[en] We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer – quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster. The available possible operations are however not as versatile as with a classical computer. However, quantum annealers (QAs) are well suited to evaluate the minimum state of a Hamiltonian quadratic potential. Therefore, we reformulate the elasto-plastic finite element problem as a double-minimisation process framed at the structural scale using the variational updates formulation. In order to comply with the expected quadratic nature of the Hamiltonian, the resulting non-linear minimisation problems are iteratively solved with the suggested Quantum Annealing-assisted Sequential Quadratic Programming (QA-SQP): a sequence of minimising quadratic problems is performed by approximating the objective function by a quadratic Taylor’s series. Each quadratic minimisation problem of continuous variables is then transformed into a binary quadratic problem. This binary quadratic minimisation problem can be solved on quantum annealing hardware such as the D-Wave system. The applicability of the proposed framework is demonstrated with one- and two-dimensional elasto-plastic numerical benchmarks. The current work provides a pathway of performing general non-linear finite element simulations assisted by quantum computing.
Research center :
A&M - Aérospatiale et Mécanique - ULiège [BE] MolSys - Molecular Systems - ULiège [BE]
Disciplines :
Mechanical engineering Engineering, computing & technology: Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
Author, co-author :
Nguyen, Van Dung ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Wu, Ling ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Remacle, Françoise ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE] ULiège - University of Liège [BE]
Funding text :
V.-D.N acknowledges the support of the Fonds National de la Recherche (F.R.S.-FNRS,
Belgium).
F.R. acknowledges the support of the Fonds National de la Recherche (F.R.S.-FNRS,
Belgium), #T0205.20.
This work is partially supported by a “Strategic Opportunity” grant from the University
of Liege.
NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Mechanics - A/Solids 105 (2024) , DOI: 10.1016/j.euromechsol.2024.105254
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