Research Interests and Activities
- 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 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.
- 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.
- 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
Current students: Emiliano Cangemi (Politecnico di Milano, Aero.Eng), Alessandro D’Amario (Politecnico di Milano, Aero.Eng), Luca Valsecchi (Politecnico di Milano, Aero.Eng), Davide Torlo (UniTS), Luca Venturi (UniTS).
- 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).
Some posters on my research activity:
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