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Seminar – Cédric Bellis ‘Variational principles for computational homogenization and strategies for improving the performances of Fourier spectral methods’
19 October 2023 à 14 h 15 – 16 h 00
Cédric Bellis, CNRS Research Fellow at LMA (Laboratoire de Mécanique et d’Acoustique, Marseille) will give a seminar on Thursday October 19, 2023 at 2.15pm at Centrale Nantes (Theater C117).
This seminar is organized jointly by the TRU Couplings and numerical methods for complex structures and Mechanics and Multiscale physics of materials.
Abstract
Variational principles for computational homogenization and strategies for improving the performances of Fourier spectral methods.
The homogenization of periodic elastic composites can be addressed through the reformulation of the local equations of the mechanical problem into energetic variational principle. We review such principles and describe a computational, FFT-based, approach that has shown effective on a variety of problems. Building on these tools, we propose some novel geometric variational formulations of the problem, which feature functionals that aim at measuring the discrepancy of arbitrary test fields to the kinematic, static or material admissibility conditions of the problem. By relaxing the corresponding local equations, this formulation aims in particular at laying the groundwork for the homogenization of composites whose constitutive properties are only partially known or uncertain, or to make use of data-driven approaches.
In addition, we will discuss some strategies for constructing a posteriori error estimators for FFT-based spectral methods and, such methods generally lack precision in the presence of discontinuities or singularities, we will propose an adaptive numerical method for improving their performance.