Session I.5 - Geometric Integration and Computational Mechanics
Tuesday, June 13, 14:30 ~ 15:00
A framework for stable geometric spectral methods
Arieh Iserles
University of Cambridge, United Kingdom - This email address is being protected from spambots. You need JavaScript enabled to view it.
Spectral methods are extraordinarily powerful for boundary-value problems with regular boundary conditions and `nice' geometries, more problematic for initial-value problems because of stability issues. In this talk we briefly review a recent theory of T-functions and W-functions, whereby evolutionary PDEs can be discretised stably in different geometries and while conserving, as necessary, the $L_2$ norm. We also discuss the conservation of the Hamiltonian in this setting.
Joint work with Marcus Webb (University of Manchester, UK) and Jing Gao (Jia-Tong University, X'ian, China).