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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2310.06911 |
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| _version_ | 1866917591439638528 |
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| author | Nguyen, Van-Dung Wu, Ling Remacle, Françoise Noels, Ludovic |
| author_facet | Nguyen, Van-Dung Wu, Ling Remacle, Françoise Noels, Ludovic |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06911 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems Nguyen, Van-Dung Wu, Ling Remacle, Françoise Noels, Ludovic Computational Engineering, Finance, and Science 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. |
| title | A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2310.06911 |