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Open AccessReview

Computational Multiscale Solvers for Continuum Approaches

Departamento de Ingeniería, Universidad Loyola Andalucía, 41014 Seville, Spain
Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Seville, Spain
Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
Author to whom correspondence should be addressed.
Materials 2019, 12(5), 691;
Received: 15 January 2019 / Revised: 15 February 2019 / Accepted: 18 February 2019 / Published: 26 February 2019
(This article belongs to the Special Issue Multi-scale Modeling of Materials and Structures)
Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest—e.g., mechanical, fluid, thermal, or electromagnetic—involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper. View Full-Text
Keywords: multiscale analysis; homogenization; proper generalized decomposition; computational simulation multiscale analysis; homogenization; proper generalized decomposition; computational simulation
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MDPI and ACS Style

Montero-Chacón, F.; Sanz-Herrera, J.A.; Doblaré, M. Computational Multiscale Solvers for Continuum Approaches. Materials 2019, 12, 691.

AMA Style

Montero-Chacón F, Sanz-Herrera JA, Doblaré M. Computational Multiscale Solvers for Continuum Approaches. Materials. 2019; 12(5):691.

Chicago/Turabian Style

Montero-Chacón, Francisco; Sanz-Herrera, José A.; Doblaré, Manuel. 2019. "Computational Multiscale Solvers for Continuum Approaches" Materials 12, no. 5: 691.

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