Publications

Below we provide a list of publications that use RBniCS.

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Year 2022

  1. Monica Nonino, Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. Projection based semi–implicit partitioned reduced basis method for non parametrized and parametrized fluid–structure interaction problems. Submitted, 2022.

Year 2021

  1. S. Ali, F. Ballarin, and G. Rozza. A reduced basis stabilization for the unsteady stokes and navier-stokes equations. Submitted, 2021.

  2. G. Carere, M. Strazzullo, F. Ballarin, G. Rozza, and R. Stevenson. A weighted pod-reduction approach for parametrized pde-constrained optimal control problems with random inputs and applications to environmental sciences. Computers & Mathematics with Applications, 102:261–276, 2021. doi:10.1016/j.camwa.2021.10.020.

  3. Alex Gorodetsky, John D. Jakeman, and Gianluca Geraci. MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources. Computational Mechanics, 68:741–758, 2021. doi:10.1007/s00466-021-02042-0.

  4. T. Kadeethum, F. Ballarin, and N. Bouklas. Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous galerkin approximation. GEM - International Journal on Geomathematics, 12:12, 2021. doi:10.1007/s13137-021-00180-4.

  5. T. Kadeethum, F. Ballarin, Y. Choi, D. O’Malley, H. Yoon, and N. Bouklas. Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques. Submitted, 2021.

  6. Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin, and Gianluigi Rozza. A reduced order cut finite element method for geometrically parametrized steady and unsteady navier-stokes problems. Computers & Mathematics with Applications, 2021. doi:10.1016/j.camwa.2021.07.016.

  7. Efthymios N. Karatzas and Gianluigi Rozza. A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements. Journal of Scientific Computing, 89:9, 2021. doi:10.1007/s10915-021-01623-8.

  8. Moaad Khamlich, Federico Pichi, and Gianluigi Rozza. Model order reduction for bifurcating phenomena in fluid-structure interaction problems. Submitted, 2021. URL: https://arxiv.org/abs/2110.06297.

  9. Son Hai Le, Shinseong Kang, Triet Minh Pham, and Kyunghoon Lee. Novel geometric parameterization scheme for the certified reduced basis analysis of a square unit cell. Journal of the Korean Society for Industrial and Applied Mathematics, 25(4):196–220, 2021. doi:10.12941/jksiam.2021.25.196.

  10. M. Nonino, F. Ballarin, and G. Rozza. A monolithic and a partitioned, reduced basis method for fluid-structure interaction problems. Fluids, 6(6):229, 2021. doi:10.3390/fluids6060229.

  11. F. Pichi, F. Ballarin, G. Rozza, and J. S. Hesthaven. An artificial neural network approach to bifurcating phenomena in computational fluid dynamics. Submitted, 2021.

  12. N. V. Shah, M. Girfoglio, P. Quintela, G. Rozza, A. Lengomin, F. Ballarin, and P. Barral. Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems. Submitted, 2021.

  13. M. Strazzullo, F. Ballarin, and G. Rozza. A certified reduced basis method for linear parametrized parabolic optimal control problems in space-time formulation. Submitted, 2021.

  14. M. Strazzullo, M. Girfoglio, F. Ballarin, T. Iliescu, and G. Rozza. Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows. Submitted, 2021.

  15. Maria Strazzullo. Model Order Reduction for Nonlinear and Time-Dependent Parametric Optimal Flow Control Problems. PhD thesis, Mathematical Analysis, Modelling, and Applications, SISSA, Italy, Sep. 2021. URL: http://hdl.handle.net/20.500.11767/124559.

  16. Maria Strazzullo, Zakia Zainib, Francesco Ballarin, and Gianluigi Rozza. Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences. In Fred J. Vermolen and Cornelis Vuik, editors, Numerical Mathematics and Advanced Applications ENUMATH 2019, 841–850. Springer International Publishing, 2021. doi:10.1007/978-3-030-55874-1_83.

  17. Zakia Zainib, Francesco Ballarin, Stephen Fremes, Piero Triverio, Laura Jiménez-Juan, and Gianluigi Rozza. Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation. International Journal for Numerical Methods in Biomedical Engineering, 37(12):e3367, 2021. doi:10.1002/cnm.3367.

  18. Matteo Zancanaro, Francesco Ballarin, Simona Perotto, and Gianluigi Rozza. Hierarchical model reduction techniques for flow modeling in a parametrized setting. Multiscale Modeling & Simulation, 19(1):267–293, 2021. doi:10.1137/19M1285330.

Year 2020

  1. Shafqat Ali, Francesco Ballarin, and Gianluigi Rozza. Stabilized reduced basis methods for parametrized steady stokes and navier-stokes equations. Computers & Mathematics with Applications, 80(11):2399–2416, 2020. doi:10.1016/j.camwa.2020.03.019.

