A Fourth Order Difference Scheme for the Maxwell Equations on Yee Grid
- ORNL
The Maxwell equations are solved by a long-stencil fourth order finite difference method over a Yee grid, in which different physical variables are located at staggered mesh points. A careful treatment of the numerical values near the boundary is introduced, which in turn leads to a 'symmetric image' formula at the 'ghost' grid points. Such a symmetric formula assures the stability of the boundary extrapolation. In turn, the fourth order discrete curl operator for the electric and magnetic vectors gives a complete set of eigenvalues in the purely imaginary axis. To advance the dynamic equations, the four-stage Runge-Kutta method is utilized, which results in a full fourth order accuracy in both time and space. A stability constraint for the time step is formulated at both the theoretical and numerical levels, using an argument of stability domain. An accuracy check is presented to verify the fourth order precision, using a comparison between exact solution and numerical solutions at a fixed final time. In addition, some numerical simulations of a loss-less rectangular cavity are also carried out and the frequency is measured precisely.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Spallation Neutron Source (SNS)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 939665
- Journal Information:
- Journal of Hyperbolic Differential Equations, Vol. 5, Issue 3
- Country of Publication:
- United States
- Language:
- English
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