Domain Decomposition for Wavelet Single Layer on Geometries with PatchesReport as inadecuate




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We focus on the single layer formulationwhich provides an integral equation of the first kind that is very badlyconditioned. The condition number of the unpreconditioned system increasesexponentially with the multiscale levels. A remedy utilizing overlapping domaindecompositions applied to the Boundary Element Method by means of wavelets isexamined. The width of the overlapping of the subdomains plays an importantrole in the estimation of the eigenvalues as well as the condition number ofthe additive domain decomposition operator. We examine the convergence analysisof the domain decomposition method which depends on the wavelet levels and onthe size of the subdomain overlaps. Our theoretical results related to theadditive Schwarz method are corroborated by numerical outputs.

KEYWORDS

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

Cite this paper

Randrianarivony, M. 2016 Domain Decomposition for Wavelet Single Layer on Geometries with Patches. Applied Mathematics, 7, 1798-1823. doi: 10.4236-am.2016.715151.





Author: Maharavo Randrianarivony

Source: http://www.scirp.org/



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