Two Preconditioners And Their Applications For Mixed Finite Element Discretization Systems Arising From A Class Of Maxwell Equation

We propose two preconditioners for the mixed finite element discrete system of a class of variable coefficient Maxwell equation,i.e.,block diagonal and block triangular preconditioners.For quasi-uniform mesh,theoretical analysis of two preconditioners are given,and it is proved that the preconditioned system with block diagonal and block triangular preconditioners have a uniformly bounded conditional number,and they are independent of mesh size.Numerical experiments show the efficiency of the two preconditioners,and the error convergence order is consistent with the theory.Second,we propose two iterative algorithms for the mixed finite element discrete system of Maxwell eigenvalue problem.One is the inverse iterative finite element algorithm for finding the minimum eigenvalue,the other is subspace iterative method for finding multiple eigenvalues.Additionally,the block diagonal and Block triangle preconditioner are used in the steps to solve the linear system of equations in these two algorithms.Numerical experimental results show that these two fast algorithms are effective,and the error of the eigenvalues converges.The order is consistent with the theory.