This chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

%B Encyclopedia of Computational Mechanics Second Edition %I John Wiley & Sons %P 1-36 %G eng %& Model Reduction Methods %R 10.1002/9781119176817.ecm2110 %0 Book Section %B Wiley Encyclopedia of Computational Mechanics, 2016 %D 2016 %T Model Order Reduction: a survey %A Francisco Chinesta %A Antonio Huerta %A Gianluigi Rozza %A Karen Willcox %B Wiley Encyclopedia of Computational Mechanics, 2016 %I Wiley %G en %U http://urania.sissa.it/xmlui/handle/1963/35194 %1 35470 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-27T00:41:12Z No. of bitstreams: 1 ECM_MOR.pdf: 746542 bytes, checksum: 93d6252fe8a175c4378b96bd4192712c (MD5) %0 Journal Article %J Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %D 2016 %T A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well. %B Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %I Elsevier %V 87 %P 208 %G en %U http://urania.sissa.it/xmlui/handle/1963/35191 %1 35471 %2 Mathematics %4 1 %# MAT/08 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-06-16T11:08:05Z (GMT) No. of bitstreams: 0 %& 198 %R doi:10.1016/j.anucene.2015.09.002 %0 Journal Article %J Advances in Computational Mathematics %D 2015 %T Model order reduction of parameterized systems (MoRePaS): Preface to the special issue of advances in computational mathematics %A Peter Benner %A Mario Ohlberger %A Anthony Patera %A Gianluigi Rozza %A Sorensen, D.C. %A Karsten Urban %B Advances in Computational Mathematics %V 41 %P 955–960 %G eng %R 10.1007/s10444-015-9443-y %0 Journal Article %J Numerische Mathematik, (2015), 36 p. Article in Press %D 2015 %T Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations %A Gianluigi Rozza %A Peng Chen %A Alfio Quarteroni %X In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems. %B Numerische Mathematik, (2015), 36 p. Article in Press %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34491 %1 34680 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-08-25T23:32:48Z No. of bitstreams: 1 06August2014_wRBM4SOC.pdf: 531409 bytes, checksum: d1a2f18b0de17872919c430779f7180c (MD5) %R 10.1007/s00211-015-0743-4 %0 Journal Article %D 2014 %T Model Order Reduction in Fluid Dynamics: Challenges and Perspectives %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %X This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. %I Springer %G en %1 34923 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T15:11:51Z No. of bitstreams: 1 preprint2014.pdf: 287014 bytes, checksum: b195410aa3f63643829ed25f1adb6520 (MD5) %R 10.1007/978-3-319-02090-7_9