Research Interests and Activities
Group activities in a glance
Research Interests
- Numerical Analysis, Numerical Simulation, Scientific Computing
- Reduced Order Modelling and Methods: special focus on viscous flows and complex geometrical parametrizations
- Efficient Reduced-Basis Methods for parametrized PDEs and a posteriori error estimation
- Computational Fluid Dynamics (Aero-Naval-Mechanical Engineering, Blood Flows (Haemodynamics), Environmental Fluid Dynamics)
- Linear and Non-linear Elasticity
- Heat and Mass Transfer
- Potential Flows
- Fluid-Structure Interaction Problems
- Small Perturbation Theory in Fluid Mechanics and Linearized Shape design
- Parametrized Navier-Stokes Equations: Bifurcations and stability of flows
- Optimal Control, Flow Control based on PDEs
- Optimal Shape Design; Shape Optimization; Shape Reconstruction; Shape Registration
- Free-Form Deformations and Radial Basis Functions
- Uncertainty quantification, data assimilation, parameter estimation
- Optimization and Inverse Problems.
Books
- P. Benner, M. Ohlberger, A. Patera, G. Rozza, K. Urban, Model Reduction of Parametrized Systems. MS&A series, Vol.17, Springer, 2017
- J. S. Hesthaven, G. Rozza, B. Stamm. Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer, 2015
- A. Quarteroni and G. Rozza Eds, Reduced Order Methods for Modeling and Computational Reduction, MS&A series, Vol.9, Springer, 2013
- D. Ambrosi, A. Quarteroni and G. Rozza Eds, Modelling of Physiological Flows, MS&A series, Vol.5, Springer, 2011.
- Reduced Basis Book: A.T. Patera and G. Rozza, Reduced Basis Approximation and A-Posteriori Error Estimation for Parametrized PDEs, MIT-Pappalardo Graduate Monographs in Mechanical Engineering, (c) MIT, 2007 with Reduced Basis Software Library: rbMIT Software, (c) MIT 2006-15, Tecnology Licensing Office (case 12600); with COMSOL interface for rbMIT.
Past Projects (before 2014)
- Co-applicant in the SNSF (Swiss National Science Foundation) Projects:
– Reduced basis methods for the optimization of complex systems (2009-2011, 2×36 months Phd Students);
– Numerical simulation of a sailing boat: dynamics and shape optimization (2011-2013, 24 months Phd Student);
– Model reduction strategies for control, optimization and uncertainty quantification of parametrized systems (2012-2015, 48 months Phd student.) - Task Coordinator in the ERC-MathCard Project: Mathematical Modelling and Simulation of the Cardiovascular System, task on Efficient Methods for Control and Optimization (2009-2013).
- Real-Time Reliable Continuum Mechanics Computations: Parametrized PDEs and A-Posteriori Error Estimation for elliptic and parabolic, coercive and non-coercive problems with affine and non-affine parametrization (2006-2010) at MIT. Examples of worked problems.
- Collaborator for aerodynamic modeling and optimization for feasibility study of Solar Impulse Project (2003-2007) at EPFL.
Past Phd Thesis
- Stefano Lorenzi’s Phd thesis, Phd student at Politecnico di Milano under my co-supervision (2016) [collaboration with Energy Dpt].
- Federico Negri’s Phd thesis, Phd student at EPFL under my co-supervision (2015).
- Francesco Ballarin’s Phd thesis, Phd student at Politecnico di Milano under my co-supervision (2015) [collaboration with MOX]
- Alberto Sartori’s Phd thesis, Phd student at Politecnico di Milano under my co-supervision (2015) [collaboration with Energy Dpt].
- Peng Chen’s PhD thesis, Phd student at EPFL under my co-supervision (2014).
- Andrea Manzoni’s PhD thesis, Phd student at EPFL under my co-supervision (2012).
- Laura Iapichino’s PhD thesis, Phd student at EPFL under my co-supervision (2012).
Past Master Thesis
- Fabrizio Garotta, in preparation (2018, University of Pavia, Italy).
