Title Computational Multiscale Solvers for Continuum Approaches
Authors MONTERO CHACÓN, FRANCISCO DE PAULA, Sanz-Herrera, Jose A., Doblare, Manuel, MONTERO CHACÓN, FRANCISCO DE PAULA
External publication No
Means Mater.
Scope Review
Nature Científica
JCR Quartile 2
SJR Quartile 2
JCR Impact 3.05700
Area International
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85062961416&doi=10.3390%2fma12050691&partnerID=40&md5=3d94328402ffd3016df335847cf5c1ec
Publication date 01/03/2019
ISI 000462543700007
Scopus Id 2-s2.0-85062961416
DOI 10.3390/ma12050691
Abstract Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of intereste.g., mechanical, fluid, thermal, or electromagneticinvolving 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.
Keywords multiscale analysis; homogenization; proper generalized decomposition; computational simulation
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