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A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients

Published online by Cambridge University Press:  15 April 2010

Chokri Chniti
Chokri Chniti*
Affiliation:
RICAM, Austrian Academy of Sciences, Altenberger strasse 69, 4040 Linz, Austria. [email protected]
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Abstract

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; CALCOLO45 (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.

Keywords

Corner singularitydomain decomposition methodKondratiev theory
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 1 , January 2011 , pp. 23 - 37
Copyright
© EDP Sciences, SMAI, 2010

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References

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Chniti, C., Nataf, F. and Nier, F., Improved interface conditions for 2D domain decomposition with corners: a theoretical determination. CALCOLO 45 (2008) 111–147. CrossRef
Chniti, C., Nataf, F. and Nier, F., Improved interface conditions for 2D domain decomposition with corners: Numerical applications. J. Sci. Comput. 38 (2009) 207–228. CrossRef
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