A transfer operator approach for raytracing on engineering structures

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• Professor Gregor Tanner, University of Nottingham
• Thursday 09 October 2025, 16:00-18:00
• Centre for Mathematical Sciences MR13, CMS.

If you have a question about this talk, please contact Dr Matthew Nethercote.

Raytracing is a well-established tool used mainly in acoustics and wireless communication to establish the spreading of wavefields – typically in complex 3D environments with straight ray paths between reflections. Similar approaches are deemed difficult when considering the distribution of vibrational energy in complex built-up structures – think airplanes or cars. I will introduce a mesh-based ray tracing method called Dynamical Energy Analysis (DEA) working at mid-to-high excitation frequencies for structure-borne sound in complex engineering structures [1]. It is based on a finite dimensional approximation of a transfer operator and interpolates between power balance methods – often used in structure borne sound estimations at high frequencies – and ray tracing methods. DEA uses ray densities instead of single trajectories and operates on small, simple cells of existing FEM meshes. The overall solution is then built up by putting together these local results leading to matrix equations. DEA can thus be seen as a drop-in replacement for FEM tools working on the same meshes but determining results at very high frequencies.

In this talk I will discuss the basic DEA formalism including convergence estimates [2] and show recent results on acoustic radiation from structures based on DEA .

[1] High-frequency structure- and air-borne sound transmission for a tractor model using Dynamical Energy Analysis, T Hartmann , S Morita , G Tanner, D J Chappell Wave Motion, 87, 132-150 (2019).

[2] Transfer operator approach to ray-tracing in circular domains, J Slipantschuk, M Richter, D J Chappell, G Tanner, W Just and O F Bandtlow, Nonlinearity, 33, 5773 (2020).

This talk is part of the Waves group seminar series.

This talk is included in these lists:

• Centre for Mathematical Sciences MR13, CMS
• Waves group seminar

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