An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case

Journal of Computational Physics

Volumn 190, Issue 1, 2003, Pages 159-183

  Cai, Wei ^a   Deng, Shaozhong ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Cartesian grid methods; Electromagnetic scattering; Finite difference time domain method

Indexed keywords

ELECTROMAGNETIC WAVE SCATTERING; INTERFACES (MATERIALS); MAXWELL EQUATIONS; NUMERICAL METHODS; WAVE EQUATIONS;

CARTESIAN GRID METHODS; CENTRAL DIFFERENCE SCHEME; ELECTROMAGNETIC SCATTERING; EMBEDDED BOUNDARY METHODS; FINITE-DIFFERENCE METHODS; JUMP CONDITIONS; MATERIAL INTERFACES; SECOND ORDERS; TIME-DEPENDENT MAXWELL'S EQUATIONS; UPWINDING;

FINITE DIFFERENCE TIME DOMAIN METHOD;

EID: 0042858321     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00269-9     Document Type: Article

References (21)

1. A. Taflove, Computational Electrodynamics - The Finite Difference Time-Domain Method, Artech House, Boston, 1995.
2. R.F. Harrington, Field Computation by Moment Methods, Macmillian, New York, 1968.
3. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media, IEEE Trans. Antenn. Propag. 14 (1966) 302.
4. A. Ditkowski, K. Dridi, J.S. Hesthaven, Convergent Cartesian grid methods for Maxwell's equations in complex geometries, J. Comput. Phys. 170 (2001) 39.
5. B. Cockburn, C.W. Shu, The local discontinuous Galerkin finite element method for convection-diffusion systems, SIAM J. Numer. Anal. 35 (1998) 2440.
6. P. LeSaint, P.A. Raviart, On a finite element method for solving the neutron transport equation, in: C. De Boor (Ed.), Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York, 1974, p. 89.
7. D. Kopriva, S.L. Woodruff, M.Y. Hussaini, Discontinuous spectral element approximation of Maxwell's equations, in: B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Springer, New York, 2000, p. 355.
8. T. Warburton, Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic hp-finite elements, in: B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Springer, New York, 2000, p. 451.
9. M.J. Berger, R.J. LeVeque, Adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries, AIAA paper 89-1930, June, 1989.
10. H. Forrer, M.J. Berger, Flow simulations on Cartesian grid involving complex moving geometries, in: Proceedings of the International Conference on Hyperbolic Problems, Zurich, Switzerland, February, 1998.
11. R.J. LeVeque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019.
12. C. Zhang, R.J. LeVeque, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion 25 (1997) 237.
13. R.E. Collin, Field Theory of Guided Waves, IEEE Press, New York, 1991.
14. Z. Zhang, Ultraconvergence of the patched recovery technique II, Math. Comp. 69 (2000) 141.
15. J.P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185.
16. R. Ziolkowski, Time derivative Lorentz model based absorbing boundary condition, IEEE Trans. Antenn. Propag. 45 (1997) 1530.
17. S. Abarbanel, D. Gottlieb, On the construction and analysis of absorbing layers in CEM, Appl. Numer. Math. 27 (1998) 331.
18. P. Lorrain, D. Corson, F. Lorrain, Electromagnetics Fields and Waves, W.H. Freeman and Company, New York, 1988.
19. K. Umashankar, A. Taflove, Computational Electrodynamics, Artech House, Boston, 1993.
20. B. Gustafsson, H.O. Kreiss, A. Sundstrom, Stability theory of difference approximations for mixed initial boundary value problems II, Math. Comput. 26 (1972) 649.
21. J. Strikewerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole, 1989.