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.
Mots clés : optimal control, shape optimization, arterial bypass grafts, uncertainty, worst-case design, reduced order modelling, Navier-Stokes equations
@article{M2AN_2013__47_4_1107_0,
author = {Lassila, Toni and Manzoni, Andrea and Quarteroni, Alfio and Rozza, Gianluigi},
title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1107--1131},
publisher = {EDP-Sciences},
volume = {47},
number = {4},
year = {2013},
doi = {10.1051/m2an/2012059},
mrnumber = {3082291},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012059/}
}
TY - JOUR AU - Lassila, Toni AU - Manzoni, Andrea AU - Quarteroni, Alfio AU - Rozza, Gianluigi TI - Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1107 EP - 1131 VL - 47 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012059/ DO - 10.1051/m2an/2012059 LA - en ID - M2AN_2013__47_4_1107_0 ER -
%0 Journal Article %A Lassila, Toni %A Manzoni, Andrea %A Quarteroni, Alfio %A Rozza, Gianluigi %T Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1107-1131 %V 47 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012059/ %R 10.1051/m2an/2012059 %G en %F M2AN_2013__47_4_1107_0
Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi. Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 4, pp. 1107-1131. doi : 10.1051/m2an/2012059. http://www.numdam.org/articles/10.1051/m2an/2012059/
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