The effect of the 2-D Laplacian operator approximation on the performance of finite-difference time-domain schemes for Maxwell's equations

Journal of Computational Physics

Volumn 227, Issue 1, 2007, Pages 513-536

  Panaretos, Anastasios H ^a   Aberle, James T ^a   Díaz, Rodolfo E ^a  

^a Arizona State University   (United States)

Author keywords

Curl operator; Electromagnetics; Finite difference time domain method; Laplacian operator

Indexed keywords

APPROXIMATION ALGORITHMS; LAPLACE EQUATION; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS;

CURL OPERATOR; ELECTROMAGNETICS; FINITE-DIFFERENCE TIME-DOMAIN SCHEMES; ISOTROPICS; LAPLACIAN OPERATOR; LAPLACIANS; PERFORMANCE; TWO DIMENSIONAL SPACES; TWO-DIMENSIONAL; YEE ALGORITHM;

FINITE DIFFERENCE TIME DOMAIN METHOD;

EID: 35348816785     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.08.019     Document Type: Article

References (39)

1. J. Fang, Time domain finite difference computation for Maxwell's equations, Ph.D. thesis, University of California at Berkeley, Berkeley, CA, 1989.
2. Yefet A., and Petropoulos P.G. A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. J. Comput. Phys. 168 2 (2001) 286-315
3. Zygiridis T.T., and Tsiboukis T.D. Low-dispersion algorithms based on the higher order (2, 4) FDTD method. IEEE Trans. Microwave Theory Tech. 52 4 (2004) 1321-1327
4. Sun G., and Trueman C.W. Optimized finite-difference time-domain methods based on the (2, 4) stencil. IEEE Trans. Microwave Theory Tech. 53 3 (2005) 832-842
5. Hadi M.F., and Piket-May M. A modified FDTD (2, 4) scheme for modeling electrically large structures with high-phase accuracy. IEEE Trans. Antennas Propagat. 45 2 (1997) 254-264
6. Young J.L., Gaitonde D., and Shang J.S. Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach. IEEE Trans. Antennas Propagat. 45 11 (1997) 1573-1580
7. Lele S.K. Compact finite difference schemes with spectral resolution. J. Comput. Phys. 101 (1992) 16-42
8. Liu Y. Fourier analysis of numerical algorithms for the Maxwell equations. J. Comput. Phys. 124 (1996) 396-416
9. Xiao F., Tang X., and Zhang X. The construction of low-dispersive FDTD on hexagon. IEEE Trans. Antennas Propagat. 53 11 (2005) 3697-3703
10. Juntunen J.S., and Tsiboukis T.D. Reduction of numerical dispersion in FDTD method through artificial anisotropy. IEEE Trans. Microwave Theory Tech. 48 4 (2000) 582-588
11. Wang S., and Teixeira F.L. A finite-difference time-domain algorithm optimized for arbitrary propagation angles. IEEE Trans. Antennas Propagat. 51 9 (2003) 2456-2463
12. Wang S., and Teixeira F.L. Dispersion-relation-preserving FDTD algorithms for large-scale three-dimensional problems. IEEE Trans. Antennas Propagat. 51 8 (2003) 1818-1828
13. Wang S., and Teixeira F.L. A three-dimensional angle-optimized finite-difference time-domain algorithm. IEEE Trans. Microwave Theory Tech. 51 3 (2003) 811-817
14. Wang S., and Teixeira F.L. Grid-dispersion error reduction for broadband FDTD electromagnetic simulations. IEEE Trans. Magn. 40 2 (2004) 1440-1443
15. Wang S., and Teixeira F.L. Lattice models for large-scale simulations of coherent wave scattering. Phys. Rev. E 69 (2004)
16. Shlager K.L., and Schneider J.B. Comparison of the dispersion properties of several low-dispersion finite-difference time-domain algorithms. IEEE Trans. Antennas Propagat. 51 3 (2003) 642-653
17. Finkelstein B., and Kastner R. Finite difference time domain dispersion reduction schemes. J. Comput. Phys. 221 1 (2007) 422-438
