Domain Decomposition for Wavelet Single Layer on Geometries with Patches

HTML  XML Download Download as PDF (Size: 1367KB)  PP. 1798-1823  
DOI: 10.4236/am.2016.715151    1,185 Downloads   1,833 Views  Citations

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.

Share and Cite:

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

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.