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Analysis of fictiti...
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Fotios, KasolisUmeå universitet,Institutionen för datavetenskap,Design Optimization
(författare)
Analysis of fictitious domain approximations of hard scatterers
- Artikel/kapitelEngelska2015
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Philadelphia :Siam publications,2015
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LIBRIS-ID:oai:DiVA.org:umu-111181
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https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-111181URI
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https://doi.org/10.1137/140981630DOI
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Språk:engelska
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Sammanfattning på:engelska
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Consider the Helmholtz equation del center dot alpha del p+k(2 alpha)p = 0 in a domain that contains a so-called hard scatterer. The scatterer is represented by the value alpha = epsilon, for 0 < epsilon << 1, whereas alpha = 1 whenever the scatterer is absent. This scatterer model is often used for the purpose of design optimization and constitutes a fictitious domain approximation of a body characterized by homogeneous Neumann conditions on its boundary. However, such an approximation results in spurious resonances inside the scatterer at certain frequencies and causes, after discretization, ill-conditioned system matrices. Here, we present a stabilization strategy that removes these resonances. Furthermore, we prove that, in the limit epsilon -> 0, the stabilized problem provides linearly convergent approximations of the solution to the problem with an exactly modeled scatterer. Numerical experiments indicate that a finite element approximation of the stabilized problem is free from internal resonances, and they also suggest that the convergence rate is indeed linear with respect to epsilon.
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Wadbro, Eddie,1981-Umeå universitet,Institutionen för datavetenskap,Design Optimization(Swepub:umu)edwa0002
(författare)
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Berggren, MartinUmeå universitet,Institutionen för datavetenskap(Swepub:umu)mabe0102
(författare)
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Umeå universitetInstitutionen för datavetenskap
(creator_code:org_t)
Sammanhörande titlar
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Ingår i:SIAM Journal on Numerical AnalysisPhiladelphia : Siam publications53:5, s. 2347-23620036-14291095-7170
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