Development of an explicit FDTD scheme with optimized dispersion relation equation for solving Maxwell's equations
Date Issued
2011
Date
2011
Author(s)
Liang, Lun-Yu
Abstract
In this thesis an explicit FDTD scheme was developed with the optimized dispersion relation equation for solving the Maxwell''s equations. Consider an isotropic, homogeneous, linear and nondispersive medium, to accommodate the Hamiltonian structure in the Maxwell''s equations, the time integrator employed in the current semi-discretization needs to fall into the explicit symplectic category. Discretization of Maxwell''s equations using the explicit Symplectic time integrator in non-staggered grids, one- and two-dimensional dispersion relation equations (DRE) were developed first, and then using the DRE property to preserve wave propagation character by using the concept of group velocity.
Application of the explicit Symplectic-DREP FDTD method to solve the Maxwell''s equations involving scatters will be verified by solving the problem in two-dimensions that is amenable to exact solutions. Results with good rates of convergence are demonstrated for the problem. For the simulation of wave problems on an open region, in this thesis the uniaxial Perfectly matched layer (UPML), Total-Field-Scattered-Field (TF/SF) and level set methods are employed for solving the scattering problems, including the two-dimensional incident wave for TM-mode Mie scattering problem, and the PC-based L-shaped waveguide problem. The results simulated from the proposed method agree well with other numerical and experimental results for the chosen problems.
Subjects
non-staggered grids
dispersion relation equation
explicit Sympletic
Type
thesis
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