01650nas a2200145   4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010701397       2014                        en  d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti  bSpringer3 aThis 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.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives00548nas a2200133   4500008004100000245009200041210006900133260001000202100001800212700002000230700002200250700002100272856012100293       2013                        en  d00aA Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics0 aReduced Computational and Geometrical Framework for Inverse Prob  bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/reduced-computational-and-geometrical-framework-inverse-problems-haemodynamics00568nas a2200133   4500008004100000245010500041210006900146260001000215100001800225700002000243700002200263700002100285856012800306       2013                        en  d00aA reduced-order strategy for solving inverse Bayesian identification problems in physiological flows0 areducedorder strategy for solving inverse Bayesian identificatio  bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/reduced-order-strategy-solving-inverse-bayesian-identification-problems-physiological00490nas a2200121   4500008004100000245007900041210006900120260001000189100001800199700002000217700002100237856011000258       2013                        en  d00aReduction Strategies for Shape Dependent Inverse Problems in Haemodynamics0 aReduction Strategies for Shape Dependent Inverse Problems in Hae  bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/reduction-strategies-shape-dependent-inverse-problems-haemodynamics01501nas a2200157   4500008004100000245010600041210006900147260003100216520095600247653002301203100001801226700002001244700002201264700002101286856003601307       2012                        en  d00aBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty0 aBoundary control and shape optimization for the robust design of  bCambridge University Press3 aWe review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.10ashape optimization1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttp://hdl.handle.net/1963/633701643nas a2200157   4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449       2012                        en  d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a  bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttp://hdl.handle.net/1963/6340