Two-level preconditioners for the helmholtz equation

Marcella Bonazzoli; Victorita Dolean; Ivan G. Graham; Euan A. Spence; Pierre Henri Tournier

doi:10.1007/978-3-319-93873-8_11

Two-level preconditioners for the helmholtz equation

Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham, Euan A. Spence, Pierre Henri Tournier

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

8 Citations (SciVal)

Abstract

In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXIV. DD 2017
Editors	P. Bjorstad
Place of Publication	Cham, Switzerland
Publisher	Springer Verlag
Pages	139-147
Number of pages	9
ISBN (Electronic)	9783319938738
ISBN (Print)	9783319938721
DOIs	https://doi.org/10.1007/978-3-319-93873-8_11
Publication status	Published - 1 Jan 2018

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	125
ISSN (Print)	1439-7358

ASJC Scopus subject areas

Modelling and Simulation
Engineering(all)
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-319-93873-8_11

Cite this

Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A., & Tournier, P. H. (2018). Two-level preconditioners for the helmholtz equation. In P. Bjorstad (Ed.), Domain Decomposition Methods in Science and Engineering XXIV. DD 2017 (pp. 139-147). (Lecture Notes in Computational Science and Engineering; Vol. 125). Springer Verlag. https://doi.org/10.1007/978-3-319-93873-8_11

Two-level preconditioners for the helmholtz equation. / Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G. et al.

Domain Decomposition Methods in Science and Engineering XXIV. DD 2017. ed. / P. Bjorstad. Cham, Switzerland : Springer Verlag, 2018. p. 139-147 (Lecture Notes in Computational Science and Engineering; Vol. 125).

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

Bonazzoli, M, Dolean, V, Graham, IG , Spence, EA & Tournier, PH 2018, Two-level preconditioners for the helmholtz equation. in P Bjorstad (ed.), Domain Decomposition Methods in Science and Engineering XXIV. DD 2017. Lecture Notes in Computational Science and Engineering, vol. 125, Springer Verlag, Cham, Switzerland, pp. 139-147. https://doi.org/10.1007/978-3-319-93873-8_11

@inbook{6a53eee70aa54b1cafc80c8f71cc41da,

title = "Two-level preconditioners for the helmholtz equation",

abstract = "In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.",

author = "Marcella Bonazzoli and Victorita Dolean and Graham, {Ivan G.} and Spence, {Euan A.} and Tournier, {Pierre Henri}",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-93873-8_11",

language = "English",

isbn = "9783319938721",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "139--147",

editor = "P. Bjorstad",

booktitle = "Domain Decomposition Methods in Science and Engineering XXIV. DD 2017",

}

TY - CHAP

T1 - Two-level preconditioners for the helmholtz equation

AU - Bonazzoli, Marcella

AU - Dolean, Victorita

AU - Graham, Ivan G.

AU - Spence, Euan A.

AU - Tournier, Pierre Henri

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.

AB - In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.

UR - http://www.scopus.com/inward/record.url?scp=85060283884&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-93873-8_11

DO - 10.1007/978-3-319-93873-8_11

M3 - Chapter or section

AN - SCOPUS:85060283884

SN - 9783319938721

T3 - Lecture Notes in Computational Science and Engineering

SP - 139

EP - 147

BT - Domain Decomposition Methods in Science and Engineering XXIV. DD 2017

A2 - Bjorstad, P.

PB - Springer Verlag

CY - Cham, Switzerland

ER -

Two-level preconditioners for the helmholtz equation

Abstract

Publication series

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this