Fast Algorithms And Program Designing For Two Kinds Of Edge Element Discrete Systems Of Maxwell's Equations

In this paper, we study the fast solvers and program designing for two kinds of edge element discrete systems of Maxwell's equations on tetrahedron mesh. The paper mainly contains two parts as follows.In the first part, we construct a two-grid method for the second family of Nedelec linear edge element equation of high frequency indefinite time-harmonious Maxwell's problem. The new method essentially transform the computation of that discrete system to the computation of a positive definite Maxwell edge element equation. We design the correlative program module. Numerical experiments indicate the efficiency and robust of the algorithm, the error results are in accord with what we predict.In the second part, we study and deduce the algebra expression on match and nonmatch grid for each constituent of the preconditioner corresponding to Mortar edge element system of positive definite Maxwell equations with variational coefficient, then design rational complex data frame and algorithm flow, develop the correlative program. Numerical experiments initially verify the efficiency and robust of the algorithm.