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The Splitting High Order Finite-Difference Time-Domain Methods for Maxwell’s Equations in Two Dimensions

Author: ShiWenHui
Tutor: GaoLiPing
School: Shandong Normal University
Course: Computational Mathematics
Keywords: MaXwell equation Grate splitting energy Conservative Finite Difference Time Domain (FDTD) Unconditional stability Higher Order Differential Symmetrical division Numerical dispersion
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 42
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Abstract

This paper studies the Maxwell equations with operator splitting finite difference method and numerical simulation methods with symmetric first order differential operator splitting method [31] combined in a previous study based on a high-dimensional Maxwell equations symmetric splitting finite difference time domain (high ss-FDTD) method, construct a numerical format, the Fourier method is straightforward format unconditional stability analysis of the numerical dispersion error and verified through numerical examples and symmetry of three-dimensional Maxwell equations splitting finite difference time domain method (ss-FDTD) gives a new energy model analysis to derive energy identities, and through numerical examples further proof of this format in the discrete and H1 is under conservation of energy: The full text The first chapter is divided into three chapters introductory section describes the research background and significance of research questions are given a model equation describes the kind commonly used numerical methods and thesis research methods utilize split second chapter skills and electromagnetic fields the symmetry of the combined fourth-order central difference method proposed order Symmetry splitting finite difference time domain format (H0 one ss-FDTD), analyzed the solvability format application format given solution step by inferring this format equivalent format, found H0 one ss-FDTD format asked about the second foot, the foot four bands of space, therefore, H0 one ss-FDTD format is a (2,4) form and, with R = Jurier method to analyze the H0 one ss-FDTD numerical dispersion properties formats deduced numerical dispersion relation, proved that this scheme is unconditionally stable growth factors through the analysis, we found that high ss-FDTD format non-dissipative (n. n-dissipative) for a more intuitive understanding of the ss-FDTD format H0 growth factors, we have shown by M Soft lab growth factors in different circumstances trend mode verified H0 format is also an unconditional ss-FDTD stable, and with c-N format to compare numerical dispersion error last detail near the border point at discrete equation methods and formats, this part is the application of high-order difference is too much trouble to solve practical problems where the third chapter Consider a zero-dimensional conductivity of Maxwell's equations symmetric splitting finite-difference time-domain (ss-FDTD) method of energy conservation of energy through new methods and the role of the differential operator бX.бY.бZ after format, for the first time gives the r values approximation scheme ss-FDTD in discrete energy conservation under the H1 model type, and proved the date format in the discrete model under H1 conservation, numerical examples verify the format of the energy conservation solutions

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