Galkowski, Jeffrey Eric;
Spence, Euan;
Lafontaine, David;
(2023)
Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves.
IMA Journal of Numerical Analysis
10.1093/imanum/drad058.
(In press).
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Abstract
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the exterior domain is truncated and a local absorbing boundary condition coming from a Padé approximation (of arbitrary order) of the Dirichlet-to-Neumann map is imposed on the artificial boundary (recall that the simplest such boundary condition is the impedance boundary condition). We prove upper- and lower-bounds on the relative error incurred by this approximation, both in the whole domain and in a fixed neighbourhood of the obstacle (i.e., away from the artificial boundary). Our bounds are valid for arbitrarily-high frequency, with the artificial boundary fixed, and show that the relative error is bounded away from zero, independent of the frequency, and regardless of the geometry of the artificial boundary.
| Type: | Article |
|---|---|
| Title: | Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/drad058 |
| Publisher version: | https://doi.org/10.1093/imanum/drad058 |
| Language: | English |
| Additional information: | © The Author(s) 2023. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4. 0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Helmholtz equation; absorbing boundary condition; high frequency |
| 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.ucl.ac.uk/id/eprint/10172070 |
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