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Lions, P. (1988) On the Schwarz Alternating Method. In: Glowinski, R., Golub, G.H., Meurant, G.A. and Periaux, J., Eds., First Proceedings of Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1-2, MR 90a: 65248.

has been cited by the following article:

• TITLE: Domain Decomposition for Wavelet Single Layer on Geometries with Patches

  AUTHORS: Maharavo Randrianarivony

  KEYWORDS: Wavelet, Single Layer, Patch, Domain Decomposition, Convergence, Graph Partitioning, Condition Number

  JOURNAL NAME: Applied Mathematics, Vol.7 No.15, September 23, 2016

  ABSTRACT: We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multiscale levels. A remedy utilizing overlapping domain decompositions applied to the Boundary Element Method by means of wavelets is examined. The width of the overlapping of the subdomains plays an important role in the estimation of the eigenvalues as well as the condition number of the additive domain decomposition operator. We examine the convergence analysis of the domain decomposition method which depends on the wavelet levels and on the size of the subdomain overlaps. Our theoretical results related to the additive Schwarz method are corroborated by numerical outputs.