### 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.

Language | English |
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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 | |

Status | Published - 1 Jan 2018 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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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

*Domain Decomposition Methods in Science and Engineering XXIV. DD 2017*(pp. 139-147). (Lecture Notes in Computational Science and Engineering; Vol. 125). Cham, Switzerland: 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.; Spence, Euan A.; Tournier, Pierre Henri.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

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 -