04337nas a2200145 4500008004100000020002200041245006600063210006300129260001900192520385200211100001704063700002404080700002104104856006604125 2024 eng d a978-3-031-55060-700aAn Online Stabilization Method for Parametrized Viscous Flows0 aOnline Stabilization Method for Parametrized Viscous Flows bSpringer, Cham3 a

The purpose of this work is to investigate the inf-sup stability of reduced basis (RB) method applied to parametric Stokes problem. While performing the Galerkin projection on the reduced space, the inf-sup approximation stability has always been a challenge for the RB community, even if the construction of reduced basis is done using a stable high-fidelity method. In this work we propose a new online stabilization strategy for RB approximation of parametrized Stokes problem. In this strategy, a stable high-fidelity method is used to construct the RB spaces, and then, online solution is improved by a post processing based on rectification method [81316]. This approach involves the computation of less expensive (but less consistent) FE approximation during the online stage and hence the improvement of online solutions using a RB-based rectification method. The consistency of the RB solution is also improved. We compare this approach with existing offline-online stabilization approach presented in our earlier work [2]. All the numerical simulations are carried out using RBniCS [414], an open-source reduced order modelling library, built on top of FEniCS [15].

1 aAli, Shafqat1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://link.springer.com/chapter/10.1007/978-3-031-55060-7_102085nas a2200253 4500008004100000020001400041245011800055210007300173260001600246300001400262490000800276520123400284653003301518653002501551653002001576653003601596653002801632100001701660700001901677700001801696700002401714700002101738856007201759 2023 eng d a0898-122100aAn optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations0 aoptimisation–based domain–decomposition reduced order model for  c2023/12/01/ a172 - 1890 v1513 a

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–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–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–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–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–decomposition algorithm.

10aComputational fluid dynamics10aDomain decomposition10aOptimal control10aProper orthogonal decomposition10aReduced order modelling1 aPrusak, Ivan1 aNonino, Monica1 aTorlo, Davide1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S089812212300424801519nas a2200145 4500008004100000245008600041210006900127300001200196490000600208520098300214100001701197700002401214700002101238856011401259 2023 eng d00aA reduced basis stabilization for the unsteady Stokes and Navier-Stokes equations0 areduced basis stabilization for the unsteady Stokes and NavierSt a180-2210 v13 a

In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order method. Therefore, in this work we aim at building a stabilized Reduced Basis (RB) method for the approximation of unsteady Stokes and Navier-Stokes problems in parametric reduced order settings. This work extends the results presented for parametrized steady Stokes and Navier-Stokes problems in a work of ours. We apply classical residual-based stabilization techniques for finite element methods in full order, and then the RB method is introduced as Galerkin projection onto RB space. We compare this approach with supremizer enrichment options through several numerical experiments. We are interested to (numerically) guarantee the parametrized reduced inf-sup condition and to reduce the online computational costs.

1 aAli, Shafqat1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://publires.unicatt.it/en/publications/a-reduced-basis-stabilization-for-the-unsteady-stokes-and-navier-03116nas a2200289 4500008004100000022001400041245012700055210006900182260001200251490000800263520211800271653003002389653001802419653002602437653002402463653004302487653003602530653003102566100001602597700002302613700002402636700002102660700002402681700002402705700002102729856007602750 2022 eng d a0168-874X00aFinite element based Model Order Reduction for parametrized one-way coupled steady state linear thermo-mechanical problems0 aFinite element based Model Order Reduction for parametrized onew c12/20220 v2123 a

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermo-mechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of reduced basis space. On the other hand, for the evaluation of the modal coefficients, we use two different methodologies: the one based on the Galerkin projection (G) and the other one based on Artificial Neural Network (ANN). We aim to compare POD-G and POD-ANN in terms of relevant features including errors and computational efficiency. In this context, both physical and geometrical parametrization are considered. We also carry out a validation of the Full Order Model (FOM) based on customized benchmarks in order to provide a complete computational pipeline. The framework proposed is applied to a relevant industrial problem related to the investigation of thermo-mechanical phenomena arising in blast furnace hearth walls.

