Computational Mathematics and Applications Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
19 October 2017
14:00
Dr David Hewett
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).
 

  • Computational Mathematics and Applications Seminar
26 October 2017
14:00
Dr Pietro Belotti
Abstract

Several optimization problems combine nonlinear constraints with the integrality of a subset of variables. For an important class of problems  called Mixed Integer Second-Order Cone Optimization (MISOCO), with applications in facility location, robust optimization, and finance, among others, these nonlinear constraints are second-order (or Lorentz) cones.

For such problems, as for many discrete optimization problems, it is crucial to understand the properties of the union of two disjoint sets of feasible solutions. To this end, we apply the disjunctive programming paradigm to MISOCO and present conditions under which the convex hull of two disjoint sets can be obtained by intersecting the feasible set with a specially constructed second-order cone. Computational results show that such cone has a positive impact on the solution of MISOCO problems.

  • Computational Mathematics and Applications Seminar
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