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On optimization, control and shape design of an arterial bypass
Author(s) -
Rozza Gianluigi
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.888
Subject(s) - shape optimization , mathematics , optimal control , sensitivity (control systems) , mathematical optimization , boundary (topology) , computational fluid dynamics , taylor series , domain (mathematical analysis) , control theory (sociology) , computer science , mathematical analysis , engineering , mechanics , control (management) , finite element method , physics , structural engineering , electronic engineering , artificial intelligence
Multi‐level geometrical approaches in the study of aorto‐coronaric bypass anastomoses configurations are discussed. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the incoming branch of the bypass (the toe) into the coronary. At this level, two possible options are available in shape design: one implements local boundary variations in computational domain, the other, based on the theory of small perturbations, makes use of a linearized design in a reference domain. At a coarser level, reduced basis methodologies based on parametrized partial differential equations are developed to provide (a) a sensitivity analysis for geometrical quantities of interest in bypass configurations and (b) rapid and reliable prediction of integral functional outputs. The aim is (i) to provide design indications for arterial surgery in the perspective of future development for prosthetic bypasses, (ii) to develop multi‐level numerical methods for optimization and shape design by optimal control, and (iii) to provide an input–output relationship led by models with lower complexity and computational costs. We have numerically investigated a reduced model based on Stokes equations and a vorticity cost functional (to be minimized) in the down‐field zone of bypass: a Taylor like patch has been found. A feedback procedure with Navier–Stokes fluid model is proposed based on the analysis of wall shear stress‐related indexes. Copyright © 2005 John Wiley & Sons, Ltd.