A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations
Author(s)Diosady, Laslo Tibor; Darmofal, David L.
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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.
DepartmentMassachusetts Institute of Technology. Aerospace Computational Design Laboratory; Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
forthcoming in SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Diosady, Laslo T. and David L. Darmofal. "A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations." forthcoming in SIAM Journal on Numerical Analysis.
Author's final manuscript