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

Toni Lassila; Andrea Manzoni; Alfio Quarteroni; Gianluigi Rozza

- Volume: 47, Issue: 4, page 1107-1131
- ISSN: 0764-583X

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topLassila, Toni, et al. "Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.4 (2013): 1107-1131. <http://eudml.org/doc/273170>.

@article{Lassila2013,

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, 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.},

author = {Lassila, Toni, Manzoni, Andrea, Quarteroni, Alfio, Rozza, Gianluigi},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {optimal control; shape optimization; arterial bypass grafts; uncertainty; worst-case design; reduced order modelling; Navier-Stokes equations},

language = {eng},

number = {4},

pages = {1107-1131},

publisher = {EDP-Sciences},

title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty},

url = {http://eudml.org/doc/273170},

volume = {47},

year = {2013},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 4

SP - 1107

EP - 1131

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, 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.

LA - eng

KW - optimal control; shape optimization; arterial bypass grafts; uncertainty; worst-case design; reduced order modelling; Navier-Stokes equations

UR - http://eudml.org/doc/273170

ER -

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