- Nirav Shah, Finite Element Reduced Basis (Proper Orthogonal Decomposition) Approach for Geometrically Parametrized Stokes Flow (2018, University of Stuttgart, Germany).
- Giulia Meglioli, (2017, Mathematical Engineering at Politecnico di Milano, Milan Italy).
- Giacomo Zuccarino, A Reduced order Variational Multiscale Method for parametric flows (2017, University of Trieste, Italy).
- Matteo Zancanaro, Hierarchical model reduction techniques for flows in parametric setting [link] (2017, Aerospace Engineering at Politecnico di Milano, Milan Italy).
- Maria Strazzullo, Reduced Order Methods for Optimal Control Problems: Application in Environmental Marine Sciences and Engineering [link] (2017, University of Trieste, Italy).
- Federico Pichi, Reduced order methods for parametric Von Karman equations in nonlinear structural mechanics [link] (2016, University of Rome, Italy).
- Saddam Hijazi, POD-Galerkin Reduced Order Model for the simulation of laminar and turbulent flows around a circular cylinder [link] (2016, University of L’Aquila, Italy).
- Luca Venturi, Weighted reduced order methods for parametrized PDEs in uncertainty quantification problems [link] (2016, University of Trieste, Italy).
- Davide Torlo, Stabilized reduced basis method for transport PDEs with random inputs [link] (2016, University of Trieste, Italy).
- Luca Valsecchi, Reduced order methods for PDEs : a comparison between proper orthogonal decomposition and proper generalized decomposition [link] (2016, Aerospace Engineering at Politecnico di Milano, Milan Italy).
- Alessandro D’Amario, A reduced-order inverse distance weighting technique for the efficient mesh-motion of deformable interfaces and moving shapes in computational problems [link] (2016, Aerospace Engineering at Politecnico di Milano, Milan Italy).
- Emiliano Cangemi, A POD reduced order method for parameterized Maxwell’s equations and applications [link] (2016, Aerospace Engineering at Politecnico di Milano, Milan Italy).
- Davide Forti, Comparison of Shape Parametrization Techniques for Fluid-Structure Interaction Problems [link] (2012, Aerospace Engineering at Politecnico di Milano).
- Paolo Pacciarini, Stabilized reduced basis method for parametrized advection-diffusion PDEs [link] (2012, Mathematics at University of Pavia).
- Federico Negri, Reduced basis method for parametrized optimal control problems governed by PDEs [link], (2011, Mathematical Engineering at Politecnico di Milano).
- Anwar Koshakji, Free Form Deformation Techniques for 3D Shape Optimization Problems [link] (2011, Aerospace Engineering at Politecnico di Milano).
- Alberto Trezzini, Reduced Basis Method for 3D problems governed by parametrized PDEs and applications [link] (2010, Aerospace Engineering at Politecnico di Milano).
- Fabrizio Gelsomino, Exploration and comparison of reduced order modelling techniques [link] (2009, Mathematical Engineering, EPFL).
- Claudia Gunther, Optimization of racing car components using reduced basis (potential, thermal and Stokes flow) [link] (2008, Applied Math, Aachen University).
- Roberto Milani, Reduced Basis and Optimization in Linear Elasticity [link] (2006, Aerospace Engineering at Politecnico di Milano)
- Annalisa Quaini, Optimal Control and Reduced Basis Techniques [link] (2005, Aerospace Engineering at Politecnico di Milano).
- Luca Dede’, Optimal Control and Mesh Adaptivity [link] (2004, Aerospace Engineering at Politecnico di Milano).
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Some posters on our research activities:
- year 2018: [1], [2], [3], [4], [5], [6] MoRePaS 2018
- year 2017: [1], [2], [3], [4], [5], [6] QUIET 2017
- year 2016: [1], [2], [3] IHP 2016
- year 2015: [1], [2], [3] MoRePaS 2015
- year 2013: [1]
- year 2012: [1], [2], [3], [4], [5], [6], [7], [8]
- year 2010: [1], [2]