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|a Diosady, Laslo Tibor
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|a Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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|a Diosady, Laslo Tibor
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|a Darmofal, David L.
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|a Darmofal, David L.
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|a A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations
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|b Society for Industrial and Applied Mathematics,
|c 2013-03-15T18:24:21Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/77918
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|a 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.
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|a Zakhartchenko Fellowship
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|a en_US
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|a Article
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|t SIAM Journal on Numerical Analysis
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