Research On The Application Of The Regularization Method To The Moment Methods

In recent years,with the development of computer technology,computational electromagnetics has been applied to the electromagnetic simulation of industrial products,the most widely used is the method of moments.The system matrices generated by the moment methods are ill-conditioned matrices,which make the iterative methods hardly converge,even accelerated by the existing preconditioning techniques.In this paper,a new regularized preconditioning method is proposed,which tests the matrix equation generated in the high order moment method to verify its effectiveness.The main study of this paper:1.How to more efficiently solve the ill-conditioned matrix equation produced by the moment method more efficiently.The traditional preconditioner matrix is constructed by using a small number of elements of the original matrix,but in this paper,the regularized preconditioner matrix is constructed by the whole element of the original matrix.This preconditioner method can directly improve the eigenvalue distribution of the original matrix.The method does not need extra space to store the precondition matrix,yet require additional time to fill the preconditioner matrix,so it is efficient.2.How to better balance the inner and outer iterations.The overall framework of the algorithm is divided into two layers,in which the generalized minimum residual method is used to solve the Tihkonov regularized matrix equation,and the outer iteration is solved by the generalized minimal residual method.The total time consumed by the algorithm is determined by the number of iterations of the inner and outer layers.This paper proposes to determine the optimized regularization parameter by finding the maximum value of the second derivative of the L-curve of the regularized matrix,which makes the preconditioned matrix equation solve the least number of iterations.Numerical experiments show that it is difficult to converge for the matrix equations generated by a class of higher order moments,but which can be converged quickly by using the preconditioned iterative method in this paper..