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Optimized interface conditions in domain decomposition methods to solve reaction–diffusion problems with strong heterogeneity in the coefficients in a sectorial domain
Journal article   Peer reviewed

Optimized interface conditions in domain decomposition methods to solve reaction–diffusion problems with strong heterogeneity in the coefficients in a sectorial domain

Chokri Chniti
Applied numerical mathematics, Vol.118, pp.117-130
08/2017
DOI: https://doi.org/10.1016/j.apnum.2017.02.015

Abstract

Corner singularity Domain decomposition methods Kondratiev theory Schwarz algorithm Transmission conditions
The aim of this paper is to derive appropriate second order transmission boundary conditions near the corner used in domain decomposition methods to study the reaction–diffusion problems (“−∇.(ν(x)∇.)+η(x).”) with strong heterogeneity in the coefficients in a singular non-convex domain with Neumann and Dirichlet boundary condition. These transmission conditions will be tested and compared numerically with other approaches.

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