Abstract
Non-intrusive approaches for the construction of computational vademecums face different challenges, especially when a parameter variation affects the physics of the problem considerably. In these situations, classical interpolation becomes inaccurate. Therefore, classical approaches for the construction of an offline computational vademecum, typically by using model reduction techniques, are no longer valid. Such problems are faced in different physical simulations, for example welding path problems, resin transfer molding, or sheet compression molding, among others. In such situations, the interpolation of precomputed solutions at prescribed parameter values (built using either intrusive or non intrusive techniques) generates spurious numerical artifacts. In this work, we propose an alternative interpolation and simulation strategy by using physically-based morphing of spaces. The morphing will transform the uncompatibe physical domains of the problem’s solution into a compatible one, where an interpolation free of artifacts can be performed. Later on, an inverse transformation can be used to push-back the solution. Different relevant examples are illustrated in this work to motivate the use of the proposed method.
Similar content being viewed by others
References
Aguado JV, Borzacchiello D, Ghnatios C, Lebel F, Upadhyay R, Binetruy C, Chinesta F (2017) A simulation app based on reduced order modeling for manufacturing optimization of composite outlet guide vanes. Adv Model Simul Eng Sci 4(1): 1–26
Aguado JV, Borzacchiello D, Lopez E, Abisset-Chavanne E, Gonzalez D, Cueto E, Modeling F. Chinesta. (2017) From Microstructure Investigations to Multiscale Bridging the Gap, chapter New trends in computational mechanics : model order reduction, manifold learning and data-driven. Wiley, pp 1–20
Bordeu F, Ghnatios C, Boulze D, Carles B, Sireude D, Leygue A, Chinesta F (2015) Parametric 3d elastic solutions of beams involved in frame structures. Adv Aircraft Spacecraft Sci 2(3):233–248
Borzacchiello D, Aguado JV, Chinesta F (2019) Non-intrusive sparse subspace learning for parametrized problems. Arch Comput Methods Eng 26:303–326
Chinesta F, Cueto E, Abisset E, Duval JL, El Khaldi F (2020) Virtual, digital and hybrid twins. a new paradigm in data-based engineering and engineered data. Arch Comput Methods Eng 27:105–134
Chinesta F, Keunings R, Leygue A (2014) The proper generalized decomposition for advanced numerical simulations. Springer, Berlin
Cueto E, Ghnatios C, Chinesta F, Monte N, Sanchez F, Falco A (2014) Improving computational efficiency in lcm by using computational geometry and model reduction techniques. Key Eng Mater 611:339–343
Dohi T, Osaki S (1993) A note on portfolio optimization with path-dependent utility. Ann Oper Research 45(1):77–90
Sol H, Morren G, Bossuyt S (2008) 2d permeability tensor identification of fibrous reinforcements for rtm using an inverse method. Compos Part A 39:1530–1536
Ghnatios C, Montes N, Tertrais H, Duval J-L, Abisset-Chavanne E, Falco A, process F. Chinesta. (2019) Towards parametric rtm the interpolative mapping. AIP Conf Proc 100004:2113
Ghnatios C, Mathis CH, Simic R, Spencer ND, Chinesta F (2017) Modeling soft permeable matter with the proper generalized decomposition (pgd) approach, and verification by means of nanoindentation. Soft Matter 13:4482–4493
Giraldi L, Litvinenko A, Liu D, Matthies HG, Nouy A (2014) To be or not to be intrusive? the solution of parametric and stochastic equations — the “plain vanilla” galerkin case. SIAM J Sci Comput 36(6):A2720–A2744
Gonzalez D, Alfaro I, Quesada C, Cueto E, Chinesta F (2015) Computational Biomechanics for Medicine, chapter Vademecums for Real-Time Computational Surgery. Springer, pp 3–12
Huang Y, Zhao L, Woensel TV, Gross J-L (2017) Time-dependent vehicle routing problem with path flexibility. Transp Res Part B: Methodol 95:169–195
Ibanez R, Abisset-Chavanne E, Ammar A, Gonzalez D, Cueto E, Huerta A, Duval JL, Chinesta F (2018) A multi-dimensional data-driven sparse identification technique: the sparse proper generalized decomposition. Complexity 2018(5608286):11
Leon A, Mueller S, de Luca P, Said R, Duval JL, Chinesta F (2019) Non-intrusive proper generalized decomposition involving space and parameters: application to the mechanical modeling of 3d woven fabrics. Adv Model Simul Eng Sci 6(13):1–20
Lopez E, Gonzalez D, Aguado JV, Abisset-Chavanne E, Cueto E, Binetruy C, Chinesta F (2018) A manifold learning approach for integrated computational materials engineering. Arch Comput Method Engineering 5(1):59–68
Lu Y, Blal N, Gravouil A (2019) Datadriven hopgd based computational vademecum for welding parameter identification. Computational mechanics:1
Ojo OO, Taban E, Kaluc E (2018) Loop travel-path of fibre laser welded alclad aa2219-o alloy. J Mater Process Technol 251:118–126
Quaranta G, Ziane M, Haug E, Duval JL, Chinesta F (2019) A minimally-intrusive fully 3d separated plate formulation in computational structural mechanics. Adv Model Simul Eng Science 6(11):1–22
Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326
Tsay JJ, Arora JS (1990) Nonlinear structural design sensitivity analysis for path dependent problems. part 1 General theory. Comput Methods Appl Mech Eng 81(2):183–208
Tsiolakis V, Giacomini M, Sevilla R, Othmer C, Huerta A (2019) Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in openfoam. Open source arXiv:1906.05403, pp 1–35
Wang X, Yan Y, Gu X (2019) Spot welding robot path planning using intelligent algorithm. J Manuf Process 42:1–10
Zhu Z, Ghong J, Huang Y, Zhan Y, Gong M, Zhang L (2019) Experimental research on transition from scale 3d printing to full-size printing in construction. Construct Build Mater 208:350–360
Zou W, Conti M, Diez P, Auricchio F (2017) A nonintrusive proper generalized decomposition scheme with application in biomechanics. Int J Numer Methods Engineering 113:230–251
Zou X, Conti M, Diez P, Auricchio F (2017) Pgd for constrained parametric space with a non-intrusive implementation. In: International conference on adaptive modeling and simulation Admos 2017, Verbania, Italy. ECCOMAS
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ghnatios, C., Cueto, E., Falco, A. et al. Spurious-free interpolations for non-intrusive PGD-based parametric solutions: Application to composites forming processes. Int J Mater Form 14, 83–95 (2021). https://doi.org/10.1007/s12289-020-01561-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12289-020-01561-0