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Analysis of fictitious domain approximations of hard scatterers
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- Fotios, Kasolis (author)
- Umeå universitet,Institutionen för datavetenskap,Design Optimization
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- Wadbro, Eddie, 1981- (author)
- Umeå universitet,Institutionen för datavetenskap,Design Optimization
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- Berggren, Martin (author)
- Umeå universitet,Institutionen för datavetenskap
- (creator_code:org_t)
- Philadelphia : Siam publications, 2015
- 2015
- English.
- In: SIAM Journal on Numerical Analysis. - Philadelphia : Siam publications. - 0036-1429 .- 1095-7170. ; 53:5, s. 2347-2362
- Journal article (peer-reviewed)
Abstract
Subject headings
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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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Helmholtz equation
- hard scatterers
- fictitious domain method
- inf-sup condition
Publication and Content Type
- ref (subject category)
- art (subject category)
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