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Modular parametric PGD enabling online solution of partial differential equations (2403.09312v1)

Published 14 Mar 2024 in cs.CE

Abstract: In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline--online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented.

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References (46)
  1. arXiv:https://epubs.siam.org/doi/pdf/10.1137/1.9781611974829, doi:10.1137/1.9781611974829. URL https://epubs.siam.org/doi/abs/10.1137/1.9781611974829
  2. doi:10.1515/9783110671490.
  3. doi:doi:10.1515/9783110499001.
  4. doi:10.1007/978-3-319-22470-1. URL https://hal.sorbonne-universite.fr/hal-01223456
  5. doi:10.1007/978-3-319-15431-2.
  6. doi:10.1007/978-3-031-29563-8_1. URL https://doi.org/10.1007/978-3-031-29563-8_1
  7. doi:10.1007/s11831-017-9241-4.
  8. doi:10.1155/2018/5608286.
  9. doi:10.1186/s40323-023-00240-4.
  10. doi:10.1007/s12289-022-01678-4.
  11. doi:https://doi.org/10.1016/j.crme.2019.11.012. URL https://www.sciencedirect.com/science/article/pii/S1631072119301834
  12. doi:10.1016/j.heliyon.2022.e12397.
  13. doi:10.3389/fmats.2023.1245347.
  14. doi:10.2514/1.35374.
  15. arXiv:2012.08851.
  16. doi:https://doi.org/10.1016/j.jsv.2021.116055. URL https://www.sciencedirect.com/science/article/pii/S0022460X21001279
  17. R. Zimmermann, Manifold interpolation and model reduction (2022). arXiv:1902.06502.
  18. doi:10.1016/j.matcom.2021.11.010.
  19. doi:10.1007/s11831-010-9049-y.
  20. doi:10.1007/978-3-319-02865-1.
  21. doi:10.1186/s40323-021-00208-2.
  22. doi:https://doi.org/10.1016/j.finel.2023.104022. URL https://www.sciencedirect.com/science/article/pii/S0168874X23001154
  23. arXiv:1902.08300.
  24. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620320604, doi:https://doi.org/10.1002/nme.1620320604. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620320604
  25. arXiv:https://doi.org/10.1137/0913020, doi:10.1137/0913020. URL https://doi.org/10.1137/0913020
  26. doi:https://doi.org/10.1016/0045-7825(94)90068-X. URL https://www.sciencedirect.com/science/article/pii/004578259490068X
  27. doi:10.1051/m2an/2012022.
  28. doi:https://doi.org/10.1016/j.camwa.2015.12.001. URL https://www.sciencedirect.com/science/article/pii/S0898122115005696
  29. doi:10.48550/arXiv.2206.09618.
  30. doi:https://doi.org/10.1016/j.renene.2023.02.067. URL https://www.sciencedirect.com/science/article/pii/S0960148123002112
  31. doi:https://doi.org/10.1016/j.finel.2022.103855. URL https://www.sciencedirect.com/science/article/pii/S0168874X22001287
  32. arXiv:https://arc.aiaa.org/doi/pdf/10.2514/6.2022-1250, doi:10.2514/6.2022-1250. URL https://arc.aiaa.org/doi/abs/10.2514/6.2022-1250
  33. doi:10.3390/en14051369. URL https://www.mdpi.com/1996-1073/14/5/1369
  34. doi:10.1002/nme.4371.
  35. doi:https://doi.org/10.1016/j.cma.2021.113997. URL https://www.sciencedirect.com/science/article/pii/S0045782521003285
  36. doi:10.3389/fphy.2022.900064.
  37. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7179, doi:https://doi.org/10.1002/nme.7179. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7179
  38. arXiv:2305.15163.
  39. doi:10.1007/s10915-022-01980-y.
  40. doi:10.48550/arXiv.2210.12551.
  41. doi:10.1016/j.cma.2022.115786.
  42. doi:10.48550/arXiv.2206.04736.
  43. doi:10.1186/s40323-022-00216-w.
  44. doi:10.1007/s00466-014-1048-7.
  45. doi:10.1002/nme.5729.
  46. doi:https://doi.org/10.1016/j.cma.2023.116484. URL https://www.sciencedirect.com/science/article/pii/S0045782523006084
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