Publications

Below we provide a list of publications that use RBniCS.

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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, 2020. doi:10.1016/j.camwa.2020.03.019.

  2. 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.

  3. 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.

  4. Alex Gorodetsky, John D. Jakeman, and Gianluca Geraci. MFNets: learning network representations for multifidelity surrogate modeling. Submitted, 2020. URL: https://arxiv.org/abs/2008.02672.

  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. Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin, and Gianluigi Rozza. A reduced order cut finite element method for geometrically parameterized steady and unsteady Navier-Stokes problems. Submitted, 2020. URL: https://arxiv.org/abs/2010.04953.

  8. 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. Submitted, 2020. URL: https://arxiv.org/abs/2009.01596.

  9. 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.

  10. 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.

  11. Federico Pichi, Annalisa Quaini, and Gianluigi Rozza. A reduced order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation. Submitted, 2020. URL: https://arxiv.org/abs/1907.07082.

  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.

  14. 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, 2020. doi:10.1002/cnm.3367.

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. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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. Submitted, 2019. URL: https://arxiv.org/abs/1912.07886.

  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.

  11. Matteo Zancanaro, Francesco Ballarin, Simona Perotto, and Gianluigi Rozza. Hierarchical model reduction techniques for flow modeling in a parametrized setting. Submitted, 2019. URL: https://arxiv.org/abs/1909.01668.

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.