  2. Francesco Ballarin, Gianluigi Rozza, and Maria Strazzullo. Space-time pod-galerkin approach for parametric flow control. In press, 2020. doi:10.1016/bs.hna.2021.12.009.

  3. Caterina Bigoni. Numerical methods for structural anomaly detection using model order reduction and data-driven techniques. PhD thesis, Mathematics, EPFL, Lausanne, Switzerland, Sep. 2020. URL: https://infoscience.epfl.ch/record/279985.

  4. Caterina Bigoni and Jan S. Hesthaven. Simulation-based anomaly detection and damage localization: an application to structural health monitoring. Computer Methods in Applied Mechanics and Engineering, 363:112896, 2020. doi:10.1016/j.cma.2020.112896.

  5. Saddam Hijazi, Shafqat Ali, Giovanni Stabile, Francesco Ballarin, and Gianluigi Rozza. The effort of increasing Reynolds number in projection-based reduced order methods: from laminar to turbulent flows. In Harald van Brummelen, Alessandro Corsini, Simona Perotto, and Gianluigi Rozza, editors, Numerical Methods for Flows: FEF 2017 Selected Contributions, pages 245–264. Springer International Publishing, 2020. doi:10.1007/978-3-030-30705-9_22.

  6. Efthymios N. Karatzas, Francesco Ballarin, and Gianluigi Rozza. Projection-based reduced order models for a cut finite element method in parametrized domains. Computers & Mathematics with Applications, 79(3):833–851, 2020. doi:10.1016/j.camwa.2019.08.003.

  7. Dillon Victor Paul Montag. Numerical approximation of inverse problems for pdes via neural network augmentation. Master’s thesis, Mathematical Engineering, Politecnico di Milano, Italy, Oct. 2020. URL: https://www.politesi.polimi.it/bitstream/10589/166565/3/Montag_Thesis.pdf.

  8. Monica Nonino. On the application of the Reduced Basis Method to Fluid-Structure Interaction problems. PhD thesis, Mathematical Analysis, Modelling, and Applications, SISSA, Italy, Sep. 2020. URL: http://hdl.handle.net/20.500.11767/114309.

  9. Federico Pichi. Reduced order models for parametric bifurcation problems in nonlinear PDEs. PhD thesis, Mathematical Analysis, Modelling, and Applications, SISSA, Italy, Sep. 2020. URL: http://hdl.handle.net/20.500.11767/114329.

  10. Federico Pichi, Annalisa Quaini, and Gianluigi Rozza. A reduced order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation. SIAM Journal on Scientific Computing, 42(5):B1115–B1135, 2020. doi:10.1137/20M1313106.

  11. Federico Pichi, Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. Driving bifurcating parametrized nonlinear pdes by optimal control strategies: application to navier-stokes equations with model order reduction. Submitted, 2020.

  12. Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. POD–Galerkin model order reduction for parametrized time dependent linear quadratic optimal control problems in saddle point formulation. Journal of Scientific Computing, 83(3):55, 2020. doi:10.1007/s10915-020-01232-x.

  13. Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. POD-Galerkin model order reduction for parametrized nonlinear time dependent optimal flow control: an application to shallow water equations. Submitted, 2020. URL: https://arxiv.org/abs/2003.09695.

Year 2019

  1. Davide Baroli and Andreas Zilian. Model order reduction applied to ALE-fluid dynamics. PAMM, 19(1):e201900437, 2019. doi:10.1002/pamm.201900437.

  2. Julien Genovese. Reduced order methods for uncertainty quantification in computational fluid dynamics. Master’s thesis, Mathematical Engineering, Politecnico di Torino, Italy, Oct. 2019. URL: https://webthesis.biblio.polito.it/11989/1/tesi.pdf.

  3. M. Gunzburger, T. Iliescu, M. Mohebujjaman, and M. Schneier. An evolve-filter-relax stabilized reduced order stochastic collocation method for the time-dependent navier–stokes equations. SIAM/ASA Journal on Uncertainty Quantification, 7(4):1162–1184, 2019. doi:10.1137/18M1221618.

  4. Max Gunzburger, Michael Schneier, Clayton Webster, and Guannan Zhang. An improved discrete least-squares/reduced-basis method for parameterized elliptic pdes. Journal of Scientific Computing, 81(1):76–91, 2019. doi:10.1007/s10915-018-0661-6.

  5. Monica Nonino, Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. Overcoming slowly decaying kolmogorov n-width by transport maps: application to model order reduction of fluid dynamics and fluid–structure interaction problems. Submitted, 2019. URL: https://arxiv.org/abs/1911.06598.

