ncm2 Grande conférence
presents
Douglas N. Arnold
(Institute for Mathematics and its Applications)
From Exact Sequences to Colliding Black Holes:
Differential Complexes in Numerical Analysis
Thursday October 16, 2003
Centre de recherches mathématiques,
Université de Montréal
Pavillon André-Aisenstadt
2920 chemin de la Tour – Room 6214
Montréal, Qc Canada
5 p.m.
Abstract
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial differential equations often hinges on capturing subtle aspects of the structure of the system in
the discretization. In many cases the differential geometric structure captured by a differential complex has been found to be an essential element, and a discrete differential complex which is appropriately related to the original complex is essential. This new geometric viewpoint provides a unifying understanding of a variety of innovative numerical methods developed over recent decades, in particular for the stable approximation of electromagnetic problems. Very recently it has enabled the development of new algorithms for elasticity problems with properties previously unattainable. And it seems likely to provide an important element for the solution of numerical problems beyond current capabilities, such as the simulation of gravitational wave emission from colliding black holes.
Reception after the lecture at Salon Maurice-L’Abbé (6245)
Organizer:
Jacques Hurtubise (McGill)
français