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 -