Transfer operator approach to ray-tracing in circular domains

Slipantschuk, J., Richter, M., Chappell, D.J. ORCID: 0000-0001-5819-0271, Tanner, G., Just, W. and Bandtlow, O.F., 2020. Transfer operator approach to ray-tracing in circular domains. Nonlinearity, 33 (11), pp. 5773-5790. ISSN 0951-7715

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The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation which involves a Perron–Frobenius operator defined on a suitable Sobolev space. Even for fairly simple geometries, let alone realistic scenarios such as typical boundary value problems in room acoustics or for mechanical vibrations, numerical approximations are necessary. Here we study the convergence of approximation schemes by rigorous methods. For circular billiards we prove that convergence of finite-rank approximations using a Fourier basis follows a power law where the power depends on the smoothness of the source distribution driving the system. The relevance of our studies for more general geometries is illustrated by numerical examples.

Item Type: Journal article
Publication Title: Nonlinearity
Creators: Slipantschuk, J., Richter, M., Chappell, D.J., Tanner, G., Just, W. and Bandtlow, O.F.
Publisher: IOP Publishing
Date: 1 November 2020
Volume: 33
Number: 11
ISSN: 0951-7715
Rights: © 2020 IOP Publishing Ltd & London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Divisions: Schools > School of Science and Technology
Record created by: Linda Sullivan
Date Added: 05 Oct 2020 09:19
Last Modified: 31 May 2021 15:15

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