Issue |
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
Direct and inverse modeling of the cardiovascular and respiratory systems
|
|
---|---|---|
Page(s) | 1107 - 1131 | |
DOI | https://doi.org/10.1051/m2an/2012059 | |
Published online | 17 June 2013 |
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
1 Modelling and Scientific Computing,
Mathematics Institute of Computational Science and Engineering, École Polytechnique
Fédérale de Lausanne, Station 8, EPFL, 1015
Lausanne,
Switzerland.
toni.lassila@epfl.ch; alfio.quarteroni@epfl.ch
2 MOX, Modellistica e Calcolo
Scientifico, Dipartimento di Matematica F. Brioschi, Politecnico di
Milano, Piazza Leonardo da Vinci
32, 20133
Milano,
Italy.
alfio.quarteroni@polimi.it
3 Now at SISSA MathLab, International
School for Advanced Studies, Via
Bonomea 265, 34136
Trieste,
Italy.
andrea.manzoni@sissa.it; gianluigi.rozza@sissa.it
Received:
1
February
2012
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.
Mathematics Subject Classification: 35Q93 / 49Q10 / 76D05
Key words: Optimal control / shape optimization / arterial bypass grafts / uncertainty / worst-case design / reduced order modelling / Navier-Stokes equations
© EDP Sciences, SMAI, 2013
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