Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
Authors:
R. A. Nicolaides and D.Q. Wang
Journal:
Math. Comp. 67 (1998), 947963
MSC (1991):
Primary 65N30, 65N15, 35L50
MathSciNet review:
1474654
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Additional Information
Abstract: This paper contains error estimates for covolume discretizations of Maxwell's equations in three space dimensions. Several estimates are proved. First, an estimate for a semidiscrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and nonuniform. By means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case.
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 4.
 T.G. JURGENS, A. TAFLOVE, K.UMASHANKAR and T.G. MOORE, Finitedifference timedomain modeling of curved surfaces, IEEE Trans. Antennas and Propagation, Vol. 40, 1992, pp. 17031708.
 5.
 T.G. JURGENS and A. TAFLOVE, Threedimensional contour FDTD modeling of scattering from single and multiple bodies, IEEE Trans. Antennas and Propagation, Vol. 41, 1993, pp. 14291438.
 6.
 J.F. LEE, Numerical solutions of TM scattering using obliquely Cartesian finite difference time domain algorithm, IEEE Proc. H (Microwaves, Antennas and Propagation), Vol. 140, 1992, pp. 2328.
 7.
 N. MADSEN, Divergence preserving discrete surface integral methods for Maxwell's equations using nonorthogonal unstructured grids, J. of Computational Physics, 119, 1995, pp. 3445. MR 96b:78002
 8.
 N. MADSEN and R.W. ZIOLKOWSKI, Numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids, Wave Motion 10, 1988, pp. 583596. MR 89j:78004
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 N. MADSEN and R.W. ZIOLKOWSKI, A three dimensional modified finite volume technique for Maxwell's equations, Electromagnetics, Vol. 10, 1990, pp. 147161.
 10.
 B.J. MCCARTIN and J.F. DICELLO, Three dimensional finite difference frequency domain scattering computation using the Control Region Approximation, IEEE Trans. Magnetics, Vol. 25, No. 4, 1989, pp. 30923094.
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 K. YEE, Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media, IEEE Trans.
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Additional Information
R. A. Nicolaides
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213
Address at time of publication:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213
Email:
rn0m@andrew.cmu.edu
D.Q. Wang
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213
Address at time of publication:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716
Email:
dqwang@math.udel.edu
DOI:
http://dx.doi.org/10.1090/S0025571898009715
PII:
S 00255718(98)009715
Keywords:
Maxwell's equations,
covolume schemes,
unstructured meshes,
convergence
Received by editor(s):
September 15, 1995
Received by editor(s) in revised form:
March 25, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
