Abstract
The convergence of the iterative ADI-FDTD method proposed by Wang et al. [S. Wang, F. Teixeira, J. Chen, An iterative ADI-FDTD with reduced splitting error, IEEE Microwave Wireless Comp. Lett. 15 (2005) 1531-1533] towards the classical implicit Crank-Nicolson scheme when applied to Maxwell curl equations, and the accuracy, stability, and dispersion properties of the resulting iterated schemes are investigated. The iterated schemes are shown both mathematically and numerically to be unconditionally stable for 2D wave problems, in agreement with numerical experiments conducted in [S. Wang, F. Teixeira, J. Chen, An iterative ADI-FDTD with reduced splitting error, IEEE Microwave Wireless Comp. Lett. 15 (2005) 1531-1533]. However these schemes lose their unconditional stability when applied to full 3D wave problems where TE and TM modes do not decouple, as illustrated by numerical experiments in a PEC box.
Original language | English (US) |
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Pages (from-to) | 9-27 |
Number of pages | 19 |
Journal | Journal of Computational Physics |
Volume | 222 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 2007 |
Keywords
- Alternate direction implicit scheme
- Dispersion relation
- Finite difference time domain
- Fixed-point iteration
- Iterated scheme
- Unconditional stability
- von Neumann stability
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics