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Erschienen in:
Effect of Load Path on Parameter Identification for Plasticity Models Using Bayesian Methods Kapitel lesen Erstes Kapitel lesen

2020 | OriginalPaper | Buchkapitel

Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains

verfasst von : Fabrizio Garotta, Nicola Demo, Marco Tezzele, Massimo Carraturo, Alessandro Reali, Gianluigi Rozza

Erschienen in: Quantification of Uncertainty: Improving Efficiency and Technology

Verlag: Springer International Publishing

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Abstract

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

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Vorheriges Kapitel Analysis of Probabilistic and Parametric Reduced Order Models
Nächstes Kapitel Uncertainty Quantification Applied to Hemodynamic Simulations of Thoracic Aorta Aneurysms: Sensitivity to Inlet Conditions
Literatur
1.
Ballarin, F., Faggiano, E., Ippolito, S., Manzoni, A., Quarteroni, A., Rozza, G., Scrofani, R.: Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD–Galerkin method and a vascular shape parametrization. J. Comput. Phys. 315, 609–628 (2016)MathSciNetMATH
2.
Ballarin, F., Faggiano, E., Manzoni, A., Quarteroni, A., Rozza, G., Ippolito, S., Antona, C., Scrofani, R.: Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomech. Model. Mechanobiol. 16(4), 1373–1399 (2017)MATH
3.
Ballarin, F., D’Amario, A., Perotto, S., Rozza, G.: A POD-selective inverse distance weighting method for fast parametrized shape morphing. Int. J. Num. Meth. Eng. 117, 860–884 (2019)MathSciNet
4.
Baroli, D., Cova, C.M., Perotto, S., Sala, L., Veneziani, A.: Hi-POD solution of parametrized fluid dynamics problems: Preliminary results. In: Model Reduction of Parametrized Systems, pp. 235–254. Springer, Berlin (2017)
5.
Buhmann, M.D.: Radial Basis Functions: Theory and Implementations, Vol. 12. Cambridge University Press, Cambridge (2003)MATH
6.
7.
8.
Chinesta, F., Keunings, R., Leygue, A.: The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer. Springer Science & Business Media, Berlin (2013)MATH
9.
10.
Christensen, E.A., Brøns, M., Sørensen, J.N.: Evaluation of proper orthogonal decomposition–based decomposition techniques applied to parameter-dependent nonturbulent flows. SIAM J. Sci. Comput. 21(4), 1419–1434 (1999)MathSciNetMATH
11.
Cottrell, J.A., Hughes, T.J., Reali, A.: Studies of refinement and continuity in isogeometric structural analysis. Comput. Method. Appl. Mech. Eng. 196(41–44), 4160–4183 (2007)MATH
12.
Cottrell, J.A., Hughes, T.J., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Hoboken (2009)MATH
13.
Cox Maurice, G.: The numerical evaluation of B-splines. IMA J. Appl. Math. 10(2), 134–149 (1972)MathSciNetMATH
14.
15.
De Falco, C., Reali, A., Vázquez, R.: GeoPDEs: a research tool for isogeometric analysis of PDEs. Adv. Eng. Softw. 42(12), 1020–1034 (2011)MATH
16.
Demo, N., Tezzele, M., Gustin, G., Lavini, G., Rozza, G.: Shape optimization by means of proper orthogonal decomposition and dynamic mode decomposition. In: Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research, pp. 212–219. IOS Press, Amsterdam (2018). https://​doi.​org/​10.​3233/​978-1-61499-870-9-212
17.
Demo, N., Tezzele, M., Mola, A., Rozza, G.: An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment. In: The 28th International Ocean and Polar Engineering Conference, ISOPE (2018)
18.
19.
20.
Forti, D., Rozza, G.: Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems. Int. J. Comput. Fluid Dyn. 28(3–4), 158–169 (2014)MathSciNet
21.
Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Math. Model. Numer. Anal. 42(2), 277–302 (2008)MathSciNetMATH
22.
23.
Hughes, T.J., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Method. Appl. Mech. Eng. 194(39–41), 4135–4195 (2005)MathSciNetMATH
24.
Lassila, T., Rozza, G.: Parametric free-form shape design with PDE models and reduced basis method. Comput. Method. Appl. Mech. Eng. 199(23–24), 1583–1592 (2010)MathSciNetMATH
25.
Manzoni, A., Quarteroni, A., Rozza, G.: Model reduction techniques for fast blood flow simulation in parametrized geometries. Int. J. Numer. Meth. Bio. Eng. 28(6–7), 604–625 (2012)MathSciNet
26.
Manzoni, A., Salmoiraghi, F., Heltai, L.: Reduced basis isogeometric methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils. Comput. Method. Appl. Mech. Eng. 284, 1147–1180 (2015)MathSciNetMATH
27.
Morris, A., Allen, C., Rendall, T.: CFD-based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation. Int. J. Numer. Method. Fluids 58(8), 827–860 (2008)MathSciNetMATH
