Dispersion-relation-preserving FDTD algorithms for large-scale three-dimensional problems

We introduce dispersion-relation-preserving (DRP) algorithms to minimize the numerical dispersion error in large-scale three-dimensional (3D) finite-difference time-domain (FDTD) simulations. The dispersion error is first expanded in spherical harmonics in terms of the propagation angle and the leading order terms of the series are made equal to zero. Frequency-dependent FDTD coefficients are then obtained and subsequently expanded in a polynomial (Taylor) series in the frequency variable. An inverse Fourier transformation is used to allow for the incorporation of the new coefficients into the FDTD updates. Butterworth or Chebyshev filters are subsequently employed to fine-tune the FDTD coefficients for a given narrowband or broadband range of frequencies of interest. Numerical results are used to compare the proposed 3D DRP-FDTD schemes against traditional high-order FDTD schemes.

[1]  J. B. Cole.  A high accuracy FDTD algorithm to solve microwave propagation and scattering problems on a coarse grid , 1995 .

[2]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[3]  W. Chew,et al.  Lattice electromagnetic theory from a topological viewpointa ... , 1998 .

[4]  Melinda Piket-May,et al.  A modified FDTD (2, 4) scheme for modeling electrically large structures with high-phase accuracy , 1997 .

[5]  W. Tabbara,et al.  A fourth order scheme for the FDTD algorithm applied to Maxwell's equations , 1992, IEEE Antennas and Propagation Society International Symposium 1992 Digest.

[6]  J. M. Sanz-Serna,et al.  High-order methods , 1994 .

[7]  E.A. Forgy,et al.  A new FDTD formulation with reduced dispersion for the simulation of wave propagation through inhomogeneous media , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[8]  J. B. Cole.  A high-accuracy realization of the Yee algorithm using non-standard finite differences , 1997 .

[9]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[10]  Boaz Porat,et al.  A course in digital signal processing , 1996 .

[11]  K. Shlager,et al.  Relative accuracy of several low-dispersion finite-difference time-domain schemes , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[12]  Andrew F. Peterson,et al.  Relative accuracy of several finite-difference time-domain methods in two and three dimensions , 1993 .

[13]  W. Chew,et al.  Lattice electromagnetic theory from a topological viewpoint , 1999 .

[14]  L. Trefethen.  Group velocity in finite difference schemes , 1981 .

[15]  Robert J. Lee,et al.  On the Accuracy of Numerical Wave Simulations Based on Finite Methods , 1992 .

[16]  Patrick Joly,et al.  Fourth order schemes for the heterogeneous acoustics equation , 1990 .

[17]  R. J. Joseph,et al.  Advances in Computational Electrodynamics: The Finite - Di erence Time - Domain Method , 1998 .

[18]  Robert J. Lee,et al.  Reducing the phase error for finite-difference methods without increasing the order , 1998 .

[19]  Thomas Weiland,et al.  On the Unique Numerical Solution of Maxwellian Eigenvalue Problems in Three-dimensions , 1984 .