A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes

Abstract

We develop, implement, and demonstrate a reflectionless sponge layer for truncating computational domains in which the time-dependent Maxwell equations are discretized with high-order staggered nondissipative finite difference schemes. The well-posedness of the Cauchy problem for the sponge layer equations is proved, and the stability and accuracy of their discretization is analyzed. With numerical experiments we compare our approach to classical techniques for domain truncation that are based on second- and third-order physically accurate local approximations of the true radiation condition. These experiments indicate that our sponge layer results in a greater than three orders of magnitude reduction of the lattice truncation error over that afforded by such classical techniques. We also show that our strongly well-posed sponge layer performs as well as the ill-posed split-field Berenger PML absorbing boundary condition. Being an unsplit-field approach, our sponge layer results in ∼25% savings in computational effort over that required by a split-field approach.