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Wavenumber explicit analysis for Galerkin discretizations of lossy Helmholtz problems


Melenk, Jens Markus; Sauter, Stefan A; Torres, Céline (2020). Wavenumber explicit analysis for Galerkin discretizations of lossy Helmholtz problems. SIAM Journal on Numerical Analysis, 58(4):2119-2143.

Abstract

We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explicit with respect to the real and imaginary parts of the complex wavenumber $\zeta\in\mathbb{C}$, $\operatorname{Re}\zeta\geq0$, $\left\vert \zeta\right\vert \geq1$. For the extreme cases $\zeta \in{\rm i} \mathbb{R}$ and $\zeta\in\mathbb{R}_{\geq0}$, the estimates coincide with the existing estimates in the literature and exhibit a seamless transition between these cases in the right complex half plane.

Abstract

We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explicit with respect to the real and imaginary parts of the complex wavenumber $\zeta\in\mathbb{C}$, $\operatorname{Re}\zeta\geq0$, $\left\vert \zeta\right\vert \geq1$. For the extreme cases $\zeta \in{\rm i} \mathbb{R}$ and $\zeta\in\mathbb{R}_{\geq0}$, the estimates coincide with the existing estimates in the literature and exhibit a seamless transition between these cases in the right complex half plane.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Numerical Analysis
Physical Sciences > Computational Mathematics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Numerical Analysis
Language:English
Date:1 January 2020
Deposited On:06 Nov 2020 08:50
Last Modified:07 Nov 2020 21:00
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
Additional Information:Copyright © 2020, Society for Industrial and Applied Mathematics
OA Status:Green
Publisher DOI:https://doi.org/10.1137/19m1253952
Project Information:
  • : FunderSNSF
  • : Grant ID200021_172803
  • : Project TitleGalerkin Discretization of High-Frequency Helmholtz Problems with Variable Coefficients

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