice,such as decomposition projective method(DPM)and domain decomposition method(DDM)[1].The main idea of these methods is to solve the problems by transforming large-scale electromagnetic problem into several small-scale problems.Partition algorithm is an iterative algorithm commonly,the convergence and convergence rate become the key to the efficiency of these algorithms.The main research work of this paper is to present a Decomposition Projective Method Based on Orthogonal Complement Space.This method has tremendously improved the convergence rate of DPM,and has reduced the theoretical infinite iterative process to the theoretical finite iterative process.Whether it is a fast DPM or an overlapped DPM,the early DPM is an algorithm iterated infinitely,it needs to iterate repeatedly in each area to approach the final numerical result.If a high accuracy has been set,the number of iterations will increase significantly.On the contrary,the DPM Based on Orthogonal Complement Space is only associated with the number of adjacent nodes in sub-areas,the numerical result can be achieved only in few finite iterations.In theory,the number of iterations is just equal to the twice number of adjacent nodes in sub-areas,which has been strictly proved in mathematics.What’s more,this paper also gives the construction method and process of the orthogonal complement space.By contrasting the numerical solution and the analytic solution in numerical examples,the reliability of this method has been fully verified.Meanwhile,in order to apply the algorithm to complex electromagnetic problems,this paper also combines the DPM Based on Orthogonal Complement Space with the sub-gridding method to analyze and simulate the electric field distribution of integrated waveguide(SIW)and the SIW filter characteristics.Besides,it also establishes the numerical discrete difference equation for the compatible sub-grid of the fourth-class node.The numerical results show that the proposed method has high computational efficiency for complex large-scale electromagnetic problem,and the number of iterations exactly the same as the theoretical value.