Wave propagation in complex domains
University College London
Thursday 30 March 2017

A one-day workshop on the mathematical analysis and numerical simulation of wave propagation problems in complex domains, with a special focus on scattering problems involving non-Lipschitz scatterers, including fractals.

David Hewett (University College London) - d.hewett@ucl.ac.uk
Simon Chandler-Wilde (University of Reading)
Andrea Moiola (University of Reading)

David Abrahams (Cambridge/INI)
Raphael Assier (Manchester)
Martin Averseng (Ecole Polytechnique)
Timo Betcke (UCL)
Donald Brown (Nottingham)
Annalisa Buffa (EPFL)
Erik Burman (UCL)
James Cann (UCL)
Simon Chandler-Wilde (Reading)
James Christian (Salford)
Radu Cimpeanu (Imperial)
Xavier Claeys (UPMC)
Martin Costabel (Rennes)
Richard Craster (Imperial)
Monique Dauge (Rennes)
Ganesh Diwan (Reading)
Andrew Gibbs (Reading)
Ben Gilvey (Durham)
Fernando Henriquez (ETH)
David Hewett (UCL)
Ralf Hiptmair (ETH)
Daan Huybrechs (KU Leuven)
Ilia Kamotski (UCL)
Antigoni Kleanthous (UCL)
Andreas Kleefeld (FZ Jülich)
Stephen Langdon (Reading)
Karina McCusker (Reading)
Andrea Moiola (Reading)
Mihai Nechita (UCL)
Alberto Paganini (Oxford)
Emile Parolin (Ecole Polytechnique)
Owen Pembery (Bath)
Matthew Scroggs (UCL)
Mikaël Slevinsky (Manitoba)
Valery Smyshlyaev (UCL)
Euan Spence (Bath)
Jon Trevelyan (Durham)
Carolina Urzúa-Torres (ETH)
Ruoyu Wang (Cambridge)
Chris Westbrook (Reading)

The workshop booklet here includes the programme, talk titles and abstracts, and a map showing the location of the department, hotels and restaurant.

1000-1100 Registration, tea/coffee
1100-1105David Hewett (UCL) Welcome and introduction
1105-1130David Hewett (UCL) Scattering by fractal screens - abstract slides
1130-1200Andrea Moiola (Reading) Sobolev spaces on non-Lipschitz domains - abstract slides
1200-1230Mikaël Slevinsky (Manitoba) A numerical method for the solution of wave scattering by fractal screens - abstract
1230-1300Timo Betcke (UCL) A computational framework for Calderon projectors for Maxwell problems - abstract
1300-1345 Lunch
1345-1415Ralf Hiptmair (ETH) Boundary integral equations on complex screens - abstract slides
1415-1445Xavier Claeys (UPMC) Second kind boundary integral equation for multi-subdomain diffusion problems - abstract slides
1445-1515Annalisa Buffa (EPFL) Electromagnetic scattering with splines - abstract
1515-1545 Tea/coffee
1545-1615 Euan Spence (Bath) Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions - abstract slides
1615-1645James Christian (Salford) On Fresnel optics problems with fractal boundaries: apertures, screens, and unstable resonators - abstract slides
1645-1715Chris Westbrook (Reading) Microwave scattering by atmospheric ice particles - abstract slides
1715-1800 Drinks reception
1800-1900 Free time for networking and hotel check-in
1900 Dinner

The workshop will take place in the Department of Mathematics at University College London on 25 Gordon Street (UCL Union Building), London WC1H 0AY.

Extended summary:
Acoustic and electromagnetic wave scattering has applications in numerous areas of science and engineering, such as noise control, mobile communications, medical and geophysical imaging, and climate science. A typical scattering problem involves an incident wave striking a scattering obstacle, generating a scattered field satisfying an appropriate partial differential equation (e.g. the time-dependent wave equation, the Helmholtz equation, or Maxwell's equations) along with suitable boundary conditions. The study of such problems continues to stimulate research in a number of areas of mathematics including PDE theory, integral equations, and functional and numerical analysis.

The classical case where the scatterer is smooth (e.g. the boundary of a Lipschitz open set) is now well understood, at least in terms of the PDE, integral equation and functional analytic theory. However, many scattering problems encountered in applications involve complex, non-smooth scatterers for which the existing theory is not valid, due to the emergence of new singularity structure and the breakdown in solution regularity. There have been a number of recent efforts to extend the theory to problems involving non-Lipschitz scatterers, such as screens (i.e. manifolds with boundaries), "multi-screens" (unions of screens intersecting nontrivially), and transmission problems involving piecewise-homogeneous media. But many more exotic problems remain unanalysed mathematically, for example the performance of "fractal antennas", used for wideband transmission in mobile communications, and the scattering of light by fractal snow/ice crystals, which is important for calculating the Earth's radiation balance in climate science.

The aim of this workshop is to bring together researchers and research students with relevant interests and expertise to spend a day focusing on the challenges of wave scattering in complex domains, sharing new mathematical ideas, strengthening existing collaborations and identifying possible new ones.

This workshop is supported by EPSRC grant EP/P511262/1.