@article {2012,
	title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty},
	journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13},
	number = {SISSA;42/2012/M},
	year = {2012},
	publisher = {Cambridge University Press},
	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.},
	keywords = {shape optimization},
	url = {http://hdl.handle.net/1963/6337},
	author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza}
}
