GenEO Coarse Spaces for Heterogeneous Indefinite Elliptic Problems

Niall Bootland, Victorita Dolean, Ivan G. Graham, Chupeng Ma, Robert Scheichl

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)

Abstract

For domain decomposition preconditioners, the use of a coarse correction as a second level is usually required to provide scalability (in the weak sense), such that the iteration count is independent of the number of subdomains, for subdomains of fixed dimension. In addition, it is desirable to guarantee robustness with respect to strong variations in the physical parameters. Achieving scalability and robustness usually relies on sophisticated tools such as spectral coarse spaces [4, 5]. In particular, we can highlight the GenEO coarse space [9], which has been successfully analysed and applied to highly heterogeneous positive definite elliptic problems. This coarse space relies on the solution of local eigenvalue problems on subdomains and the theory in the SPD case is based on the fact that local eigenfunctions form an orthonormal basis with respect to the energy scalar product induced by the bilinear form.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXVI
EditorsSusanne C. Brenner, Axel Klawonn, Jinchao Xu, Eric Chung, Jun Zou, Felix Kwok
Place of PublicationCham, Switzerland
PublisherSpringer
Pages117-125
Number of pages9
ISBN (Print)9783030950248
DOIs
Publication statusPublished - 16 Mar 2023
Event26th International Conference on Domain Decomposition Methods, 2020 - Virtual, Online
Duration: 7 Dec 202012 Dec 2020

Publication series

NameLecture Notes in Computational Science and Engineering
Volume145
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference26th International Conference on Domain Decomposition Methods, 2020
CityVirtual, Online
Period7/12/2012/12/20

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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