An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations

Mathematics of Computation

Volumn 68, Issue 226, 1999, Pages 607-631

  Alonso, Ana ^a   Valli, Alberto ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Domain decomposition methods; Maxwell equations

Indexed keywords

EID: 0033461714     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01013-3     Document Type: Article

References (18)

1. R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. MR 56:9247
2. A. Alonso and A. Valli, Some remarks on the characterization of the space of tangential traces of H(rot;Ω) and the construction of an extension operator, Manuscr. Math. 89 (1996), 159-178. MR 96k:46057
3. A. Alonso and A. Valli, A domain decomposition approach for heterogeneous time-harmonic Maxwell equations, Comput. Meth. Appl. Mech. Engrg. 143 (1997), 97-112. MR 98b:78020
4. A. Alonso and A. Valli, Unique solvability for high-frequency heterogeneous time-harmonic Maxwell equations via the Fredholm alternative theory, Math. Meth. Appl. Sci., to appear.
5. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains, preprint R 96001, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris, 1996.
6. M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Meth. Appl. Sci. 12 (1990), 365-368. MR 91c:35028
7. M. Dauge, Elliptic Boundary Value Problems on Corner Domains, Springer-Verlag, Berlin, 1988. MR 91a:35078
8. M. Křížek and P. Neittaanmäki, On time-harmonic Maxwell equations with nonhomogeneous conductivities: solvability and FE-approximation, Apl. Mat. 34 (1989), 480-499. MR 90m:35177
9. R. Leis, Exterior boundary-value problems in mathematical physics, in Trends in Applications of Pure Mathematics to Mechanics, Vol. 11, H. Zorski ed., Pitman, London, 1979, pp. 187-203. MR 81d:78016
10. P. Monk, A finite element method for approximating the time-harmonic Maxwell equations, Numer. Math. 63 (1992), 243-261. MR 94b:65134
11. P. Monk, Analysis of a finite element method for Maxwell's equations, SIAM J. Numer. Anal. 29 (1992), 714-729. MR 93k:65096
12. 3, Numer. Math. 35 (1980), 315-341. MR 81k:65125
13. 3, Numer. Math. 50 (1986), 57-81. MR 88e:65145
14. A. Quarteroni, G. Sacchi Landriani and A. Valli, Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements, Numer. Math. 59 (1991), 831-859. MR 93b:65190
15. J. Saranen, On generalized harmonic fields in domains with anisotropic nonhomogeneous media, J. Math. Anal. Appl. 88 (1982), 104-115; Erratum: J. Math. Anal. Appl. 91 (1983), 300. MR 84d:78004a, MR 84d:78004b
16. J. Saranen, On generalized harmonic fields in domains with anisotropic nonhomogeneous media, J. Math. Anal. Appl. 88 (1982), 104-115; Erratum: J. Math. Anal. Appl. 91 (1983), 300. MR 84d:78004a, MR 84d:78004b
17. J. Saranen, On electric and magnetic problems for vector fields in anisotropic nonhomogeneous media, J. Math. Anal. Appl. 91 (1983), 254-275. MR 85i:78004
18. 3, preprint UTM 493, Dipartimento di Matematica, Università di Trento, 1996.