Chniti, Chokri (2005) Unified treatment of singularities in domain decomposition methods. PhD thesis IRMAR, IRMAR, EP/X p.148.

Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Chniti.pdf

Abstract

This thesis treats a version of treatment of the singularities in dmain decomposition. Initially, we pointed out the principles of the methods of domain decomposition, then we recalled in some points the theory of V.Kondratiev which makes it!
possible to study the regularity of the elliptic problems in!
domain with corners. we introduced the Mellin transform which makes it possible to describe the regularity H^ {s} in the domain with corners, as well as the asymptotic types which intervene in the resolution of the elliptic problems in dmain with conical singularities. The transform of Mellin is a fundamental tool which makes it possible to understand the inadequacy between the problems in subdomain and the global problem: all is played on level of the asymptotic types. We considered two types of problem: the first case is where the global domain is singular and nonconvex and the second case where the global domain is regular and in this case we create singularities. We built an operator of interface of order two in the tangent derivative and we have propose an algorithm of which we study convergence according to his parameters and we dealt with the problem numerically and it is shown that convergence with the optimized parameters found theoretica!
lly led to a profit of speed of convergence compared to other parameters.

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