Applied Mathematics Seminars Summer 2015

All seminars (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room 505 in the Mathematics Department (25 Gordon Street). See see how to find us for further details. There will be tea afterwards in Maths Room 606. If you require any more information on the Applied seminars please contact Prof Slava Kurylev e-mail: y.kurylev AT ucl.ac.uk or tel: 020-7679-7896.

12 May 2015

Prof Helmut Halbrecht - University of Basel

Title: Wavelet Galerkin schemes for boundary integral equations

Abstract:
Solving boundary integral equations by the Galerkin scheme leads to densely populated system matrices which are often ill conditioned. Thus, the memory consumption and the computation of the solution is of at least quadratic complexity. This makes the boundary element method unattractive for the practical usage.

In the last years, fast algorithms like the Fast Multipole Method and the Panel Clustering have been developed to reduce the complexity considerably. Another fast method is the wavelet Galerkin scheme: one employs biorthogonal wavelet bases with vanishing moments for the discretization of the given boundary integral equation. The resulting system matrix is quasi-sparse and can be compressed without loss of accuracy such that linear over-all complexity is realized.

This talk concerns with the principles as well as new developments of the wavelet Galerkin scheme for boundary integral equations, particularly assembling the compressed system matrix, preconditioning and adaptivity. Numerical experiments are presented which corroborate the theory. The matrix compression does not compromise the accuracy of the Galerkin scheme. However, we save a factor of storage 100—1000 and accelerate the computing time up to a factor 100.

26 May 2015

Prof Dmitry E. Pelinovsky - McMaster University, Canada

Title: Global existence and wave breaking in the inviscid Burgers equation with low-frequency disperison

Abstract:
I will review well-posedness results for the class of inviscid Burgers equations with low-frequency dispersion. This class includes the reduced Ostrovsky equation and the short-pulse equation, which are integrable by the inverse scattering transform. These low-dispersive equations admit global solutions for small initial data in some Sobolev spaces and wave breaking in a finite time for large initial data. I will show how conserved quantities of the integrable equations can be used to prove global existence for all times. I will also discuss the comparison results which provide sufficient conditions for wave breaking in a finite time.