An upwinding boundary condition capturing method for Maxwell's equations in media with material interfaces

Journal of Computational Physics

Volumn 225, Issue 1, 2007, Pages 342-362

  Xue, Changfeng ^a,b   Deng, Shaozhong ^c  

^a YANCHENG INSTITUTE OF TECHNOLOGY   (China)

^b Peking University   (China)

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

Author keywords

Finite difference time domain method; Ghost fluid method; Maxwell's equations

Indexed keywords

BOUNDARY CONDITIONS; CIRCULAR CYLINDERS; FINITE DIFFERENCE TIME DOMAIN METHOD; INTERFACES (MATERIALS); NUMERICAL METHODS; WAVE EQUATIONS;

CARTESIAN GRID; CENTRAL FINITE DIFFERENCE; FINITE DIFFERENCE SCHEME; GHOST FLUID METHOD; JUMP CONDITIONS; MATERIAL INTERFACES; PROPERTY; SECOND ORDERS; TIME-DOMAIN MAXWELL EQUATIONS; UPWINDING;

MAXWELL EQUATIONS;

EID: 34447260291     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.12.001     Document Type: Article

References (41)

1. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media. IEEE Trans. Antennas Propagat. 14 3 (1966) 302-307
2. Taflove A., and Hagness S.C. Computational Electrodynamics: The Finite-Difference Time-Domain Method. third ed. (2005), Artech House, Boston
3. Monk P., and Suli E. Error estimates of Yee's method on nonuniform grids. IEEE Trans. Magn. 30 5 (1994) 3200-3203
4. Ditkowski A., Dridi K., and Hesthaven J.S. Convergent Cartesian grid methods for Maxwell's equations in complex geometries. J. Comput. Phys. 170 5 (2001) 39-80
5. A. Ditkowski, J.S. Hesthaven, C.H. Teng, Modeling dielectric interfaces in the FDTD-method: a comparative study, in: 2000 Progress in Electromagnetics Research (PIERS 2000) Proceedings, Cambridge, MA, July 5-14, 2000.
6. Xiao T., and Liu Q.H. A staggered upwind embedded boundary method to eliminate the FDTD staircasing error. IEEE Trans. Antennas Propagat. 52 3 (2004) 730-741
7. Hesthaven J.S. High-order accurate methods in time-domain computational electromagnetics. A review. Adv. Imag. Electron Phys. 127 (2003) 59-117
8. 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
9. Yefet A., and Turkel E. Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients. Appl. Numer. Math. 33 1 (2000) 125-134
10. Xie Z.Q., Chan C.H., and Zhang B. An explicit fourth order staggered finite-difference time-domain method for Maxwell's equations. J. Comput. Appl. Math. 147 1 (2002) 75-98
11. Xie Z.Q., Chan C.H., and Zhang B. An explicit fourth order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations. J. Comput. Phys. 175 2 (2002) 739-763
12. Zhao S., and Wei G.W. High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces. J. Comput. Phys. 200 1 (2004) 60-103
13. Cai W., and Deng S. An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case. J. Comput. Phys. 190 1 (2003) 159-183
14. Berger M.J., Helzel C., and LeVeque R.J. h-box methods for the approximation of hyperbolic conservation laws on irregular grids. SIAM J. Numer. Anal. 41 3 (2003) 893-918
15. Bell J.B., Collella P., Crutchfield W.Y., and Welcome M. An adaptive Cartesian grid method for unsteady compressible flow in irregular regions. J. Comput. Phys. 120 2 (1995) 278-304
16. Zhang C., and LeVeque R.J. The immersed interface method for acoustic wave equations with discontinuous coefficients. Wave Motion 25 3 (1997) 237-263
17. Fedkiw R., Aslam T., Merriman B., and Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152 2 (1999) 457-492
18. Fedkiw R., Aslam T., and Xu S. The ghost fluid method for deflagration and detonation discontinuities. J. Comput. Phys. 154 2 (1999) 393-427
19. Liu X.D., Fedkiw R., and Kang M. A boundary condition capturing method for Poisson's equation on irregular domains. J. Comput. Phys. 160 1 (2000) 151-178
20. Kang M., Fedkiw R., and Liu X.D. A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15 3 (2000) 323-360
21. Nguyen D., Fedkiw R., and Kang M. A boundary condition capturing method for incompressible flame discontinuities. J. Comput. Phys. 172 1 (2001) 71-98
22. Gibou F., Fedkiw R., Cheng L.T., and Kang M. A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. J. Comput. Phys. 176 1 (2002) 205-227
23. Gibou F., and Fedkiw R. A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem. J. Comput. Phys. 202 2 (2005) 577-601
24. Hu X.Y., and Khoo B.C. An interface interaction method for compressible multifluids. J. Comput. Phys. 198 1 (2004) 35-64
25. Lombard B., and Piraux J. Numerical treatment of two-dimensional interfaces for acoustic and elastic waves. J. Comput. Phys. 195 1 (2004) 90-116
26. Yokoia K., Xiao F., Liu H., and Fukasaku K. Three-dimensional numerical simulation of flows with complex geometries in a regular Cartesian grid and its application to blood flow in cerebral artery with multiple aneurysms. J. Comput. Phys. 202 1 (2005) 1-19
27. Kreiss H.O., Petersson N.A., and Yström J. Difference approximations for the second order wave equation. SIAM J. Numer. Anal. 40 5 (2002) 1940-1967
28. Kreiss H.O., and Petersson N.A. A second order accurate embedded boundary method for the wave equation with Dirichlet data. SIAM J. Sci. Comput. 27 4 (2006) 1141-1167
29. Kreiss H.O., Petersson N.A., and Yström J. Difference approximations of the Neumann problem for the second order wave equation. SIAM J. Numer. Anal. 42 2 (2004) 1292-1323
30. H.O. Kreiss, N.A. Petersson, An embedded boundary method for the wave equation with discontinuous coefficients, UCRL-JRNL 215702, Lawrence Livermore National Lab, 2005.
31. Aslam T. A partial differential equation approach to multidimensional extrapolation. J. Comput. Phys. 193 1 (2003) 349-355
32. Gustafsson G. The convergence rate for difference approximations to mixed initial boundary value problems. Math. Comput. 29 (1975) 396-406
33. Gustafsson G. The convergence rate for difference approximations to general mixed initial boundary value problems. SIAM J. Numer. Anal. 18 2 (1981) 179-190
34. Kreiss H.O. Stability theory for difference approximations of mixed initial boundary value problems I. Math. Comput. 22 (1968) 703-714
35. Gustafsson B., Kreiss H.O., and Sundstrom A. Stability theory of difference approximations for mixed initial boundary value problems II. Math. Comput. 26 (1972) 649-686
36. Strikewerda J. Finite Difference Schemes and Partial Differential Equations (1989), Wadsworth and Brooks/Cole
37. Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 2 (1994) 185-200
38. Ziolkowski R. Time derivative Lorentz model based absorbing boundary condition. IEEE Trans. Antennas Propagat. 45 10 (1997) 1530-1535
39. Abarbanel S., and Gottlieb D. On the construction and analysis of absorbing layers in CEM. Appl. Numer. Math. 27 4 (1998) 331-340
40. Lorrain P., Corson D., and Lorrain F. Electromagnetics Fields and Waves (1988), Freeman, New York
41. Umashankar K., and Taflove A. Computational Electrodynamics (1993), Artech House, Boston