An unconditional stable modified finite element methods for Maxwell’s equation in Kerr-type nonlinear media

The purpose of this paper is to construct a newly efficient finite element method which named as modified finite element method, for Maxwell’s equation in Kerr-type nonlinear media. Because the efficient unconditional stable alternative direction implicit method can’t extend to the Maxwell’s equations in Kerr-type nonlinear media (the difficulty will be discussed in section 3.1), we design the modified method to construct an efficient unconditional stable scheme for Maxwell’s equations in Kerr-type nonlinear media. Furthermore, combined with the direct method, we construct a more efficient direct modified scheme. Comparisons of the efficiency, stability, convergence rate for our modified method and classical explicit leapfrog method were done by theoretical analysis and numerical experiments. The modified method is unconditional stable and its efficiency is not less than leapfrog method.