A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations
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 th...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/77918 |
| _version_ | 1826212765568598016 |
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| author | Diosady, Laslo Tibor Darmofal, David L. |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Diosady, Laslo Tibor Darmofal, David L. |
| author_sort | Diosady, Laslo Tibor |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:37:52Z |
| format | Article |
| id | mit-1721.1/77918 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:37:52Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/779182022-10-02T03:00:41Z A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations Diosady, Laslo Tibor Darmofal, David L. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Diosady, Laslo Tibor Darmofal, David L. 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. Zakhartchenko Fellowship 2013-03-15T18:24:21Z 2013-03-15T18:24:21Z 2012-06 2010-10 Article http://purl.org/eprint/type/JournalArticle 0036-1429 http://hdl.handle.net/1721.1/77918 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 en_US http://dx.doi.org/10.1137/100812434 SIAM Journal on Numerical Analysis 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. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Diosady, Laslo Tibor Darmofal, David L. A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title | A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title_full | A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title_fullStr | A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title_full_unstemmed | A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title_short | A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations |
| title_sort | unified analysis of balancing domain decomposition by constraints for discontinuous galerkin discretizations |
| url | http://hdl.handle.net/1721.1/77918 |
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