  6. Federico Pichi and Gianluigi Rozza. Reduced basis approaches for parametrized bifurcation problems held by non-linear von kármán equations. Journal of Scientific Computing, 81(1):112–135, 2019. doi:10.1007/s10915-019-01003-3.

  7. Giovanni Stabile, Francesco Ballarin, Giacomo Zuccarino, and Gianluigi Rozza. A reduced order variational multiscale approach for turbulent flows. Advances in Computational Mathematics, 45(5):2349–2368, 2019. doi:10.1007/s10444-019-09712-x.

  8. Luca Venturi, Francesco Ballarin, and Gianluigi Rozza. A weighted POD method for elliptic PDEs with random inputs. Journal of Scientific Computing, 81(1):136–153, 2019. doi:10.1007/s10915-018-0830-7.

  9. Luca Venturi, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza. Weighted reduced order methods for parametrized partial differential equations with random inputs. In Flavio Canavero, editor, Uncertainty Modeling for Engineering Applications, pages 27–40. Springer International Publishing, 2019. doi:10.1007/978-3-030-04870-9_2.

  10. Zakia Zainib. Reduced order parametrized viscous optimal flow control problems and applications in coronary artery bypass grafts with patient-specific geometrical reconstruction and data assimilation. PhD thesis, Mathematical Analysis, Modelling, and Applications, SISSA, Italy, Sep. 2019. URL: http://hdl.handle.net/20.500.11767/103036.

Year 2018

  1. Shafqat Ali. Stabilized reduced basis methods for the approximation of parametrized viscous flows. PhD thesis, Mathematical Analysis, Modelling, and Applications, SISSA, Italy, Sep. 2018. URL: http://hdl.handle.net/20.500.11767/82794.

  2. Dinh Bao Phuong Huynh, Federico Pichi, and Gianluigi Rozza. Reduced basis approximation and a posteriori error estimation: applications to elasticity problems in several parametric settings, pages 203–247. Volume 15. Springer International Publishing, 2018. doi:10.1007/978-3-319-94676-4_8.

  3. Maria Strazzullo, Francesco Ballarin, Renzo Mosetti, and Gianluigi Rozza. Model reduction for parametrized optimal control problems in environmental marine sciences and engineering. SIAM Journal on Scientific Computing, 40(4):B1055–B1079, 2018. doi:10.1137/17M1150591.

  4. Marco Tezzele, Francesco Ballarin, and Gianluigi Rozza. Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods. In Daniele Boffi, Luca F. Pavarino, Gianluigi Rozza, Simone Scacchi, and Christian Vergara, editors, Mathematical and Numerical Modeling of the Cardiovascular System and Applications, pages 185–207. Springer International Publishing, Cham, 2018. doi:10.1007/978-3-319-96649-6_8.

  5. Davide Torlo, Francesco Ballarin, and Gianluigi Rozza. Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs. SIAM/ASA Journal on Uncertainty Quantification, 6(4):1475–1502, 2018. doi:10.1137/17M1163517.

Year 2017

  1. Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. Reduced-order semi-implicit schemes for fluid-structure interaction problems. In Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, and Karsten Urban, editors, Model Reduction of Parametrized Systems, volume 17, pages 149–167. Springer International Publishing, 2017. doi:10.1007/978-3-319-58786-8_10.

  2. Giulia Meglioli. Comparison of model order reduction approaches in parametrized optimal control problems. Master’s thesis, Mathematical Engineering, Politecnico di Milano, Italy, Dec. 2017. URL: http://hdl.handle.net/10589/137279.

  3. Maria Strazzullo. Reduced order methods for parametric optimal flow control problems: applications in environmental and marine sciences and engineering. Master’s thesis, Mathematics, University of Trieste, Italy, Mar. 2017. URL: http://people.sissa.it/~grozza/wp-content/uploads/2018/03/Strazzullo.pdf.

  4. Matteo Zancanaro. Hierarchical model reduction techniques for flows in a parametric setting. Master’s thesis, Aeronautical Engineering, Politecnico di Milano, Italy, Apr. 2017. URL: https://www.politesi.polimi.it/handle/10589/134020.

Year 2016

  1. Davide Torlo. Stabilized reduced basis method for transport PDEs with random inputs. Master’s thesis, Mathematics, University of Trieste, Italy, Jul. 2016. URL: http://people.sissa.it/~grozza/wp-content/uploads/2018/03/torlo.pdf.

  2. Luca Venturi. Weighted reduced order methods for parametrized PDEs in uncertainty quantification problems. Master’s thesis, Mathematics, University of Trieste, Italy, Jul. 2016. URL: http://people.sissa.it/~grozza/wp-content/uploads/2018/03/venturi.pdf.

Year 2015

  1. Jan S. Hesthaven, Gianluigi Rozza, and Benjamin Stamm. Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer International Publishing, 2015. ISBN 978-3-319-22469-5.