BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers
Author(s)Yano, Masayuki; Darmofal, David L.; Darmofal, David L
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A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for large-scale, convection-dominated problems. The algorithm is applied to the linear system arising from the discretization of the two-dimensional advection–diffusion equation and Euler equations for compressible, inviscid flow. A Robin–Robin interface condition is extended to the Euler equations using entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization of the diffusion-dominated flows, and achieves low iteration count in the advection-dominated regime. The BDDC method based on inexact local solvers with incomplete factorization and p = 1 coarse correction maintains the performance of the exact counterpart for the wide range of the Peclet numbers considered while at significantly reduced memory and computational costs.
DepartmentMassachusetts Institute of Technology. Aerospace Computational Design Laboratory; Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Computer Methods in Applied Mechanics and Engineering
Yano, Masayuki, and David L. Darmofal. “BDDC Preconditioning for High-Order Galerkin Least-Squares Methods Using Inexact Solvers.” Computer Methods in Applied Mechanics and Engineering 199, no. 45–48 (November 2010): 2958–2969.
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