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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A Hausdorff-measure BEM for acoustic scattering by
fractal screens - part 1 - Andrea Moiola (Univers
itÃ degli Studi di Pavia)
DTSTART;TZID=Europe/London:20230418T110000
DTEND;TZID=Europe/London:20230418T114500
UID:TALK198712AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198712
DESCRIPTION:Sound-soft fractal screens can scatter acoustic wa
ves even when they have zero surface measure.We fo
rmulate such scattering problems as singular integ
ral equations and we approximate them using the bo
undary element method (BEM).Each BEM basis functio
n is supported in a fractal set\, and the integrat
ion involved in the formation of the BEM matrix is
with respect to a non-integer order Hausdorff mea
sure rather than the usual (Lebesgue) surface meas
ure.Using recent results on function spaces on fra
ctals\, we prove convergence of the Galerkin formu
lation of this ``Hausdorff BEM'' for acoustic scat
tering when the scatterer is a compact $d$-set for
some suitable Hausdorff dimension $d$.For a class
of fractals that are attractors of iterated funct
ion systems (IFS)\, we prove convergence rates for
the Hausdorff BEM and superconvergence for smooth
antilinear functionals\, under certain natural re
gularity assumptions on the solution of the underl
ying boundary integral equation.Quadrature rules a
nd numerical results will be presented in the seco
nd part of the presentation. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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