2002/05/16 by E Weinan, Weinan E, Björn Engquist +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Cartography #Composite Material Mechanics #Computational Physics (physics.comp-ph) #Computer science #FOS: Physical sciences #Geography #Scale (ratio) #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.physics/0205048
24 pages, 2 figures
openalex publication_date 2002/05/16 · arxiv created 2002/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 several existing multi-scale methods, but also provide a methodology for designing new algorithms for new applications. In this paper, we review the history of multi-scale modeling and simulation that led to the development of HMM, the methodology itself together with some applications, and the mathematical theory of stability and accuracy.