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A class of efficient locally constructed preconditioners based on coarse spaces

Hussam Al Daas 1 Laura Grigori 1
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : In this paper we present a class of robust and fully algebraic two-level preconditioners for SPD matrices. We introduce the notion of algebraic local SPSD splitting of an SPD matrix and we give a characterization of this splitting. This splitting leads to construct algebraically and locally a class of efficient coarse spaces which bound the spectral condition number of the preconditioned system by a number defined a priori. We also introduce the τ-filtering subspace. This concept helps compare the dimension minimality of coarse spaces. Some PDEs-dependant preconditioners correspond to a special case. The examples of the algebraic coarse spaces in this paper are not practical due to expensive construction. We propose a heuristic approximation that is not costly. Numerical experiments illustrate the efficiency of the proposed method.
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Submitted on : Friday, June 15, 2018 - 1:24:24 PM
Last modification on : Friday, April 10, 2020 - 5:20:10 PM
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Hussam Al Daas, Laura Grigori. A class of efficient locally constructed preconditioners based on coarse spaces. [Research Report] RR-9184, Inria – Centre Paris-Rocquencourt; Laboratoire Jacques-Louis Lions, UPMC, Paris. 2018. ⟨hal-01816513⟩



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