Communications in Mathematical Sciences

Seamless multiscale modeling via dynamics on fiber bundles

Weinan E and Jianfeng Lu

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We present a general mathematical framework for modeling the macroscale behavior of a multiscale system using only microscale models, by formulating the effective macroscale models as dynamic models on the underlying fiber bundles. This framework allows us to carry out seamless multiscale modeling using traditional numerical techniques. At the same time, they give rise to an interesting mathematical structure and new interesting mathematical problems. We discuss several examples from homogenization problems, continuum modeling of solids based on atomistic or electronic structure models, macroscale behavior of interacting diffusion, and continuum modeling of complex fluids based on kinetic and Brownian dynamics models.

Article information

Commun. Math. Sci., Volume 5, Issue 3 (2007), 649-663.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65J05: General theory
Secondary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 74B20: Nonlinear elasticity 74Q05: Homogenization in equilibrium problems 76M25: Other numerical methods

multiscale modeling seamless fiber bundle


E, Weinan; Lu, Jianfeng. Seamless multiscale modeling via dynamics on fiber bundles. Commun. Math. Sci. 5 (2007), no. 3, 649--663.

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