@article {2023, title = {An optimisation{\textendash}based domain{\textendash}decomposition reduced order model for the incompressible Navier-Stokes equations}, volume = {151}, year = {2023}, month = {2023/12/01/}, pages = {172 - 189}, abstract = {

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain{\textendash}decomposition (DD) methods and reduced{\textendash}order modelling (ROM). In particular, we consider an optimisation{\textendash}based domain{\textendash}decomposition algorithm for the parameter{\textendash}dependent stationary incompressible Navier{\textendash}Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal{\textendash}control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward{\textendash}facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain{\textendash}decomposition algorithm.

}, keywords = {Computational fluid dynamics, Domain decomposition, Optimal control, Proper orthogonal decomposition, Reduced order modelling}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122123004248}, author = {Ivan Prusak and Monica Nonino and Davide Torlo and Francesco Ballarin and Gianluigi Rozza} } @booklet {2022, title = {Projection based semi{\textendash}implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid{\textendash}Structure Interaction problems}, year = {2022}, abstract = {

The goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

}, author = {Monica Nonino and Francesco Ballarin and Gianluigi Rozza and Yvon Maday} } @unpublished {2021, title = {An artificial neural network approach to bifurcating phenomena in computational fluid dynamics}, year = {2021}, author = {Federico Pichi and Francesco Ballarin and Gianluigi Rozza and Jan S Hesthaven} } @unpublished {2021, title = {A CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION}, year = {2021}, author = {Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza} } @unpublished {2021, title = {Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows}, year = {2021}, author = {Maria Strazzullo and Michele Girfoglio and Francesco Ballarin and T. Iliescu and Gianluigi Rozza} } @article {2021, title = {Non-intrusive data-driven ROM framework for hemodynamics problems}, journal = {Acta Mechanica Sinica}, volume = {37}, year = {2021}, pages = {1183{\textendash}1191}, author = {Michele Girfoglio and Leonardo Scandurra and Francesco Ballarin and Giuseppe Infantino and Francesca Nicol{\`o} and Andrea Montalto and Gianluigi Rozza and Roberto Scrofani and Marina Comisso and Francesco Musumeci} } @article {2021, title = {A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences}, journal = {Computers and Mathematics with Applications}, volume = {102}, year = {2021}, pages = {261-276}, doi = {10.1016/j.camwa.2021.10.020}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561\&doi=10.1016\%2fj.camwa.2021.10.020\&partnerID=40\&md5=cb57d59a6975a35315b2cf5d0e3a6001}, author = {G. Carere and Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza and R. Stevenson} }