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Coffee Talk - "Construction of general multiscale methods using dimensionality reduction", by Dr. Joaquín A. Hernández

Published: 01/04/2019

Tuesday, April 30th, 2019. Time: 12h.

Place: O.C. Zienkiewicz Conference Room, C1 Building, UPC Campus Nord, Barcelona


This talk is about how to construct general multiscale methods for periodic structures. Contrary to classical approaches, such as first order homogenization, the proposed method is independent of both the size of the unit cell and the external forces acting on the structure. The idea is to regard the equilibrium of the structure as a domain decomposition problem in which simplifications are made in the way subdomains deform, as well as in the way subdomains interact with each other. Domain displacements, Lagrange multipliers and interface displacements are approximated as linear combinations of dominant modes, which are obtained via dimensionality reduction tools from 3D numerical experiments. The computational cost of solving the partitioned system depends only on the number of domains in the partition, but not on the size of the finite element discretization of each partition. Recovery of 3D fields can be made in a post-process stage by simple matrix multiplication. The performance of the method is illustrated with prismatic and cellular structures. It is shown that in the former case (in which the subdomains are "slices"), the resulting system of equations has the same format as the one obtained in a classical finite element beam method, yet with the remarkable difference that the proposed scheme furnishes stress and displacement fields that are totally consistent with results computed using a full-order, 3D formulation.


Dr. Joaquín A. Hernández is an associate professor of Structural Engineering and Strength of Materials at the School of Industrial and Aeronautic Engineering of Terrassa. His research revolves around the field of multiscale modeling of composite material and reduced-order modeling. More specifically, he has been working since 2013 in the development of a novel high-performance reduction method able to speedup conventional multilevel finite element methods by factors of three orders of magnitude.