Preconditioners for hierarchical matrices based on their extended sparse form

Darya A. Sushnikova; Ivan V. Oseledets

doi:10.1515/rnam-2016-0003

Preconditioners for hierarchical matrices based on their extended sparse form

Darya A. Sushnikova^*, Ivan V. Oseledets

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with H²-matrices. We propose several new preconditioners for such matrices that are based on the equivalent sparse extended form of H²-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.

Original language	English (US)
Pages (from-to)	29-40
Number of pages	12
Journal	Russian Journal of Numerical Analysis and Mathematical Modelling
Volume	31
Issue number	1
DOIs	https://doi.org/10.1515/rnam-2016-0003
State	Published - Jan 1 2016

Keywords

H-matrix
integral equations
preconditioning

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation

Access to Document

10.1515/rnam-2016-0003

Cite this

@article{756d2ec9ff774633a782db3465cfa2ed,

title = "Preconditioners for hierarchical matrices based on their extended sparse form",

abstract = "In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with H2-matrices. We propose several new preconditioners for such matrices that are based on the equivalent sparse extended form of H2-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.",

keywords = "H-matrix, integral equations, preconditioning",

author = "Sushnikova, {Darya A.} and Oseledets, {Ivan V.}",

note = "Publisher Copyright: {\textcopyright} 2016 Walter de Gruyter GmbH.",

year = "2016",

month = jan,

day = "1",

doi = "10.1515/rnam-2016-0003",

language = "English (US)",

volume = "31",

pages = "29--40",

journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",

issn = "0927-6467",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Preconditioners for hierarchical matrices based on their extended sparse form

AU - Sushnikova, Darya A.

AU - Oseledets, Ivan V.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with H2-matrices. We propose several new preconditioners for such matrices that are based on the equivalent sparse extended form of H2-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.

AB - In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with H2-matrices. We propose several new preconditioners for such matrices that are based on the equivalent sparse extended form of H2-matrices. In the numerical experiments we show that the most efficient approach is based on the so-called reverse-Schur preconditioning technique.

KW - H-matrix

KW - integral equations

KW - preconditioning

UR - http://www.scopus.com/inward/record.url?scp=84959018923&partnerID=8YFLogxK

U2 - 10.1515/rnam-2016-0003

DO - 10.1515/rnam-2016-0003

M3 - Article

AN - SCOPUS:84959018923

SN - 0927-6467

VL - 31

SP - 29

EP - 40

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

IS - 1

ER -

Preconditioners for hierarchical matrices based on their extended sparse form

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this