Tue, 10 Oct 2023

14:00 - 14:30
L4

A sparse hp-finite element method for the Helmholtz equation posed on disks, annuli and cylinders

Ioannis Papadopoulos
(Imperial)
Abstract

We introduce a sparse and very high order hp-finite element method for the weak form of the Helmholtz equation.  The domain may be a disk, an annulus, or a cylinder. The cells of the mesh are an innermost disk (omitted if the domain is an annulus) and concentric annuli.

We demonstrate the effectiveness of this method on PDEs with radial direction discontinuities in the coefficients and data. The discretization matrix is always symmetric and positive-definite in the positive-definite Helmholtz regime. Moreover, the Fourier modes decouple, reducing a two-dimensional PDE solve to a series of one-dimensional solves that may be computed in parallel, scaling with linear complexity. In the positive-definite case, we utilize the ADI method of Fortunato and Townsend to apply the method to a 3D cylinder with a quasi-optimal complexity solve.

Tue, 03 Oct 2023
17:00
Lecture Theatre 1

Around the World in 80 Games - Marcus du Sautoy

Marcus du Sautoy
(University of Oxford)
Further Information

Oxford Mathematics Public Lecture: Around the World in 80 Games - Marcus du Sautoy

Join Marcus as he takes us on a mathematical journey across the centuries and through countries, continents and cultures in search of the games we love to play.  Based on his new book, he looks at the way mathematics has always been deeply intertwined with games and investigates how games themselves can provide us with opportunities for mathematical insight into the world.

From backgammon to chess, Catan to Snakes and Ladders, games are not simply an enjoyable diversion. They are rather the height of human ingenuity. Ours is the species that loves playing games: not homo sapiens but homo ludens.  The lecture is suitable for everyone ‘from age 8 to 108.’  Come and join Marcus on his journey Around the World in 80 Games. You simply can’t lose…

Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science in Oxford and Professor of Mathematics.

Please email @email to register.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on 24th October at 5pm, and can be watched any time after.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Localization of sensory levels in traumatic quadriplegia by segmental somatosensory evoked potentials
 Louis, A Gupta, P Perkash, I Clinical Neurophysiology volume 62 issue 4 313-316 (Jul 1985)
Regional cooling of human nerve and slowed Na+ inactivation
 Louis, A Hotson, J Clinical Neurophysiology volume 63 issue 4 371-375 (Apr 1986)
Deletions of 20p12 in Alagille syndrome: Frequency and molecular characterization
 Krantz, I Rand, E Genin, A Hunt, P Jones, M Louis, A Graham, J Bhatt, S Piccoli, D Spinner, N American Journal of Medical Genetics volume 70 issue 1 80-86 (02 May 1997)
Subscribe to