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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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/77918 |
| Summary: | 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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