We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed-FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
Keywords: Eddy-current, boundary element, mixed finite element
@article{M2AN_2003__37_2_291_0,
author = {Meddahi, Salim and Selgas, Virginia},
title = {A {mixed-FEM} and {BEM} coupling for a three-dimensional eddy current problem},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {291--318},
year = {2003},
publisher = {EDP Sciences},
volume = {37},
number = {2},
doi = {10.1051/m2an:2003027},
zbl = {1031.78012},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2003027/}
}
TY - JOUR AU - Meddahi, Salim AU - Selgas, Virginia TI - A mixed-FEM and BEM coupling for a three-dimensional eddy current problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 291 EP - 318 VL - 37 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2003027/ DO - 10.1051/m2an:2003027 LA - en ID - M2AN_2003__37_2_291_0 ER -
%0 Journal Article %A Meddahi, Salim %A Selgas, Virginia %T A mixed-FEM and BEM coupling for a three-dimensional eddy current problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 291-318 %V 37 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2003027/ %R 10.1051/m2an:2003027 %G en %F M2AN_2003__37_2_291_0
Meddahi, Salim; Selgas, Virginia. A mixed-FEM and BEM coupling for a three-dimensional eddy current problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 291-318. doi: 10.1051/m2an:2003027
[1] and, An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations, Math. Comp. 68 (1999) 607-631. | Zbl
[2] , and, A justification of eddy currents model for the Maxwell equations. SIAM J. Appl. Math. 60 (2000) 1805-1823. | Zbl
[3] ,, and, Vector potentials in three-dimensional nonsmooth domains. Math. Methods Appl. Sci. 21 (1998) 823-864. | Zbl
[4] , and, A finite element method with Lagrange multipliers for low-frequency harmonic Maxell equations. SIAM J. Numer. Anal. 40 (2002) 1823-1849. | Zbl
[5] and, The TRIFOU code: Solving the 3-D eddy-currents problem by using H as state variable. IEEE Trans. Mag. 19 (1983) 2465-2470.
[6] , Two dual formulations of the 3-D eddy-currents problem. COMPEL 4 (1985) 103-116.
[7] , A rationale for edge elements in 3-D field computations. IEEE Trans. Mag. 24 (1988) 74-79.
[8] , The computation of eddy-currents in dimension 3 by using mixed finite elements and boundary elements in association. Math. Comput. Modelling 15 (1991) 33-42. | Zbl
[9] , Électromagnétisme, en vue de la modélisation. Springer-Verlag, Paris, Berlin, Heidelberg (1993). | Zbl | MR
[10] and, Mixed and hybrid finite element methods. Springer, Berlin, Heidelberg, New York (1991). | Zbl | MR
[11] , Hodge decompositions on the boundary of a polyhedron: the multi-connected case. Math. Models Methods Appl. Sci. 11 (2001) 1491-1504. | Zbl
[12] , Traces for functional spaces related to Maxwell equations: an overview, in Proceedings of GAMM-Workshop, Kiel (2001).
[13] and, On traces for functional spaces related to Maxwell's equation. Part I: An integration by parts formula in lipschitz polyhedra. Math. Methods Appl. Sci. 24 (2001) 9-30. | Zbl
[14] , and, On traces for in Lipschitz domains. University of Pavia, IAN-CNR 1185 (2000). | Zbl
[15] , and, Boundary element methods for Maxwell's equations on non-smooth domains. Numer. Math. (2001) (electronic) DOI 10.1007/s002110100372. | Zbl
[16] , Symmetric methods for the coupling of finite elements and boundary elements, in The Mathematics of Finite Elements and Applications IV, Academic Press, London (1988). | Zbl | MR
[17] and, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 5. Masson, Paris, Milan, Barcelone (1988). | Zbl | MR
[18] and, Boundary-field equation methods for a class of nonlinear problems. Longman (1995). | Zbl | MR
[19] and, Finite element approximation of the Navier-Stokes equations: theory and algorithms. Springer, Berlin, Heidelberg, New York (1986). | Zbl | MR
[20] , Symmetric coupling for eddy current problems. SIAM J. Numer. Anal. 40 (2002) 41-65. | Zbl
[21] and, On the coupling of boundary integral and finite element methods. Math. Comp. 35 (1980) 1063-1079. | Zbl
[22] , Strongly elliptic systems and boundary integral equations. Cambridge University Press (2000). | Zbl | MR
[23] , An optimal iterative process for the Johnson-Nedelec method of coupling boundary and finite elements. SIAM J. Numer. Anal. 35 (1998) 1393-1415. | Zbl
[24] , A mixed-FEM and BEM coupling for a two-dimensional eddy current problem. Numer. Funct. Anal. Optim. 22 (2001) 675-696. | Zbl
[25] and, A fully discrete BEM-FEM for the exterior Stokes problem in the plane. SIAM J. Numer. Anal. 37 (2000) 2082-2102. | Zbl
[26] ,, and, On the coupling of boundary integral and mixed finite element methods. J. Comput. Appl. Math. 69 (1996) 127-141. | Zbl
[27] , Mixed finite elements in . Numer. Math. 35 (1980) 315-341. | Zbl
[28] , Acoustic and electromagnetic equations. Integral representations for harmonic problems. Springer-Verlag, New York (2001). | Zbl | MR
[29] and, Mixed and hybrid methods, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991) 523-639. | Zbl
Cité par Sources :
