A comparative study of characteristic-based algorithms for the Maxwell Equations
Characteristic-based finite-difference and finite-volume schemes have been developed for solving the three-dimensional Maxwell equations in the time domain. A detailed eigenvector analysis for the Maxwell equations in a general curvilinear coordinate has also been completed to provide a basic framework for future finite-difference schemes. Although the basic concepts of the two algorithms are identical, the detailed formulations are vastly different for achieving split flux vectors according to the sign of the eigenvalues. A comparative study of these algorithms applied to an oscillating electric dipole is carried out to assess their relative merit for further development. In spherical coordinates, second-order windward numerical simulations of the radiating phenomenon are closely comparable in terms of accuracy and efficiency. These methods also demonstrate an ability to suppress reflected waves from the truncated boundary by a simple compatibility condition. © 1996 Academic Press, Inc.
Journal of Computational Physics
Shang, J. S. and Fithen, R. M. (1996). A comparative study of characteristic-based algorithms for the Maxwell Equations. Journal of Computational Physics 125(2): 378–394. DOI:https://doi.org/10.1006/jcph.1996.0100