A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations
Name
Diosady-2012-A UNIFIED ANALYSIS OF BALANCING DOMAIN DECOMPOSITION.pdf
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321.49 KB
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Adobe PDF
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Author(s)
Diosady, Laslo Tibor
Darmofal, David L.
Date Issued
June 2012
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Diosady, Laslo T., and David L. Darmofal. “A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations.” SIAM Journal on Numerical Analysis 50.3 (2012): 1695–1712. © 2012, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
The BDDC algorithm is extended to a large class of discontinuous Galerkin (DG) discretizations of second order elliptic problems. An estimate of $C(1+\log(H/h))^2$ is obtained for the condition number of the preconditioned system where $C$ is a constant independent of $h$ or $H$ or large jumps in the coefficient of the problem. Numerical simulations are presented which confirm the theoretical results. A key component for the development and analysis of the BDDC algorithm is a novel perspective presenting the DG discretization as the sum of elementwise „local” bilinear forms. The elementwise perspective allows for a simple unified analysis of a variety of DG methods and leads naturally to the appropriate choice for the subdomainwise local bilinear forms. Additionally, this new perspective enables a connection to be drawn between the DG discretization and a related continuous finite element discretization to simplify the analysis of the BDDC algorithm.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/100812434
