Summary
We present an iterative algorithm for time harmonic Maxwell’s equation, using a particular integral formulation proposed in [13], [8]. We discuss the rate of convergence of the algorithm. In the case of of sphere scatterer the condition number of the method is adressed by means of Fourier transform.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Abboud and T. Sayah, Potentiels retardés pour les Equations de Maxwell avec condition d’impédance généralisée, Tech. Report R.I. 387, Ecole Polytechnique, France, 2000.
X. Antoine, H. Barucq and A. Bendali, Bayliss-Turkel-like Radiation Conditions on Surfaces of Arbitrary Shapes, Journal of Math. Anal. and Appl., 229(2000), pp. 184211.
N. Bartoli and F. Collino, Integral Equations via Saddle Point Problems for the 2-D electromagnetic Problems, M2AN, 34(2000),no 5, pp. 1023–1050.
A. Bendali, Boundary Element Solution of Scattering Problems Relative to a Generalized Impedance Boundary Condition, proccedings of the Boca Raton Cerfacs conference, London-New-York, 1999.
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, no. 15 in Springer series in Computational Mathematics, Springer-Verlag, 1991.
M. Cessenat, Mathematical Methods in Electromagnetism, no. 41 in Series on advances in Mathematics for Applied Sciences, World-Scientific, 1996.
G. Chen and J. Zhou, Boundary Element Methods, Academic Press, 1992.
F. Collino and B. Despres, Integral Equations via Saddle Point Problems for Time Harmonic Maxwell’s Equations ., to appear in Journal of Ap. and Comp. Math.
F. Collino and S. Ghanemi and P. Joly, Domain Decomposition Method for the Helmholtz Equation: A General Presentation., Comput. Methods Appl. Mech. Engrg, 184 (2000), no. 2–4, pp. 171–211.
D. Colton and R. Kress, Inverse Acoustic and electromagnetic scattering theory, Applied Mathematical Sciences 93, Springer-Verlag, 1992.
E. Darve, The fast multipole method: numerical implementation., J. Comput. Phys. 160 (2000), no. 1, pp. 195–240.
R. Dautray and J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, no. 2, Masson, 1985.
B. Després, Fonctionnelle quadratique et équations intégrales pour les équations de Maxwell en domaine extérieur, Comptes Rendus de l’Académie des Sciences, Paris, Série I, 323 (1996), pp. 547–552.
B. Després, Fonctionnelle quadratique et Équations Integrales pour les problèmes d’onde harmonique en domaine extérieur, M2AN, 31 (1997), pp. 679–732.
B. Després, Quadratic functional and integral equations for harmonic wave equations, in Mathematical and numerical aspects of wave propagation (Golden, CO, 1998),SIAM, Philadelphia, 1998, pp. 56–64.
B. Després and B. Stupfel, A domain decomposition for the solution of large electromagnetic scattering problem, J. of Electromagnetic Waves and Applications, vol. 13number 11 (1999), pp. 1553–1568.
B. Després and P. Joly and J. E. Roberts, A domain decomposition method for the harmonic Maxwell’s equations., in Proceedings of the IMACS international symposium on iterative methods in linear algebra, North Holland, 1990.
M. Epton and B. Dembart, Multipole translation theory for the three-dimensional Laplace and Helmholtz equations., SIAM J. Sci. Comput., 16 (1995), pp. 865–897.
G.C. Hsiao and R.F. Kleinman, Mathematical foundations for error estimations in numerical solutions of integral equations in electromagnetism, IEEE Trans. Antennas and Propag., no. 3 45(1997), pp. 316–328.
R. E. Kleinman and P. M. Van den Berg, Iterative methods for solving integral equations., Elsevier, 1988.
P. Lascaux and R. Theodor, Analyse numérique matricielle appliquée à l’art de l’ingénieur, Masson, 1987.
J. C. Nédelec, Cours de l’école d’été d’analyse numérique, tech. report, CEA-EDFIRIA, 1977.
M. D. Pocock and S. P. Walker, The complex bi-conjugate gradient solver applied to large electromagnetic scattering problems, computational costs, and costs scaling, IEEE Trans. Antennas and Propag., no. 1 45(1997), pp.140–146.
M. Reed and M. Simon, Scattering Theory, Academic-Press, New York, 1979.
T. K. Sarkar, Application of conjugate gradient method to electromagnetics and signal analysis, in From reaction concept to conjugate gradient: have we made any progress?, Elsevier, 1988.
T. B. A. Senior and J. L. Volakis, Approximate Boundary conditions in Electromagnetism, no. 41 in IEEE Electromagnetism Waves Series, The institution of Electric Engineers, 1995.
J. Song and C. C. Luand W. C. Chew, Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Complex Objects, IEEE Trans. Antennas Propagat., 45 (1997), pp. 1488–1493.
B. Stupfel and B. Despres, A domain decomposition method for the solution of large electromagnetic scattering problems, Journal of Electromagnetic waves and applications, 13 (1999), pp. 1553–1568.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Collino, F., Després, B. (2003). An Iterative Method for Time-harmonic Integral Maxwell’s Equations. In: Barton, N.G., Periaux, J. (eds) Coupling of Fluids, Structures and Waves in Aeronautics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44873-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-44873-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07294-9
Online ISBN: 978-3-540-44873-0
eBook Packages: Springer Book Archive