18. Liu Q.H. The PSTD algorithm: a time-domain method requiring only two cells per wavelength. Microwave Opt. Technol. Lett. 15 3 (1997) 158-165
19. Liu Q.H. Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm. IEEE Trans. Geosci. Remote Sens. 37 2 (1999) 917-926
20. Liu Q.H., and Zhao G. Review of PSTD methods for transient electromagnetics. Int. J. Numer. Model. 17 3 (2004) 99-323
21. Hesthaven J.S. High-order accurate methods in time-domain computational electromagnetics: a review. Adv. Imag. Elect. Phys. 127 (2003) 59-123
22. Kantartzis N.V., and Tsiboukis T.D. Higher-order FDTD Schemes for Waveguide and Antenna Structures (2006), Morgan & Claypool, San Rafel, CA
23. Kantartzis N.V., and Tsiboukis T.D. A higher order nonstandard FDTD-PML method for the advanced modeling of complex EMC problems in generalized 3-D curvilinear coordinates. IEEE Trans. Electromagn. Compat. 46 1 (2004) 2-11
24. Kantartzis N.V., and Tsiboukis T.D. A generalized methodology based on higher-order conventional and non-standard FDTD concepts for the systematic development of enhanced dispersionless wide-angle absorbing perfectly matched layers. Int. J. Numer. Model. 13 5 (2000) 417-440
25. Panaretos A.H., Aberle J.T., and Díaz R.E. A three-dimensional finite-difference time-domain scheme based on a transversely extended curl operator. IEEE Trans. Microwave Theory Tech. 54 12 (2006) 4237-4246
26. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propagat. 14 8 (1966) 302-307
27. Taflove A.T., and Hagness S.C. Computational Electrodynamics: The Finite-Difference Time-Domain Method. second ed. (2000), Artech House
28. Kunz K.S., and Luebbers R.J. The Finite Difference Time Domain Method for Electromagnetics (1993), CRC Press
29. Patra M., and Karttunen M. Stencils with isotropic discretization error for differential operators. Numer. Methods Part. Diff. Equ. 22 4 (2006) 936-953
30. Cohen G.H. Higher-order Numerical Methods for Transient Wave Equations (2002), Springer
31. E.A. Forgy, A time-domain method for computational electromagnetics with isotropic numerical dispersion on an overlapped lattice, Master's thesis, University of Illinois at Urbana, Champaign, 1998.
32. Bi Z., Wu K., Wu C., and Litva J. A new finite-difference time-domain algorithm for solving Maxwell's equations. IEEE Microwave Guided Wave Lett. 1 12 (1991) 382-384
33. Min M.S., and Teng C.H. The instability of the Yee scheme for the magic time step. J. Comput. Phys. 166 (2001) 418-424
34. Ray S.L. Grid decoupling in finite element solutions of Maxwell's equations. IEEE Trans. Antennas Propagat. 40 4 (1992) 443-445
35. Forgy E.A., and Chew W.C. A time-domain method with isotropic dispersion and increased stability on an overlapped lattice. IEEE Trans. Antennas Propagat. 50 7 (2002) 983-996
36. Celuch-Marcysiak M., and Gwarek W.K. On the nature of solutions produced by finite difference schemes in the time domain. Int. J. Numer. Model. 12 (1999) 23-40
37. Koh I.S., Kim H., Lee J.M., Yook J.G., and Pil C.S. Novel explicit 2-D FDTD scheme with isotropic dispersion and enhanced stability. IEEE Trans. Antennas Propagat. 54 11 (2006) 3505-3510
38. Collatz L. The Numerical Treatment of Differential Equations. third ed. (1966), Springer-Verlag
39. G. Cohen, A class of schemes, fourth order in space and time, for the 2D wave equation, in: Proceedings of the Sixth IMACS Intenational Symposium on Computer Methods for Partial Differential Equations, Bethlehem, PA, USA, 1987, pp. 23-27.