A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations

• Main Authors: Diosady, Laslo Tibor (Contributor), Darmofal, David L. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Aerospace Computational Design Laboratory (Contributor), Massachusetts Institute of Technology. Department of Aeronautics and Astronautics (Contributor)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics, 2012-07-19T20:13:50Z.
• Subjects: Article
• Online Access: Get fulltext

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 element-wise "local" bilinear forms. The element-wise perspective allows for a simple unified analysis of a variety of DG methods and leads naturally to the appropriate choice for the subdomain-wise 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.
Boeing Company
Massachusetts Institute of Technology (Zakhartchenko Fellowship)