Sakkaplangkul, Puttha
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Item type:Publication, Convergence analysis of yee-fdtd schemes for 3d maxwell’s equations in linear dispersive media(2021-01-01); Bokil, Vrushali A.In this paper, we develop and analyze finite difference methods for the 3D Maxwell’s equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Convergence analysis of operator splitting methods for Maxwell’s equations in dispersive media of Debye type(2023-12-01)In this paper, two new effective operator splitting methods (SS-MD and SM-MD) for the Maxwell’s equations for dispersive media in two dimensions transverse electric polarization (the 2D Maxwell–Debye TE model) are presented and analyzed. The splitting schemes consist of two sub-stages in each time step, each of which requires solving a number of 1D discrete sub-problems. The Crank–Nicolson approach is used to solve each sub-problem’s time discretization. Both splitting methods satisfy the energy decay and are unconditionally stable. The convergence result of the SS-MD scheme is shown to be of first order in time and of second order in space based on the energy technique, whereas the SM-MD scheme is of second order in both time and space. We also analyze numerical dispersion analysis to obtain two identities of the discrete numerical dispersion relations of both splitting schemes. Examples and numerical experiments are provided to demonstrate and support our theoretical results.