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- W2474876208 abstract "Preconditioned Krylov subspace (KSP) methods are widely used for solving very large and sparse linear systems arising from PDE discretizations. For modern applications, these linear systems are often nonsymmetric due to the nature of the PDEs, the boundary or jump conditions, or the discretization methods. While a number of preconditioned KSP methods and their implementations are readily available, it is often unclear to users which ones are the best choices for different classes of problems. In this work, we present a systematic comparison of some representative KSP methods and preconditioners. We consider four KSP methods, namely restarted GMRES, TFQMR, BiCGSTAB, and QMRCGSTAB, coupled with three preconditioners, namely Gauss-Seidel, incomplete LU factorization (ILU), and algebraic multigrid (AMG). We assess these preconditioned KSP methods using large, sparse, nonsymmetric linear systems arising from PDE discretizations in 2D and 3D. We compare the convergence and timing results of these different combinations, and assess the scalability of these methods with respect to the number of unknowns. Our results show that GMRES tends to deliver the best performance when coupled with AMG preconditioners, but it is far less competitive than the other three methods due to restarts when using Gauss-Seidel or ILU preconditioners. Our results also show that the smoothed-aggregation AMG delivers better performance and exhibits better scalability than classical AMG, but it is less robust, especially for ill-conditioned systems. The study helps establish some practical guidelines for choosing preconditioned KSP methods. It also motivates the further development of more effective and robust multigrid preconditioners for large, sparse, nonsymmetric, and potentially ill-conditioned linear systems." @default.
- W2474876208 created "2016-07-22" @default.
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- W2474876208 date "2016-07-01" @default.
- W2474876208 modified "2023-09-27" @default.
- W2474876208 title "A Comparison of Preconditioned Krylov Subspace Methods for Nonsymmetric Linear Systems" @default.
- W2474876208 hasPublicationYear "2016" @default.
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