Controllability method for the Helmholtz equation with higher-order discretizations

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dc.contributor.author Heikkola, Erkki
dc.contributor.author Mönkölä, Sanna
dc.contributor.author Pennanen, Anssi
dc.contributor.author Rossi, Tuomo
dc.date.accessioned 2012-10-11T09:27:47Z
dc.date.available 2012-10-11T09:27:47Z
dc.date.issued 2007
dc.identifier.citation Heikkola, E., Mönkölä, S., Pennanen, A., & Rossi, T. (2007). Controllability method for the Helmholtz equation with higher-order discretizations. Journal of Computational Physics , 225 (2), 1553-1576. fi
dc.identifier.issn 0021-9991
dc.identifier.other TUTKAID_25668
dc.identifier.uri http://hdl.handle.net/123456789/39956
dc.description.abstract We consider a controllability technique for the numerical solution of the Helmholtz equation. The original time-harmonic equation is represented as an exact controllability problem for the time-dependent wave equation. This problem is then formulated as a least-squares optimization problem, which is solved by the conjugate gradient method. Such an approach was first suggested and developed in the 1990s by French researchers and we introduce some improvements to its practical realization. We use higher-order spectral elements for spatial discretization, which leads to high accuracy and lumped mass matrices. Higher-order approximation reduces the pollution effect associated with finite element approximation of time-harmonic wave equations, and mass lumping makes explicit time-stepping schemes for the wave equation very efficient. We also derive a new way to compute the gradient of the least-squares functional and use algebraic multigrid method for preconditioning the conjugate gradient algorithm. Numerical results demonstrate the significant improvements in efficiency due to the higher-order spectral elements. For a given accuracy, spectral element method requires fewer computational operations than conventional finite element method. In addition, by using higher-order polynomial basis the influence of the pollution effect is reduced. fi
dc.language.iso eng
dc.publisher Elsevier
dc.relation.ispartof Journal of Computational Physics
dc.rights © Elsevier. This is an author's final draft version of an article whose final and definitive form has been published by Elsevier.
dc.subject.other akustinen sironta fi
dc.title Controllability method for the Helmholtz equation with higher-order discretizations
dc.type Article en
dc.identifier.urn URN:NBN:fi:jyu-201210102638
dc.contributor.laitos Tietotekniikan laitos fi
dc.contributor.laitos Department of Mathematical Information Technology en
jyx.tutka.volyme 225
jyx.tutka.mnumber 2
jyx.tutka.pagetopage 1553-1576
dc.type.uri http://purl.org/eprint/type/SubmittedJournalArticle
dc.identifier.doi 10.1016/j.jcp.2007.02.003
dc.date.updated 2012-10-10T03:30:12Z
dc.description.version Author's Final draft
eprint.status http://purl.org/eprint/type/status/PeerReviewed

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