Characteristic Based Methods For The Time Domain Maxwell Equations

Characteristic Based Methods for the Time-domain Maxwell Equations

Numerical procedures for solving the time-domain Maxwell equations based on the theory of characteristics were successfully developed. Both explicit and implicit methods were formulated by the time-central and spatial-windward algorithm to better describe wave motion. A new trapezoidal consistent implicit scheme was shown to be unconditionally stable for the linear initial value system and was able to generate numerical solutions comparable to those of the established explicit method. The formulation of the three-dimensional system including generalized coordinate system was completed but not explored. The present 2-D results on Cartesian frame demonstrated a potential for numerical efficiency improvement. Time-domain Maxwell equation, Trapezoidal consistent implicit scheme, Cartesian frame.

An implicit characteristic based method for electromagnetics

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both u iform and nonuniform grids. The explicit FDTD algorithm is used as a convenient reference algorithm for comparison.