UDC 519.63 Parallel Second Order Finite Volume Scheme for Maxwell’s Equations with Discontinuous Dielectric Permittivity on Structured Meshes T. Z. Ismagilov Department of Information Technology Novosibirsk State University 2, Pirogova str., Novosibirsk, Russia, 630090 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. <...> Test results demonstrate second order of convergence and support second order of approximation in space and time. <...> Computations in each subregion were carried out independently using halo cells. <...> 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. <...> Key words and phrases: Maxwell’s equations, Godunov scheme, finite volume, discontinuous permittivity, second order, photonic crystals, waveguides. 1. <...> Introduction Finite difference time domain method based on structured cartesian grids is arguably the most popular method for numerical solution of Maxwell’s equations [1]. <...> In this paper we suggest a second order finite volume scheme on structured meshes for numerical solution of Maxwell’s equations with discontinuous dielectric permittivity with parallel implementation. <...> The key idea of the scheme is to use stencils for gradient approximation that don’t cross dielectric permittivity discontinuity. <...> Numerical Scheme edges Γk assuming constant dielectric permittivity in the cell an integral conservation law can be obtained By integrating the system of Maxwell’s equations over a quadrilateral cell Ci with Q ∂ ∂t ∫ Ci VdΩ+ ∑ k=1 4 ∫ Γk where (n1,n2) is a unit normal. <...> For approximation of this integral conservation law consider a finite volume Godunov scheme QΩCi Flux F is calculated using exact solution to the Riemann problem F = A+VL (XΓ)+ A−VR (XΓ) where VL,R(XΓ) are interpolations of V <...>