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 - 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.
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

https://hal.inria.fr/hal-01816513
Contributor : Hussam Al Daas <>
Submitted on : Friday, June 15, 2018 - 1:24:24 PM
Last modification on : Friday, September 20, 2019 - 4:34:04 PM
Long-term archiving on : Monday, September 17, 2018 - 12:34:12 PM

File

RR-9184.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01816513, version 1

Citation

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⟩

Share

Metrics

Record views

371

Files downloads

221