Bounding acoustic layer potentials via oscillatory integral techniques
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| 003 | CHVBK | ||
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| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150301xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10543-014-0506-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0506-0 | ||
| 100 | 1 | |a Spence |D E. |u Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK |4 aut | |
| 245 | 1 | 0 | |a Bounding acoustic layer potentials via oscillatory integral techniques |h [Elektronische Daten] |c [E. Spence] |
| 520 | 3 | |a We consider the Helmholtz single-layer operator (the trace of the single-layer potential) as an operator on $$L^2(\Gamma )$$ L 2 ( Γ ) where $$\Gamma $$ Γ is the boundary of a 3-d obstacle. We prove that if $$\Gamma $$ Γ is $$C^2$$ C 2 and has strictly positive curvature then the norm of the single-layer operator tends to zero as the wavenumber $$k$$ k tends to infinity. This result is proved using a combination of (1) techniques for obtaining the asymptotics of oscillatory integrals, and (2) techniques for obtaining the asymptotics of integrals that become singular in the appropriate parameter limit. This paper is the first time such techniques have been applied to bounding norms of layer potentials. The main motivation for proving this result is that it is a component of a proof that the combined-field integral operator for the Helmholtz exterior Dirichlet problem is coercive on such domains in the space $$L^2(\Gamma )$$ L 2 ( Γ ) . | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Helmholtz equation |2 nationallicence | |
| 690 | 7 | |a High frequency |2 nationallicence | |
| 690 | 7 | |a Boundary integral equation |2 nationallicence | |
| 690 | 7 | |a Layer potential |2 nationallicence | |
| 690 | 7 | |a Oscillatory integral operator |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 279-318 |x 0006-3835 |q 55:1<279 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0506-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0506-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Spence |D E. |u Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 279-318 |x 0006-3835 |q 55:1<279 |1 2015 |2 55 |o 10543 | ||