Improved Version of the Second-Order Mur Absorbing Boundary Condition Based on a Nonstandard Finite Difference Model
Keywords:
Improved Version of the Second-Order Mur Absorbing Boundary Condition Based on a Nonstandard Finite Difference ModelAbstract
It is often necessary to terminate the computational domain of an FDTD calculation with an absorbing boundary condition (ABC). The Perfectly Matched Layer (PML) is an excellent ABC, but it is complicated and costly. Typically at least 8 layers are needed to give satisfactory absorption. Thus in a 1003 domain less than 843 or 59% of the grid points are usable. The second-order Mur ABC requires just 2 layers, but its absorption is inadequate for many problems. In this paper we introduce an improved version of the secondorder Mur ABC based on a nonstandard finite difference (NSFD) model which has the same low computational cost but with much better absorption on a coarse grid.
Downloads
References
G. Mur, “Absorbing boundary conditions for the
finite-difference approximation of the time domain
electromagnetic field equations,” IEEE Transactions
on Electromagnetic Compatibility, vol. 23, pp. 377-
, 1981.
A. Taflove and S. C. Hagness, “Computational
electrodynamics: the finite-difference time-domain
method. norwood,” Artech House, Inc., Norwood,
MA, 2000.
B. Engquist and A. Majda, “Absorbing boundary
conditions for the numerical simulation of waves,”
Mathematics of Computation, vol. 31, pp. 629-651,
R. E. Mickens, “Nonstandard finite difference
models of differential equations,” World Scientific,
Singapore, 1994.
S. K. Godunov, “Difference Schemes,” North-
Holland, Amsterdam, 1987.
J. B. Cole, “High accuracy Yee algorithm based on
nonstandard finite differences: new developments
and verifications”, IEEE Trans. Antennas and
Propagation, vol. 50, no. 9, pp. 1185-1191, Sept.
J. B. Cole, “High accuracy nonstandard finite-
difference time-domain algorithms for
computational electromagnetics: applications to
optics and photonics,” Chapter 4, pp. 89-109 in
Advances in the Applications of Nonstandard Finite
Difference Schemes, R. E. Mickens, ed., Scientific,
Singapore, 2005.
T. G. Moore, J. G. Blaschak, A. Taflove, and G. A.
Kriegsmann, “Theory and application of radiation
boundary operators,” IEEE Trans. Antennas and
Propagation, vol. 36, pp. 1797-1812, 1988.
