Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
Thursday 9th February 2012
Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.
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 the worst-case in terms of recirculation effects is inferred to correspond to a residual strong orifice flow through near-complete occlusion. Worst-case optimization is performed to identify an anastomosis angle and a cuffed shape that are robust with respect to a possible range of residual flows. We also consider a reduced order modelling framework based on reduced basis methods in order to make the robust design problem computationally feasible. Keywords: optimal control, shape optimization, arterial bypass grafts, uncertainty, worst-case design, reduced order modelling, Navier-Stokes equations.