Reduced Order Modelling in Computational Mechanics: state of the art, challenges and applications
Gianluigi Rozza, SISSA
07 March 2023
We provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and we focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in offline-online Computational Fluid Dynamics (CFD). Efficient parametrisations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: (i) a better use of stable high fidelity methods, to enhance the quality of the reduced model too, and allowing to incorporate turbulence models and increasing the Reynolds number; (ii) more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, as well as the dimension of online systems; (iii) the improvements of the certification of accuracy based on residual based error bounds and of the stability factors, as well as the guarantee of the stability of the approximation with proper space enrichments. All the previous aspects are quite relevant in CFD problems to focus on real time simulations for complex parametric industrial, environmental and biomedical flow problems, or even in a control flow setting with data assimilation and uncertainty quantification. Model flow problems will focus on few benchmarks, as well as on simple fluid-structure interaction problems and shape optimisation applied to some industrial problems of interest.
About the speaker
He is a member of the recently created (2010) SISSA mathLab laboratory. Research Affiliate at MIT since 2008. He is lecturer in the SISSA doctoral program in Mathematical Analysis, Modelling and Applications since 2013, in the SISSA-ICTP master in High Performance Computing and at the master degree in Mathematics of University of Trieste since 2014. Author of more than 90 scientific publications (editor of two books and author of two books). Co-advisor of 14 master thesis since 2004, co-director of 7 PhD theses (4 at EPFL and 3 at Politecnico di Milano) since 2009. PI/coPI of 4 projects at FNS, Swiss National Science Foundation (2006-2012), task coordinator for an ERC project (2009-2013), coordinator of three INDAM-GNCS projects (2015-2017), Principal Investigator of an ERC Consolidator Grant (H2020) and local PI of H2020 ITN ROMSOC project for European Industrial Doctorate. Within SISSA mathLab he is responsible of UBE (Under Water Blue Efficiency project), SOPHYA and PRELICA projects, within the technological cluster MARE tc FVG (PAR-FSC and POR-FESR FVG regional projects), co-responsible of TRIM project (within the Technological Cluster Trasporti 2020), and responsible of industrial projects with local industries worldwide leaders, such as Danieli, Bormioli and Fincantieri. Winner of the 2004 Bill Morton CFD Prize (Oxford University); MIT fellowship for his research in CFD (2005); ECCOMAS Award 2006 for the best Phd Thesis in applied sciences and engineering. Springer Computational Science and Engineering prize in 2009 for the development of a reduced basis software library for computational mechanics problems (rbMIT), recipient of the 2014 ECCOMAS young investigator Jacques Louis Lions Award in Computational Mathematics for researcher under 40 years old. He has been invited speaker at more than 60 national and international conferences or workshops. He has organized national and international workshops and served in the scientific and organizing committee of some conferences, in particular SIAM CSE13 in Boston, MoRePaS 2015 at SISSA, IACM FEF 2017 in Rome, QUIET 2017 at SISSA. He is in the management committee for EU-MORNET COST (Model Reduction Network, Cooperation in Science and Technology of European Union), representing Italy, and chair of one workgroup (methodological developments). He is associate editor of SIAM/ASA Journal of Uncertainty Quantification since 2013, SIAM Journal of Numerical Analysis since 2015, Computing and Visualization in Science since 2016. He is in the scientific committee of ARPA FVG, Friuli Venezia Giulia Agency for Environment Protection. In the quater 2018-2021 he is serving in the Applied Mathematics Committee of European Mathematical Society (EMS).