Yosemite Educational Symposium

Yosemite National Park
October 29 - November 1, 2000

 

"Advanced Multiscale and Multiresolution Methods"

 

Motivation

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. 

 

Technical Topics

Multiscale Data Representation

Wavelets, ridgelets, curvelets representations
Multiresolution decomposition of irregular domains, subdivisions, and geometry
Multiresolution methods in image processing, scientific visualization and data analysis

Multiscale modeling techniques

PDE homogenization
Algebraic homogenization of numerical PDEs
Multigrid and multilevel numerical methods
Reynolds and Favre averaging
Large eddy simulation
Multiscale finite element methods

Optimal complexity algorithms for multiscale problems

Multilevel algorithms
Algebraic multigrid
Renormalization multigrid
Fast N-body solution techniques

 

Final Schedule

Symposium Organization

Invited Plenary Presentations

Call for Abstracts and Student Participation

Scientific Committee

Special Dates

Registration

Lodging Arrangements

Symposium Administration

About Yosemite

 

Sponsors:

MIT


 

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