Multiscale Petrov-Galerkin FEM for acoustic scattering

D. Gallistl; D. Peterseim; C. Carstensen

doi:10.1002/pamm.201610361

Multiscale Petrov-Galerkin FEM for acoustic scattering

D. Gallistl, D. Peterseim, C. Carstensen

Research output: Contribution to journal › Conference article › Academic › peer-review

Abstract

We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1

Original language	English
Pages (from-to)	745-746
Number of pages	2
Journal	Proceedings in Applied Mathematics and Mechanics
Volume	16
Issue number	1
DOIs	https://doi.org/10.1002/pamm.201610361
Publication status	Published - 2016
Externally published	Yes
Event	87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mahematiker-Vereinigung (DMV) 2016 - Braunschweig, Germany Duration: 7 Mar 2016 → 11 Mar 2016 Conference number: 87 https://jahrestagung.gamm-ev.de/index.php/2016/joint-dmv-and-gamm-annual-meeting

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10.1002/pamm.201610361

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title = "Multiscale Petrov-Galerkin FEM for acoustic scattering",

abstract = "We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1",

author = "D. Gallistl and D. Peterseim and C. Carstensen",

year = "2016",

doi = "10.1002/pamm.201610361",

language = "English",

volume = "16",

pages = "745--746",

journal = "Proceedings in Applied Mathematics and Mechanics",

issn = "1617-7061",

publisher = "Wiley-VCH Verlag",

number = "1",

note = "87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mahematiker-Vereinigung (DMV) 2016 ; Conference date: 07-03-2016 Through 11-03-2016",

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TY - JOUR

T1 - Multiscale Petrov-Galerkin FEM for acoustic scattering

AU - Gallistl, D.

AU - Peterseim, D.

AU - Carstensen, C.

N1 - Conference code: 87

PY - 2016

Y1 - 2016

N2 - We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1

AB - We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1

U2 - 10.1002/pamm.201610361

DO - 10.1002/pamm.201610361

M3 - Conference article

VL - 16

SP - 745

EP - 746

JO - Proceedings in Applied Mathematics and Mechanics

JF - Proceedings in Applied Mathematics and Mechanics

SN - 1617-7061

IS - 1

T2 - 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mahematiker-Vereinigung (DMV) 2016

Y2 - 7 March 2016 through 11 March 2016

ER -

Multiscale Petrov-Galerkin FEM for acoustic scattering

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