Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the /spl Delta/t time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to /spl Delta/t, and as such, increasing /spl Delta/t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.

[1]  A. Zhao.  The influence of the time step on the numerical dispersion error of an unconditionally stable 3‐D ADI‐FDTD method: A simple and unified approach to determine the maximum allowable time step required by a desired numerical dispersion accuracy , 2002 .

[2]  Christopher L. Holloway,et al.  Time-domain modeling, characterization, and measurements of anechoic and semi-anechoic electromagnetic test chambers , 2002 .

[3]  A. Scarlatti,et al.  An equivalent transmission-line model containing dispersion for high-speed digital lines-with an FDTD implementation , 2001 .

[4]  Zhizhang Chen,et al.  Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method , 2001 .

[5]  Fenghua Zhen,et al.  Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method , 2000 .

[6]  Zhizhang Chen,et al.  A finite-difference time-domain method without the Courant stability conditions , 1999 .

[7]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[8]  T. Namiki,et al.  A new FDTD algorithm free from the CFL condition restraint for a 2D-TE wave , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[9]  Christopher L. Holloway,et al.  Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices , 1997 .

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

[11]  Patrick Joly,et al.  Construction and Analysis of Fourth-Order Finite Difference Schemes for the Acoustic Wave Equation in Nonhomogeneous Media , 1996 .

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

[13]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[14]  J. Faires.  Numerical Analysis , 1981 .

[15]  A. Taflove,et al.  Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations , 1975 .

[16]  Dennis M. Sullivan,et al.  Z-transform theory and the FDTD method , 1996 .

[17]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[18]  A. Iserles,et al.  A first course in the numerical analysis of differential equations , 1996 .

[19]  S.,et al.  Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media , 1966 .

[20]  G. Hedstrom,et al.  Numerical Solution of Partial Differential Equations , 1965 .