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

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, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady Navier-Stokes equations in 2D 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. The results obtained in 2D are compared with simulations in a 3D geometry but without model reduction or the robust framework.


Published in:
Mathematical Modelling and Numerical Analysis, 47, 4, 1107-1131
Year:
2013
Publisher:
Les Ulis Cedex A, EDP Sciences
ISSN:
0764-583X
Keywords:
Note:
EPFL MATHICSE Report 03.2012
Laboratories:




 Record created 2012-10-17, last modified 2018-03-17

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