Parallel Second Order Finite Volume Scheme for Maxwell’s Equations with Discontinuous Dielectric Permittivity on Structured Meshes

A second order finite volume scheme on structured meshes is presented for numerical solution of time dependent Maxwell’s equations with discontinuous dielectric permittivity. The scheme is based on approaches of Godunov, Van Leer and Lax Wendroff and employs a special technique for gradient calculation near dielectric permittivity discontinuities. The scheme was tested for problems with linear and curvilinear discontinuities. Test results demonstrate second order of convergence and support second order of approximation in space and time. A parallel implementation of the scheme based on geometric decomposition was developed. Computational region was partitioned into subregions. Computations in each subregion were carried out independently using halo cells. Test results indicate linear scalability. Parallel implementation was applied to modelling photonic crystal devices. Computational results for photonic crystal waveguide with a bend correctly confirm bend configurations and frequencies with zero reflection.

Maxwell’s equations, Godunov scheme, finite volume, discontinuous permittivity, second order, photonic crystals, waveguides