| Issue |
ESAIM: M2AN
Volume 45, Number 1, January-February 2011
|
|
|---|---|---|
| Page(s) | 23 - 37 | |
| DOI | https://doi.org/10.1051/m2an/2010031 | |
| Published online | 15 April 2010 | |
A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
RICAM, Austrian Academy of Sciences, Altenberger strasse 69, 4040 Linz, Austria. chokri.chniti@ricam.oeaw.ac.at
Received:
1
July
2008
Revised:
6
August
2009
Revised:
21
December
2009
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci. 342 (2006) 883–886; CALCOLO 45 (2008) 111–147; J. Sci. Comput. 38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions to obtain fast convergence of domain decomposition methods. After explaining the theoretical results, we explicitly compute the coefficients in the transmission boundary conditions. The numerical results presented in this paper confirm the optimality properties.
Mathematics Subject Classification: 65N55 / 35J05 / 65N30 / 35J25 / 35R05
Key words: Corner singularity / domain decomposition method / Kondratiev theory
© EDP Sciences, SMAI, 2010
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