Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case

Block pseudospectral (BPS) methods are examined for Maxwell's equations in two-dimensional inhomogeneous media. For the case of a rectangular strip with a straight-line interface, blocks may be coupled via fictitious points or a generalization of characteristic outflow conditions. The BPS methods generalize to curvilinear strips described by a change of variables. Such strips can conform to interfaces while overlapping with a high-order free-space grid to form a composite grid method. Numerical experiments on strips with dielectrics, lossy materials, perfect conductors, and absorbing layers indicate that the two coupling methods are comparable and accurate with just 3--4 points per wavelength. Full composite examples are included to demonstrate high accuracy and geometric flexibility.