zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An explicit fourth-order staggered finite-difference time-domain method for Maxwell’s equations. (English) Zbl 1014.78015
The authors present a new finite-difference time-domain method which is fourth-order accurate both in time and space. The computational efficiency of the method is essentially improved compared to the original FD-TD method, but retains much of its simplicity. It can be easily adapted to cope with material discontinuities and different boundary conditions. Several numerical experiments illustrate the efficiency of the method, they indicate that dispersive errors can be effectively reduced.

78M20Finite difference methods (optics)
65M06Finite difference methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
78-05Experimental papers (optics, electromagnetic theory)
Full Text: DOI
[1] Abarbanel, S.; Gottlieb, D.: A mathematical analysis of the PML method. J. comput. Phys. 134, 357-363 (1997) · Zbl 0887.65122
[2] Abarbanel, S.; Gottlieb, D.: On the construction and analysis of absorbing layers in CEM. Appl. numer. Math. 27, 331-340 (1998) · Zbl 0924.35160
[3] Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.: A fourth-order accurate finite difference scheme for the computation of elastic waves. Bull. seismol. Soc. amer. 76, 1115-1132 (1986)
[4] Berenger, J. P.: A perfectly matched layer for the absorption of electromagnetic waves. J. comput. Phys. 114, 185-200 (1994) · Zbl 0814.65129
[5] Cohen, G.; Joly, P.: Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media. SIAM J. Numer. anal. 33, 1266-1302 (1996) · Zbl 0863.65048
[6] Driscoll, T. A.; Fornberg, B.: A block pseudospectral method for Maxwell’s equations I: One-dimensional case. J. comput. Phys. 140, 1-19 (1998) · Zbl 0908.65090
[7] Driscoll, T. A.; Fornberg, B.: Block pseudospectral methods for Maxwell’s equations II: Two-dimensional, discontinuous-coefficient case. SIAM J. Sci. comput. 21, 1146-1167 (1999) · Zbl 0949.65107
[8] J. Fang, Time domain finite difference computation for Maxwell’s equations, Ph.D. dissertation, Univ. California, Berkeley, CA, 1989.
[9] Gustafsson, B.: The convergence rate for difference approximations to mixed initial boundary value problems. Math. comput. 29, 396-406 (1975) · Zbl 0313.65085
[10] Gustafsson, B.: The convergence rate for difference approximations to general mixed initial boundary value problems. SIAM J. Numer. anal. 18, 179-190 (1981) · Zbl 0469.65068
[11] Leveque, R. J.; Zhang, C.: The immersed interface method for acoustic wave equations with discontinuous coefficients. Wave motion 25, 237-263 (1997) · Zbl 0915.76084
[12] Pathria, D.: The correct formulation of intermediate boundary conditions for Runge--Kutta time integration of initial boundary value problems. SIAM J. Sci. comput. 18, 1255-1266 (1997) · Zbl 0897.65057
[13] Petropoulos, P. G.: Phase error control for FD-TD methods of second- and fourth-order accuracy. IEEE trans. Antennas propag. 42, 859-862 (1994)
[14] Petropoulos, P. G.; Zhao, L.; Cangellaris, A. C.: A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell’s equations with high-order staggered finite difference schemes. J. comput. Phys. 139, 184-208 (1998) · Zbl 0915.65123
[15] Shlager, K. L.; Maloney, J. G.; Ray, S. L.; Peterson, A. F.: Relative accuracy of several finite-difference time-domain methods in two and three dimensions. IEEE trans. Antennas propag. 41, 1732-1737 (1993)
[16] Taflove, A.: Computational electrodynamics: the finite-difference time-domain method. (2000) · Zbl 0963.78001
[17] E. Turkel, A. Yefet, Fourth order method for Maxwell’s equations on a staggered mesh, IEEE AP-S International Symposium, Vol. 4, 1997, pp. 2156--2159.
[18] Xie, Z.; Chan, C. H.; Zhang, B.: An explicit fourth-order orthogonal curvilinear staggered grid FDTD method for Maxwell’s equations. J. comput. Phys. 175, 739-763 (2002) · Zbl 1009.78008
[19] Yee, K. S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE trans. Antennas propag. 14, 302-307 (1966) · Zbl 1155.78304
[20] Yefet, A.; Petropoulos, P. G.: A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell’s equations. J. comput. Phys. 168, 286-315 (2001) · Zbl 0981.78012
[21] Young, J. L.: A higher order FDTD method for EM propagation in a collisionless cold plasma. IEEE trans. Antennas propag. 44, 1283-1289 (1996)
[22] Young, J. L.; Gaitonde, D.; Shang, J. J. S.: Toward the construction of a fourth-order difference scheme for transient EM wave simulationstaggered grid approach. IEEE trans. Antennas propag. 45, 1573-1580 (1997) · Zbl 0947.78612
[23] Zhao, L.; Cangellaris, A. C.: GT-pmlgeneralized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids. IEEE trans. Microwave theory techn. 44, 2555-2563 (1996)
[24] Ziokowski, R.: Time-derivative Lorentz-material model-based absorbing boundary condition. IEEE trans. Antennas propag. 45, 1530-1535 (1997)