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CATEGORIES:Applied and Computational Analysis
SUMMARY:Integral equations for wave scattering by fractals
- David Hewett (UCL)
DTSTART;TZID=Europe/London:20230608T150000
DTEND;TZID=Europe/London:20230608T160000
UID:TALK198055AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198055
DESCRIPTION:Integral equations are a powerful and popular tool
for the numerical solution of linear PDEs for whi
ch a fundamental solution is available. They are o
f particular importance in the study of acoustic\,
electromagnetic and elastic wave propagation\, wh
ere wave scattering problems posed in unbounded do
mains can often be formulated as an integral equat
ion over the (typically bounded) scatterer or its
boundary. For scatterers with smooth boundaries th
is is classical\, but many real-life scatterers (e
.g. trees/vegetation\, snowflakes/ice crystal aggr
egates) are highly irregular. The case where the s
catterer (or its boundary) is fractal poses partic
ularly interesting challenges\, and our recent inv
estigations into this topic have led to new result
s in function spaces\, variational problems\, nume
rical quadrature and integral equations\, which I
will survey in this talk. Computationally\, we hav
e studied two main approaches: (1) approximate the
fractal by a smoother "prefractal" shape\, and (2
) work with integral equations formulated directly
on the fractal\, with respect to the appropriate
fractal (Hausdorff) measure. The latter approach s
eems to provide a clearer pathway for rigorous con
vergence analysis\, but for numerical implementati
on requires accurate quadrature rules for evaluati
ng singular integrals with respect to fractal meas
ures.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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