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On Controllability Methods for the Helmholtz Equation

Grote, Marcus J. and Tang, Jet Hoe. (2019) On Controllability Methods for the Helmholtz Equation. Journal of computational and applied mathematics, 358. pp. 306-326.

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Official URL: https://edoc.unibas.ch/75285/

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Abstract

When the Helmholtz equation is discretized by standard finite difference or finite element methods, the resulting linear system is highly indefinite and thus notoriously difficult to solve, in fact increasingly so at higher frequency. The exact controllability approach (Bristeau et al., 1994) instead reformulates the problem in the time domain and seeks the time-harmonic solution of the corresponding wave equation. By iteratively reducing the mismatch between the solution at initial time and after one period, the controllability method greatly speeds up the convergence to the time-harmonic asymptotic limit. Moreover, each conjugate gradient iteration solely relies on standard numerical algorithms, which are inherently parallel and robust against higher frequencies. The original energy functional used to penalize the departure from periodicity is strictly convex only for sound-soft scattering problems. To extend the controllability approach to general boundary-value problems governed by the Helmholtz equation, new penalty functionals are proposed, which are numerically efficient. Numerical experiments for wave scattering from sound-soft and sound-hard obstacles, inclusions, but also for wave propagation in closed wave guides illustrate the usefulness of the resulting controllability methods.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
UniBasel Contributors:Grote, Marcus J. and Tang, Jet Hoe
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0377-0427
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:25 Jun 2020 14:21
Deposited On:24 Jun 2020 15:32

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