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A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface
Umeå University.
Umeå University.
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7352-1550
Umeå University.
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2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 304, 479-500 p.Article in journal (Refereed) Published
Abstract [en]

We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche’s method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles a complex-valued impedance function Z that is allowed to vanish. In the case of a vanishing impedance, the proposed method reduces to the classic Nitsche method to weakly enforce continuity over the interface. We show stability of the method, in terms of a discrete Gårding inequality, for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. Moreover, we prove an a priori error estimate under the assumption that the absolute value of the impedance is bounded away from zero almost everywhere. Numerical experiments illustrate the performance of the method for a number of test cases in 2D and 3D with different interface conditions.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 304, 479-500 p.
Keyword [en]
Helmholtz equation; Finite element method; Nitsche’s method; Acoustic impedance; Surface wave, Gårding inequality
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-29654DOI: 10.1016/j.cma.2016.02.032ISI: XYZOAI: oai:DiVA.org:hj-29654DiVA: diva2:914156
Available from: 2016-03-23 Created: 2016-03-23 Last updated: 2017-01-26Bibliographically approved

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Hansbo, Peter
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JTH, Product DevelopmentJTH. Research area Product Development - Simulation and Optimization
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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