Dipartimento di Matematica ''F. Casorati''

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Scattering by fractal screens - functional analysis and computation

Dr. David Hewett, University College London

Sala conferenze IMATI-CNR, Pavia - Martedì 17 Aprile 2018 h.15:00

Abstract. The mathematical analysis and numerical simulation of acoustic and
electromagnetic wave scattering by planar screens is a classical
topic. The standard technique involves reformulating the problem as a
boundary integral equation on the screen, which can be solved
numerically using a boundary element method. Theory and computation
are both well-developed for the case where the screen is an open
subset of the plane with smooth (e.g. Lipschitz or smoother) boundary.
In this talk I will explore the case where the screen is an arbitrary
subset of the plane; in particular, the screen could have fractal
boundary, or itself be a fractal. Such problems are of interest in the
study of fractal antennas in electrical engineering, light scattering
by snowflakes/ice crystals in atmospheric physics, and in certain
diffraction problems in laser optics. The roughness of the screen
presents challenging questions concerning how boundary conditions
should be enforced, and the appropriate function space setting. But
progress is possible and there is interesting behaviour to be
discovered: for example, a sound-soft screen with zero area (planar
measure zero) can scatter waves provided the fractal dimension of the
set is large enough. Accurate computations are also challenging
because of the need to adapt the mesh to the fine structure of the
fractal. As well as presenting numerical results, I will outline some
of the outstanding open questions from the point of view of numerical
analysis. This is joint work with Simon Chandler-Wilde (Reading) and
Andrea Moiola (Pavia).

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Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602