The DOI matches its OpenAlex record; 85 of the 85 references it cites were found in a registry or an index.
Heterogeneous Multiscale Methods: A Review
Abstract
This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem. This is illustrated by examples from several application areas, including complex fluids, micro-fluidics, solids, interface problems, stochastic problems, and statistically self-similar problems. Emphasis is given to the technical tools, such as the various constrained molecular dynamics, that have been developed, in order to apply HMM to these problems. Examples of mathematical results on the error analysis of HMM are presented. The review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool.
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Citations
Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
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Density Functional Theory of Atoms and Molecules
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Unified Approach for Molecular Dynamics and Density-Functional Theory
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The theory of polymer dynamics
Doi, M., & Edwards, S. F. (1986) · Cited by 8,928
Bhatia, R., Bredon, G. E., Walter, W. L., Rotman, J. J., Murty, M. R., Gilman, J., Walters, P., Golubitsky, M., Karatzas, I., Cohen, H., et al. (1977) · Cited by 8,252
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Cited by
Schneider, T., Lan, S., Stuart, A., & Teixeira, J. (2017) · Geophysical Research Letters · doi:10.1002/2017gl076101 · Cited by 391
Metadata
- Authors
- Weinan, E., Engquist, B., Li, X., Ren, W., & Vanden‐Eijnden, E.
- Venue
- Communications in Computational Physics
- Publisher
- Cambridge University Press
- Published
- 2007-02-01
- Volume
- 2
- Issue
- 3
- Pages
- 367-450
- ISSN
- 1815-2406 (ISSN-L)
- OpenAlex
- W1390923
- Cited by
- 687
- References
- 85
- FWCI
- 44.91
- Type
- journal article
- Language
- en
- Open access
- closed
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- Weinan, E., Engquist, B., Li, X., Ren, W., & Vanden‐Eijnden, E. (2007). Heterogeneous Multiscale Methods: A Review. Communications in Computational Physics. https://doi.org/10.4208/cicp.2007.v2.p367
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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