A method for complex geometries in finite-difference solutions of Maxwellʹs equations

Numerous techniques have been developed to extend the basic FDTD method todomains whose boundaries do not lie on mesh surfaces. Usually these methods are not simple to apply and may involve mesh generation, nonstandard differencing, and other difficulties. For the time periodic problem, this paper describes an alternative approach which uses only uniform mesh differencing. Restricting to time periodic problems avoids some well-known stability issues which occur with most discretizations of the fully time dependent problem. The boundary conditions are imposed by an interpolation scheme. The method is described and applied to some two-dimensional problems for which exact solutions are known.