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SUMMARY:Efficient frequency-dependent numerical simulation of wave scatter
 ing problems - Daan Huybrechs (KU Leuven)
DTSTART:20240229T150000Z
DTEND:20240229T160000Z
UID:TALK210133@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:Wave propagation in homogeneous media is often modelled using 
 integral equation methods. The boundary element method (BEM) is for integr
 al equations what the finite element method is for partial differential eq
 uations. One difference is that BEM typically leads to dense discretizatio
 n matrices. A major focus in the field has been the development of fast so
 lvers for linear systems involving such dense matrices. Developments inclu
 de the fast multipole method (FMM) and more algebraic methods based on the
  so-called H-matrix format. Yet\, for time-harmonic wave propagation\, the
 se methods solve the original problem only for a single frequency. In this
  talk we focus on the frequency-sweeping problem: we aim to solve the scat
 tering problem for a range of frequencies. We exploit the wavenumber-depen
 dence of the dense discretization matrix for the 3D Helmholtz equation and
  demonstrate a memory-compact representation of all integral operators inv
 olved which is valid for a continuous range of frequencies\, yet comes wit
 h a cost of a only small number of single frequency simulations. This is j
 oined work at KU Leuven with Simon Dirckx\, Kobe Bruyninckx and Karl Meerb
 ergen.
LOCATION:Centre for Mathematical Sciences\, MR14
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