This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods,
including the fundamental design principles behind the HMM philosophy and the main …

In many applications, the primary objective of numerical simulation of time-evolving systems
is the prediction of coarse-grained, or macroscopic, quantities. The purpose of this review is …

Mathematics is playing an ever more important role in the physical and biological sciences,
provoking a blurring of boundaries between scienti? c disciplines and a resurgence of …

We present and discuss a framework for computer-aided multiscale analysis, which enables
models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a …

Our goal in this paper is to show that many of the tools of signal processing, adapted Fourier
and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs, and …

The heterogenous multiscale method (HMM) is presented as a general methodology for the
efficient numerical computation of problems with multiscales and multiphysics on multigrids …

Mathematical modeling, analysis and simulation are set to play crucial roles in explaining
tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial …

The best available descriptions of systems often come at a fine level (atomistic, stochastic,
microscopic, agent based), whereas the questions asked and the tasks required by the …

In traditional physicochemical modeling, one derives evolution equations at the
(macroscopic, coarse) scale of interest; these are used to perform a variety of tasks …

The heterogeneous multi-scale method (HMM) is a general strategy for dealing with
problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies …