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Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

TitleBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
Publication TypeJournal Article
Year of Publication2012
AuthorsLassila, T, Manzoni, A, Quarteroni, A, Rozza, G
JournalMathematical Modelling and Numerical Analysis, in press, 2012-13
Keywordsshape optimization
Abstract

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.

URLhttp://hdl.handle.net/1963/6337

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