28.
Perotto, S., Ern, A., Veneziani, A.: Hierarchical local model reduction for elliptic problems: a domain decomposition approach. Multiscale Model. Simul. 8(4), 1102–1127 (2010)MathSciNetMATH
29.
Perotto, S., Reali, A., Rusconi, P., Veneziani, A.: Higamod: a hierarchical isogeometric approach for model reduction in curved pipes. Comput. Fluids 142, 21–29 (2017)MathSciNetMATH
30.
Peterson, J.S.: The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10(4), 777–786 (1989)MathSciNetMATH
31.
Quarteroni, A.: Numerical Models for Differential Problems, vol. 2. Springer, Berlin (2009)MATH
32.
Quarteroni, A., Rozza, G.: Reduced Order Methods for Modeling and Computational Reduction. MS&A – Modeling, Simulation and Applications, vol. 9. Springer, Berlin (2014)
33.
Quarteroni, A., Rozza, G., Manzoni, A.: Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Ind. 1(1), 3 (2011)MathSciNetMATH
34.
Ripepi, M., Verveld, M., Karcher, N., Franz, T., Abu-Zurayk, M., Görtz, S., Kier, T.: Reduced-order models for aerodynamic applications, loads and MDO. CEAS Aeronaut. J. 9(1), 171–193 (2018)
35.
Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Meth. Eng.15(3), 1 (2007)
36.
Rozza, G., Lassila, T., Manzoni, A.: Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. In: Spectral and High Order Methods for Partial Differential Equations, pp. 307–315. Springer, Berlin (2011)
37.
Rozza, G., Malik, M.H., Demo, N., Tezzele, M., Girfoglio, M., Stabile, G., Mola, A.: Advances in reduced order methods for parametric industrial problems in computational fluid dynamics. In: Owen, R., de Borst, R., Reese, J., Chris, P. (eds.) ECCOMAS ECFD 7 - Proceedings of 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7), Glasgow, pp. 59–76 (2018)
38.
Salmoiraghi, F., Ballarin, F., Corsi, G., Mola, A., Tezzele, M., Rozza, G.: Advances in Geometrical Parametrization and Reduced Order Models and Methods for Computational Fluid Dynamics Problems in Applied Sciences and Engineering: Overview and Perspectives. ECCOMAS, Crete (2016). https://​doi.​org/​10.​7712/​100016.​1867.​8680
39.
Salmoiraghi, F., Ballarin, F., Heltai, L., Rozza, G.: Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes. Adv. Model. Simul. Eng. Sci. 3(1), 21 (2016)
40.
41.
42.
Sederberg, T., Parry, S.: Free-form deformation of solid geometric models. In: Proceedings of SIGGRAPH - Special Interest Group on Graphics and Interactive Techniques. SIGGRAPH, pp. 151–159. (1986)
43.
Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings-1968 ACM National Conference, pp. 517–524. ACM, New York (1968)
44.
Sieger, D., Menzel, S., Botsch, M.: On shape deformation techniques for simulation-based design optimization. In: Perotto, S., Formaggia, L. (eds.) New Challenges in Grid Generation and Adaptivity for Scientific Computing, pp. 281–303. Springer, Berlin (2015)MATH
45.
Sirovich, L.: Turbulence and the dynamics of coherent structures. I. coherent structures. Q. Appl. Math. 45(3), 561–571 (1987)MathSciNetMATH
46.
47.
48.
Tezzele, M., Ballarin, F., Rozza, G.: Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods. In: Mathematical and Numerical Modeling of the Cardiovascular System and Applications. SEMA SIMAI Springer Series, vol. 16. Springer, Berlin (2018). https://​doi.​org/​10.​1007/​978-3-319-96649-6_​8
49.
Tezzele, M., Demo, N., Gadalla, M., Mola, A., Rozza, G.: Model order reduction by means of active subspaces and dynamic mode decomposition for parametric hull shape design hydrodynamics. In: Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research, pp. 569–576. IOS Press, Amsterdam (2018). https://​doi.​org/​10.​3233/​978-1-61499-870-9-569
50.
51.
52.
53.
Volkwein, S.: Proper orthogonal decomposition: theory and reduced-order modelling. Lect. Notes Univ. Konstanz 4(4), 1–29 (2013)MathSciNet
54.
Witteveen, J., Bijl, H.: Explicit mesh deformation using inverse distance weighting interpolation. In: 19th AIAA Computational Fluid Dynamics. AIAA (2009)
55.
Zhu, S., Dedè, L., Quarteroni, A.: Isogeometric analysis and proper orthogonal decomposition for parabolic problems. Numer. Math. 135(2), 333–370 (2017)MathSciNetMATH
Metadaten
Titel
Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized Domains
verfasst von
Fabrizio Garotta
Nicola Demo
Marco Tezzele
Massimo Carraturo
Alessandro Reali
Gianluigi Rozza
Copyright-Jahr
2020
Buch
Quantification of Uncertainty: Improving Efficiency and Technology

Print ISBN: 978-3-030-48720-1

Electronic ISBN: 978-3-030-48721-8

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-48721-8_7