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 | |
| 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
Cite this
Two-level preconditioners for the helmholtz equation. / Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre Henri.
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 in Book/Report/Conference proceeding › Chapter
}
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
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 -