Fictitious domain method for unsteady problems: Application to electromagnetic scattering

Journal of Computational Physics

Volumn 138, Issue 2, 1997, Pages 907-938

  Collino, Francis ^a,b   Joly, Patrick ^a,b   Millot, Florence ^b  

^a INRIA   (France)

^b CERFACS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC FIELDS; ELECTROMAGNETIC WAVE SCATTERING; ELECTROMAGNETIC WAVES;

ELECTROMAGNETIC SCATTERING; FICTITIOUS DOMAIN METHOD; PROPERTY; SCATTERING BY OBSTACLES; SURFACE CURRENT; TIME-DEPENDENT PROBLEM; UNIFORM MESH; UNSTEADY PROBLEMS;

LAGRANGE MULTIPLIERS;

EID: 0031539346     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5849     Document Type: Article

References (22)

1. Astrakmantev G. P. Methods of fictitious domains for a second order elliptic equation with natural boundary conditions. U.S.S.R. Comput. Math. Math. Phys. 18:1978;114.
2. C. Atamian, R. Glowinski, J. Periaux, H. Steve, G. Terrason, 1989, Control approach to fictitious domain in electro-magnetism, Conference sur l'approximation et les methodes numeriques pour la resolution des equations de Maxwell, Hotel Pullmann, Paris, 1989.
3. Atamian C., Joly P. An analysis of the method of fictitious domains for the exterior Helmholtz problem. RAIRO Modèl. Math. Anal. Numér. 27:1993;251.
4. A. Bendali, 1984, Approximation par elements finis de surface de problemes de diffraction des ondes electro-magnetiques, Université Paris VI.
5. Brezzi F. On the existence uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO Anal. Numér. R-2:1974.
6. G. Cohen, P. Joly, N. Tordjman, 1995, Higher order triangular finite elements with mass lumping for the wave equation, Third International Conference on Mathematical and Numerical Aspects of Wave Propagation, 1, 1995, 270.
7. F. Collino, S. Garcés, P. Joly, F. Millot, 1995, Fictitious domain method for unsteady problems: Application to electromagnetic scattering, International Conference on Electromagnetics in Advanced Applications, 1995.
8. Dautray R., Lions J. L. Analyse mathématique et calcul numérique pour les sciences et les techniques. 1988;Masson, Paris.
9. 2. SIAM J. Numer. Anal. 10:1973.
10. Engquist B., Majda A. Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31:1977.
11. Finogenov S. A., Kuznetsov Y. A. Two stage fictitious components methods for solving the Dirichlet boundary value problem. Sov. J. Num. Anal. Math. Modelling. 3:1988;301.
12. S. Garcés, Application des méthodes de domaines fictifs à la modélisation des structures rayonnantes tridimensionnelles Étude mathématique et numérique d'un modèle, Eacute;cole National Supérieure de l'Aeronautique et de l'Espace, Toulouse.
13. Girault V., Glowinski R. Error analysis of a fictitious domain method applied to a Dirichlet problem. Japan J. Indus. Appl. Math. 12:1995;487.
14. Glowinski R., Pan T. W., Periaux J. A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Eng. 111:1994;283.
15. Glowinski R., Pan T. W., Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comp. Meth. Appl. Mech. Eng. 112:1994;133.
16. Hsiao G. C., Kleinmann R. E. Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics. IEEE Trans. Antennas propagat. 45:1997;316.
17. Marchuk G. I., Kuznetsov Y. A., Matsokin A. M. Fictitious domain and domain decomposition methods. Sov. J. Num. Anal. Math. Modelling. 1:1986;3.
18. Monk P. A mixed method for approximating Maxwell's equations. SIAM J. on Num. Anal. Math. Modelling. 28:1991;1610.
19. 3. Num. Math. 142:1984;79.
20. Raviart P. A., Thomas J. M. Introduction à l'analyse numérique des équations aux dérivées partielles. 1983;Masson, Paris.
21. Taflove A. Computational Electrodynamics, The Finite-Difference Time Domain method. 1995;Artech House, London.
22. Yee K. S. Numerical Solutions of Initial Boundary Value Problems involving Maxwell's Equations in isotropic media. IEEE trans. on Antennas and Propagation. 14:1966;302.