Second Order Scheme for Maxwell’s Equations with Discontinuous Electromagnetic Properties
A second order finite volume scheme for numerical solution of non-stationary Maxwell’s equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes is suggested. The scheme is based on Godunov, Lax-Wendroff, and Van Leer approaches. The distinctive feature of the considered scheme is calculation of derivatives that ensures approximation even near electromagnetic properties discontinuity. Numerical tests confirm the second order of approximation of the proposed scheme for cases of linear and curvilinear discontinuities.
KeywordsMaxwell’s equations finite volume Godunov scheme discontinuous permittivity discontinuous permeability second order
Unable to display preview. Download preview PDF.
- 2.Godunov, S.K.: A Difference Scheme for Numerical Solution of Discontinuos Solution of Hydrodynamic Equations. Math. Sbornik 47, 271–306 (1959)Google Scholar
- 4.Ismagilov, T.Z.: Parallel Algorithm for Numerical Solution of Three-dimensional Maxwell’s Equations with Discontinuous Dielectric Permittivity on Tetrahedral Meshes (In Russian). USATU Vestnik 14, 152–159 (2010)Google Scholar
- 5.Ismagilov, T.Z., Gorbachev, A.I.: Parallel Algorithm for Numerical Solution of Three-dimensional Maxwell’s Equations with Discontinuous Dielectric Permittivity on Prismatic Meshes (in Russian). Comp. Meth. and Progr. 12, 128–136 (2011)Google Scholar
- 8.Lebedev, A.S., Fedoruk, M.P., Shtyrina, O.V.: Finite-Volume Algorithm for Solving the Time-Dependent Maxwell Equations on Unstructured Meshes. Comp. Math. and Math. Phys. 47, 1286–1301 (2006)Google Scholar
- 10.Shankar, V., Hall, W.F., Mohammadian, A.H.: A CFD-based Finite-Volume Procedure for Computational Electromagnetics - Interdisciplinary Applications of CFD Methods. AIAA A89-41776 18-02, 551–564 (1989)Google Scholar
- 12.Sullivan, D.M.: Electromagnetic Simulation Using the Finite-Difference Time-Domain Method. Wiley-IEEE Press (2000)Google Scholar
- 15.Yee, K.S.: Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media. IEEE Trans. Antennas Propagat. 14, 585–589 (1966)Google Scholar