[Dottorcomp] Seminari di Matematica Applicata, 14/05/2025, Simon Chandler-Wilde

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Mercoledì 14 Maggio 2025 alle *ore 15 precise*, presso l'aula Beltrami del
Dipartimento di Matematica,

Simon Chandler-Wilde (University of Reading)

terrà un seminario dal titolo:

First kind BIEs and BEM for acoustic scattering.

Abstract: We consider the so-called sound-soft problem in time-harmonic
acoustic scattering, where the total field, a solution to the Helmholtz
equation in the exterior of some obstacle, vanishes on the boundary of the
obstacle.  Making an ansatz for the scattered field as a single-layer
potential with some unknown density, a BIE for the density is obtained by
applying this sound-soft boundary condition. This is an old formulation; it
can be found, in the context of scattering by screens and apertures,
already in 19th century texts [1]. In this talk we make a survey of
previous results, and we explain in what sense this formulation applies
when the obstacle is some arbitrary compact set. In the case when the
scattering obstacle is a self-similar fractal of some fractal dimension d,
we implement and establish convergence rates for a fully discrete Galerkin
BEM where all integrals are with respect to d-dimensional Hausdorff measure
[2,3].
[1] Lord Rayleigh, “Theory of Sound”, 2nd Ed., Vol. II, Macmillan, New
York, 1896
[2] A. M. Caetano, S. N. Chandler-Wilde, A. Gibbs, D. P. Hewett and A.
Moiola, A Hausdorff-measure boundary element method for acoustic scattering
by fractal screens. Numer. Math., 156, 463-532 (2024).
[3] A. M. Caetano, S. N. Chandler-Wilde, X. Claeys, A. Gibbs, D. P. Hewett
and A. Moiola, Integral equation methods for acoustic scattering by
fractals. Proc. R. Soc. A.


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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/