10aArtificial Neural Network10aBlast furnace10aFinite Element Method10aGalerkin projection10aGeometric and physical parametrization10aProper orthogonal decomposition10aThermo-mechanical problems1 aShah, Nirav1 aGirfoglio, Michele1 aQuintela, Peregrina1 aRozza, Gianluigi1 aLengomin, Alejandro1 aBallarin, Francesco1 aBarral, Patricia uhttps://www.sciencedirect.com/science/article/abs/pii/S0168874X2200110X01169nas a2200133 4500008004100000245014700041210007100188520056100259100001900820700002400839700002100863700001600884856013500900 2022 eng d00aProjection based semi–implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid–Structure Interaction problems0 aProjection based semi–implicit partitioned Reduced Basis Method 3 a

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.

1 aNonino, Monica1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon uhttps://www.math.sissa.it/publication/projection-based-semi%E2%80%93implicit-partitioned-reduced-basis-method-non-parametrized-and00464nas a2200121 4500008004100000245006500041210006300106490000700169100002400176700002100200700002200221856009900243 2022 eng d00aSpace-time POD-Galerkin approach for parametric flow control0 aSpacetime PODGalerkin approach for parametric flow control0 v231 aBallarin, Francesco1 aRozza, Gianluigi1 aStrazzullo, Maria uhttps://www.math.sissa.it/publication/space-time-pod-galerkin-approach-parametric-flow-control00546nas a2200121 4500008004100000245009900041210006900140100002000209700002400229700002100253700002200274856012800296 2021 eng d00aAn artificial neural network approach to bifurcating phenomena in computational fluid dynamics0 aartificial neural network approach to bifurcating phenomena in c1 aPichi, Federico1 aBallarin, Francesco1 aRozza, Gianluigi1 aHesthaven, Jan, S uhttps://www.math.sissa.it/publication/artificial-neural-network-approach-bifurcating-phenomena-computational-fluid-dynamics00537nas a2200109 4500008004100000245012200041210006900163100002200232700002400254700002100278856012800299 2021 eng d00aA CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION0 aCERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC1 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/certified-reduced-basis-method-linear-parametrized-parabolic-optimal-control-problems00623nas a2200133 4500008004100000245014300041210006900184100002200253700002300275700002400298700001600322700002100338856013000359 2021 eng d00aConsistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows0 aConsistency of the full and reduced order models for EvolveFilte1 aStrazzullo, Maria1 aGirfoglio, Michele1 aBallarin, Francesco1 aIliescu, T.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/consistency-full-and-reduced-order-models-evolve-filter-relax-regularization-convection00750nas a2200217 4500008004100000245007000041210006800111300001600179490000700195100002300202700002400225700002400249700002400273700002300297700002100320700002100341700002200362700002000384700002400404856010400428 2021 eng d00aNon-intrusive data-driven ROM framework for hemodynamics problems0 aNonintrusive datadriven ROM framework for hemodynamics problems a1183–11910 v371 aGirfoglio, Michele1 aScandurra, Leonardo1 aBallarin, Francesco1 aInfantino, Giuseppe1 aNicolò, Francesca1 aMontalto, Andrea1 aRozza, Gianluigi1 aScrofani, Roberto1 aComisso, Marina1 aMusumeci, Francesco uhttps://www.math.sissa.it/publication/non-intrusive-data-driven-rom-framework-hemodynamics-problems00698nas a2200157 4500008004100000245015800041210006900199300001200268490000800280100001500288700002200303700002400325700002100349700001800370856015200388 2021 eng d00aA weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences0 aweighted PODreduction approach for parametrized PDEconstrained o a261-2760 v1021 aCarere, G.1 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi1 aStevenson, R. uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561&doi=10.1016%2fj.camwa.2021.10.020&partnerID=40&md5=cb57d59a6975a35315b2cf5d0e3a600100583nas a2200121 4500008004100000245014300041210007100184490000700255100002200262700002400284700002100308856013200329 2020 eng d00aPOD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation0 aPOD–Galerkin Model Order Reduction for Parametrized Time Depende0 v831 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-model-order-reduction-parametrized-time-dependent-linear-quadratic-002865nas a2200169 4500008004100000022001400041245009800055210006900153260002000222300001400242490000700256520229800263100001702561700002402578700002102602856007202623 2020 eng d a0898-122100aStabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations0 aStabilized reduced basis methods for parametrized steady Stokes  c1 December 2020 a2399-24160 v803 a

It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf–sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf–sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf–sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi–Pitkaranta, Franca–Hughes, streamline upwind Petrov–Galerkin, Galerkin Least Square. In the spirit of offline–online reduced basis computational splitting, two such options are proposed, namely offline-only stabilizationand offline–online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf–sup stability is still preserved at the reduced order level.

1 aAli, Shafqat1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S0898122120301231