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

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; 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.