Lecture 5 (part 2) : Introduction to numerical multiscale methods

What this episode covers

In this lecture, we continue lecture 5. After a brief recap of the first part, we show how the properties of classical numerical schemes result in a prohibitive computational cost when applied to multiscale problems and why, as a consequence, dedicated numerical multiscale techniques are of interest. This lecture was given in two parts. The first part was stopped after an hour, because, due to an administrative error, the auditorium was not reserved. This entry therefore contains only the second part of the lecture. If the movie does not display nicely in your browser, here is a direct link to the movie file. Slides The slides can be downloaded here. Background reading I only mention here the background reading for part 2 of this lecture. All the material contains a thorough introduction, recent research results and extensive pointers to the literature. An introductory overview of equation-free methods can be found here: I.G. Kevrekidis and G. Samaey, Equation-free modeling, Scholarpedia, 5(9):4847, 2010. I.G. Kevrekidis and G. Samaey, Equation-free multiscale computation: algorithms and applications, Annual Review of Physical Chemistry 60:321-344, 2009. For the related heterogeneous multiscale methods, I refer to W. E et al. Heterogeneous multiscale methods: A review. Commun Comput Phys 2(3):367-450, 2007. Disclaimer : These notes are provided for the benefit of participants in this course. If you are not participating in the course, and finding these pages useful, please drop me an email so I can assess the impact of this site.

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