Convergence analysis of a finite volume method for Maxwell's equations in nonhomogeneous media

SIAM Journal on Numerical Analysis

Volumn 41, Issue 1, 2003, Pages 37-63

  Chung, Eric T ^a   Du, Qiang ^b,c   Zou, Jun ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^d CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Convergence; Finite volume method; Inhomogeneous medium; Maxwell's equations; Stability

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; CURRENT DENSITY; DIELECTRIC MATERIALS; ELECTRIC FIELDS; ERROR ANALYSIS; FINITE VOLUME METHOD; MAGNETIC FIELDS; MAGNETIC PERMEABILITY; MAXWELL EQUATIONS; PERMITTIVITY;

ERROR ESTIMATION; INHOMOGENOUS MEDIUM; POLYHEDRAL DOMAIN; TETRAHEDRAL TRIANGULATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0142171338     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901398453     Document Type: Article

References (21)

1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. H. T. Banks and J. Zou, Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials. Numer. Funct. Anal. Optim., 20 (1999), pp. 609-627.
3. A. Chatterjee, L. C. Kempel, and J. L. Volakis, Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications, IEEE Press, New York, 1998.
4. J. S. Chen and K. S. Yee, The finite-difference time-domain and the finite-volume time-domain methods in solving Maxwell's equations. IEEE Trans. Antennas and Propagation, 45 (1997), pp. 354-363.
5. Z Chen, Q. Du, and J. Zou, Finite element methods with matching and non-matching meshes for Maxwell equations with discontinuous coefficients, SIAM J. Numer. Anal., 37 (2000), pp. 1542-1570.
6. T. S. Chung and J. Zou, A finite volume method for Maxwell's equations with discontinuous physical coefficients, Int. J. Appl. Math., 7 (2001), pp. 201-223.
7. P. Ciarlet, Jr., and J. Zou, Fully discrete finite element approaches for time-dependent Maxwell equations, Numer. Math., 82 (1999), pp. 193-219.
8. G. Duvaut and J. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, New York, 1976.
9. S. Fortune, Voronoi diagrams and Delaunay triangulations, in Computing in Euclidean Geometry, World Scientific, Singapore, 1992, pp. 193-233.
10. V. Girault and P. A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Springer-Verlag, New York, 1979.
11. J. Jin, The Finite Element Method in Electromagnetics, John Wiley and Sons, New York, 1993.
12. J. L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications I, Springer-Verlag, Berlin, Heidelberg, 1972.
13. P. Monk, Analysis of a finite element method for Maxwell's equations, SIAM J. Numer. Anal., 29 (1992), pp. 714-729.
14. P. Monk and E. Süli, A convergence analysis of Yee's scheme on nonuniform grids, SIAM J. Numer. Anal., 31 (1994), pp. 393-412.
15. R. A. Nicolaides, Direct discretization of planer div-curl problems, SIAM J. Numer. Anal., 29 (1992), pp. 32-56.
16. R. A. Nicolaides and D. Q. Wang, Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions, Math. Comp., 67 (1998), pp. 947-963.
17. R. A. Nicolaides and X. Wu, Covolume solutions of three-dimensional div-curl equations, SIAM J. Numer. Anal., 34 (1997), pp. 2195-2203.
18. P. A. Raviart, Finite Element Approximation of the Time Dependent Maxwell Equations, Technical Report GdR SPARCH #6, Ecole Polytechnique, Palaiseau Cedex, France, 1993.
19. N. O. Sadiku, Elements of Electromagnetics, Oxford University Press, Oxford, UK, 2001.
20. A. Taflove, Computational Electrodynamics, Artech House, Boston, MA, 1995.
21. K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas and Propagation, 14 (1966), pp. 302-307.