Modelling material interfaces in structured nonorthogonal finite-difference methods

Structured nonorthogonal finite-difference discretisations of Maxwell's equations are often employed to model curved dielectric-vacuum interfaces. As part of this process, it is necessary to employ a suitable procedure to enforce the tangential field continuity conditions at the locations of the interfaces where the components of the permittivity tensor are discontinuous. This paper presents a second-order domain-splitting procedure that can accomplish this task without assuming that the permittivity tensor components are piecewise constant or diagonal. Such a feature is needed to exploit the full geometrical flexibility of structured grids. The proposed procedure consistently yields a global error that is second-order accurate even in extreme cases where the components of the permittivity tensor have a sharp jump or change of sign.