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.