Galkowski, J;
Marchand, P;
Spence, EA;
(2021)
High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem.
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Abstract
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing Γ for the boundary of the obstacle, the relevant integral operators map L2(Γ) to itself. We prove new frequency-explicit bounds on the norms of both the integral operator and its inverse. The bounds on the norm are valid for piecewise-smooth Γ and are sharp, and the bounds on the norm of the inverse are valid for smooth Γ and are observed to be sharp at least when Γ is curved. Together, these results give bounds on the condition number of the operator on L2(Γ); this is the first time L2(Γ) condition-number bounds have been proved for this operator for obstacles other than balls.
| Type: | Working / discussion paper |
|---|---|
| Title: | High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://arxiv.org/abs/2109.06017v1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10138598 |
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