A split step approach for the 3-D Maxwell's equations

Journal of Computational and Applied Mathematics

Volumn 158, Issue 2, 2003, Pages 485-505

  Lee, Jongwoo ^a   Fornberg, Bengt ^b  

^a Kwangwoon University   (South Korea)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

FDTD; Maxwell's equations; Split step

Indexed keywords

HAMILTONIANS; NONLINEAR EQUATIONS; WAVE EQUATIONS;

SPLIT-STEP APPROACHES;

MAXWELL EQUATIONS;

MATHEMATICAL METHOD;

EID: 0141849302     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00484-9     Document Type: Article

References (18)

1. Forest E. Ruth R.D. Fourth order symplectic integration Phys. D 43 1990 105-117
2. Fornberg B. A Practical Guide to Pseudospectral Methods Cambridge Monographs on Applied and Computational Mathematics Vol. 1 1996 Cambridge University Press Cambridge, UK
3. Fornberg B. Driscoll T.A. A fast spectral algorithm for nonlinear wave equations with linear dispersion J. Comput. Phys. 155 1999 456-467
4. J. Lee, B. Fornberg, Some unconditionally stable time stepping methods for the 3-D Maxwell's equations, J. Comput. Appl. Math., submitted.
5. McLachlan R. Symplectic integration of Hamiltonian wave equations Numer. Math. 66 1994 465-492
6. Namiki T. A new FDTD algorithm based on alternating-direction implicit method IEEE Trans. Microwave Theory Technol. 47 1999 2003-2007
7. F. Neri, Lie algebras and canonical integration, Dept. of Physics, University of Maryland, Preprint, 1987.
8. Okunbor D.I. Skeel R.D. Canonical Runge-Kutta-Nyström methods of order five and six J. Comput. Appl. Math. 51 1994 375-382
9. Pereyra V. Accelerating the convergence of discretization algorithm SIAM J. Numer. Anal. 4 1967 508-532
10. Richardson L. The deferred approach to the limit Philos. Trans. A 226 1927 299-349
11. Sanz-Serna J.M. Calvo M.P. Numerical Hamiltonian Problems 1994 Chapman - Hall London, UK
12. Strang G. On construction and comparison of difference schemes SIAM J. Numer. Anal. 5 1968 506-516
13. Suzuki M. General theory of fractal path integrals with applications to many-body theories and statistical physics J. Math. Phys. 32 1991 400-407
14. Taflove A. Hagness S. Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd Edition 2000 Artech House Boston, MA
15. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media IEEE Trans. Antennas and Propagation 14 1966 302-307
16. Yoshida H. Construction of higher order symplectic integrators Phys. Lett. A 150 1990 262-268
17. Yoshida H. Recent progress in the theory and application of symplectic integrators Celestial Mech. Dynamics Astronom. 56 1993 27-43
18. Zheng F. Chen Z. Zhang J. Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method IEEE Trans. Microwave Theory Technol. 48 2000 1550-1558