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SUMMARY:A transfer operator approach for raytracing on engineering structu
 res - Professor Gregor Tanner\, University of Nottingham
DTSTART:20251009T150000Z
DTEND:20251009T170000Z
UID:TALK235270@talks.cam.ac.uk
CONTACT:Dr Matthew Nethercote
DESCRIPTION:Raytracing is a well-established tool used mainly in acoustics
  and wireless communication to establish the spreading of wavefields – t
 ypically in complex 3D environments with straight ray paths between reflec
 tions. Similar approaches are deemed difficult when considering the distri
 bution of vibrational energy in complex built-up structures – think airp
 lanes or cars. I will introduce a mesh-based ray tracing method called Dyn
 amical Energy Analysis (DEA) working at mid-to-high excitation frequencies
  for structure-borne sound in complex engineering structures [1]. It is ba
 sed on a finite dimensional approximation of a transfer operator and inter
 polates between power balance methods – often used in structure borne so
 und estimations at high frequencies – and ray tracing methods. DEA uses 
 ray densities instead of single trajectories and operates on small\, simpl
 e cells of existing FEM meshes. The overall solution is then built up by p
 utting together these local results leading to matrix equations. DEA can t
 hus be seen as a drop-in replacement for FEM tools working on the same mes
 hes but determining results at very high frequencies.\n\nIn this talk I wi
 ll discuss the basic DEA formalism including convergence estimates [2] and
  show recent results on acoustic radiation from structures based on DEA.\n
 \n\n[1] High-frequency structure- and air-borne sound transmission for a t
 ractor model using Dynamical Energy Analysis\, T Hartmann \, S Morita \, G
  Tanner\, D J Chappell\nWave Motion\, 87\, 132-150 (2019).\n\n[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\, Nonlinearit
 y\, 33\, 5773 (2020).
LOCATION:Centre for Mathematical Sciences MR13\, CMS
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