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Parallel design and performance of nested filtering factorization preconditioner

Long Qu 1 Laura Grigori 2 Frédéric Nataf 3 
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
Abstract : In this paper we present the parallel design and performance of the nested ltering factorization preconditioner (NFF). This preconditioner can be used for solving linear systems arising from the discretization of a system of PDEs on unstructured grids. It is based on a recursive decomposition that exploits a bordered block diagonal structure of the input matrix, obtained priorly by using graph partitioning techniques. It also allows to preserve several directions of interest of the input matrix to alleviate the e ect of low frequency modes on the convergence of iterative methods. Due to its recursive formulation, NFF has limited memory requirements and it is also naturally suitable for hierarchical parallel machines. We show experimentally its convergence rate and its time to solution on a boundary value problem with highly heterogeneous coe cients, discretized on threedimensional grids.
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Submitted on : Tuesday, October 8, 2013 - 1:56:07 PM
Last modification on : Sunday, June 26, 2022 - 11:59:49 AM


  • HAL Id : hal-00870934, version 1


Long Qu, Laura Grigori, Frédéric Nataf. Parallel design and performance of nested filtering factorization preconditioner. SuperComputing 2013, IEEE/ACM, 2013, Denver, United States. ⟨hal-00870934⟩



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