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>.