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Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D
Authors:LGiraud  AHaidar  YSaad
Institution:1. Joint INRIA-CERFACS Lab-42 AV.Coriolis,31057,Toulouse,France
2. Department of Computer Science,University of Tennessee,Knoxville,TN37996,USA
3. Department of Computer Science and Engineering,University of Minnesota,Minneapolis,MN 55455,USA
Abstract:In this paper we study the computational performance of variants of an al-gebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems. In earlier works, the local Schur complements were com- puted exactly using a sparse direct solver. The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems. In this work we investigate the use of sparse approximation of the dense local Schur complements. These approximations are com-puted using a partial incomplete LU factorization. Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.
Keywords:Hybrid direct/iterative solver  domain decomposition  incomplete/partial factorization  Schur approximation  scalable preconditioner  convection-diffusion  large 3D problems  parallel scientific computing  High Performance Computing
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