TY - JOUR
T1 - Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
Y1 - 2014
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
AB - 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.
PB - Springer
U1 - 34923
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics
Y1 - 2013
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
PB - SISSA
U1 - 6571
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -
TY - RPRT
T1 - A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows
Y1 - 2013
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
PB - SISSA
U1 - 6555
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -
TY - RPRT
T1 - Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics
Y1 - 2013
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Gianluigi Rozza
PB - SISSA
U1 - 6554
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -
TY - JOUR
T1 - Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
JF - Mathematical Modelling and Numerical Analysis, in press, 2012-13
Y1 - 2012
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
KW - shape optimization
AB - We 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.
PB - Cambridge University Press
UR - http://hdl.handle.net/1963/6337
U1 - 6267
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -
TY - CHAP
T1 - Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs
T2 - Springer, Indam Series, Vol. 4, 2012
Y1 - 2012
A1 - Toni Lassila
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
KW - solution manifold
AB - The 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.
JF - Springer, Indam Series, Vol. 4, 2012
PB - Springer
UR - http://hdl.handle.net/1963/6340
U1 - 6270
U2 - Mathematics
U4 - 1
U5 - MAT/08 ANALISI NUMERICA
ER -