A Distributed Lagrange Multiplier Based Fictitious Domain Method for Maxwell's Equations

We consider a time-dependent problem of scattering by an obstacle involving the solution of the two dimensional Maxwell's equations in the exterior of a domain with a perfectly conducting condition on the boundary of this domain. We propose a novel fictitious domain method based on a distributed Lagrange multiplier technique for the solution of this problem. Perfectly matched layers are constructed to model the unbounded problem. Comparisons are performed with the finite difference scheme, that demonstrate the advantages of our fictitious domain method over the staircase approximation of the finite difference method. We conclude that our distributed multiplier approach is a simple, effective and far more accurate alternative to the popular FDTD method for solving Maxwell's equations.