October 29 - November 1, 2000

Many computationally challenging problems ubiquitous in science and engineering exhibit multiscale phenomena so that the prospect of numerically computing or even representing all scales of action is either very expensive or completely intractable. Some examples of practical interest include: fluid turbulence at large Reynolds number, weather forecasting, flow through porous media, spray combustion and detonation, structural analysis of composite and foam materials, many-body galaxy formation, large scale molecular dynamic simulations, ab-initio physics and chemistry, terabyte data mining, large scale data visualization, and a multitude of others.

The computational challenge has several origins. For many of the cited multiscale problems, one seeks to compute as many scales as possible but quickly finds that the algorithmic complexity of conventional algorithms rises too steeply with the number of degrees of freedom. For another class of multiscale problems, one does not actually desire the fine scale information, but owing to nonlinearity in the modeled physics it is found that the effect of fine scale information on course scales must be included to achieve quantitative predictive capability. Compounding the computational problem is the fundamental question of optimal data representation for multiscale problems where it is known that even modern wavelet basis representations can yield overall suboptimal algorithmic complexity, e.g. problems containing embedded manifolds of discontinuity or discontinuous derivatives.

An arguable conclusion is that these multiscale problems will remain computationally expensive or completely intractable for the foreseeable future unless new algorithmic paradigms of computation are developed which fundamentally embrace the multiscale nature of these problems. The Yosemite Educational Symposium is devoted to this problem with the focus on recent developments.

Multiscale Data Representation

Wavelets, ridgelets, curvelets representations

Multiresolution decomposition of irregular domains, subdivisions, and geometry

Multiresolution methods in image processing, scientific visualization and data analysisMultiscale modeling techniques

PDE homogenization

Algebraic homogenization of numerical PDEs

Multigrid and multilevel numerical methods

Reynolds and Favre averaging

Large eddy simulation

Multiscale finite element methodsOptimal complexity algorithms for multiscale problems

Multilevel algorithms

Algebraic multigrid

Renormalization multigrid

Fast N-body solution techniques

MIT

This site has been created by Jean Sofronas <jeans@mit.edu>.