On overlapping domain decomposition methods for high-contrast multiscale problems
Refereed conference paper presented and published in conference proceedings


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AbstractWe review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of iterations. The main novelty of our approaches is the construction of coarse spaces, which are computed using spectral information of local bilinear forms. We present several approaches to incorporate the spectral information into the coarse problem in order to obtain minimal coarse space dimension. We show that using these coarse spaces, we can obtain a domain decomposition preconditioner with the condition number independent of contrast and small scales. To minimize further the number of iterations until convergence, we use this minimal dimensional coarse spaces in a construction combining them with large overlap local problems that take advantage of the possibility of localizing global fields orthogonal to the coarse space. We obtain a condition number close to 1 for the new method. We discuss possible drawbacks and further extensions.
All Author(s) ListJuan Galvis, Eric Chung, Yalchin Efendiev, Wing Tat Leung
Name of Conference24th International Conference on Domain Decomposition Methods in Science and Engineering
Start Date of Conference06/02/2017
End Date of Conference10/02/2017
Place of ConferenceSvalbard
Country/Region of ConferenceNorway
Proceedings TitleDomain Decomposition Methods in Science and Engineering XXIV
Series TitleLecture Notes in Computational Science and Engineering
Number in Series125
Year2018
PublisherSpringer International Publishing
ISBN978-3-319-93872-1
eISBN978-3-319-93873-8
LanguagesEnglish-United Kingdom

Last updated on 2018-27-12 at 15:25