A Fast Construction Method Of Orthogonal Complementary Space In Projection Decomposition Method Research And Application

The electromagnetic field problem calculation has a wide range of applications in the military and civilian fields,such as communications,radar,electromagnetic protection,electromagnetic compatibility,and medical protection.With the rapid development of electronic computers,the application of electromagnetic computing has become more and more extensive,and the scale of calculation has become larger and larger,making the solution of large-scale and complex multi-scale electromagnetic structure problems a research hotspot.For large-scale electromagnetic field problems,the number of unknown nodes generated after numerical discretization is huge,and the corresponding linear algebra equations are also very large.With limited computing resources,the huge storage and calculation capacity make electromagnetic problems difficult to solve.At this point,the advantages of the partitioning algorithm are revealed.The main idea of the partitioning algorithm is to decompose a largescale problem into several small problems on sub-regions to solve.Since partitioning algorithms are usually iterative algorithms,their convergence and convergence speed become the key to the effectiveness of the algorithm.The projection decomposition method based on orthogonal complementary space theoretically reduces the infinite iteration process to only a finite iteration process,and the number of iterations is only related to the total number of adjacent nodes in the subregion.Early research results show that the number of iterations is equal to twice the number of adjacent nodes in all subregions.And for the electromagnetic structure optimization problem,the relative invariance of the orthogonal complement space can be used to directly calculate the optimization area without iteration,which greatly improves the calculation efficiency.However,the iterative process of constructing the orthogonal complement space takes a lot of calculation time.How to reduce the number of iterations and the amount of calculation requires further research.In order to solve the above problems,this paper proposes a rapid construction method of orthogonal complement space in the projection decomposition method,which reduces the number of iterations from twice the total number of associated nodes in all subregions to the maximum value of adjacent nodes between the two subregions.Times,and rigorously proved the conclusion mathematically.Numerical examples verify the correctness and effectiveness of the method.For the new algorithm,the number of iterations to construct the orthogonal complement space is no longer related to the number of subregions,which greatly improves the computational efficiency.On the other hand,the basis vector in the orthogonal complement space is modified,most of which are unit vectors,that is,there is only one non-zero element,which greatly reduces the amount of calculation.In this paper,the rapid construction method of orthogonal complementary space in the projection decomposition method is combined with the sub-grid technology to solve the multiscale structure in large-scale electromagnetic problems.The algorithm is applied to complex structures and SIW filters,and verified by numerical examples.The combination of these two methods improves the calculation efficiency.The number of iterations and calculation time are far less than the earlier algorithms.Compared with the software Matlab,there is also certain advantage.