A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations |
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| Authors: | Hakan Bağcı Joseph E. Pasciak Kostyantyn Y. Sirenko |
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| Affiliation: | 1. Division of Computer, Electrical, and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;2. Department of Mathematics, Texas A&M University, College Station, TX 77843‐3368, USA |
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| Abstract: | We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off‐diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | Helmholtz equation perfectly matched layer cartesian PML sweeping preconditioner |
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