Back to regular grids?
W.Hackbusch, MPI Leipzig
The development of the numerical treatment of differential equations in the last 50 years is not only characterised by the increasing storage (corresponding to smaller grid sizes, increase of spatial dimension, etc.), but also by the switch from regular grids to irregular discretisation allowing locally refined grids.
Today it is a general belief that only with local, adaptive discretisations efficient discretisations can be constructed.
The success of the numerical tensor calculus points into another direction. If functions are sought in product domains (maybe even of high spatial dimension), regular grids offer an efficiency which is better than adaptive ones. The lecture tries to detail this statement.
Literature: W. H.: Tensor spaces and numerical tensor calculus. Springer 2012
25.09.2012 at 16:00