01664nas a2200181   4500008004100000020002200041245016600063210006900229260005200298520089600350100002201246700001801268700001701286700002101303700002201324700001901346856011701365       2021                        eng d  a978-3-030-55874-100aReduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences0 aReduced Order Methods for Parametrized Nonlinear and Time Depend  aChambSpringer International Publishingc2021//3 a<p>We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.</p>1 aStrazzullo, Maria1 aZainib, Zakia1 aBallarin, F.1 aRozza, Gianluigi1 aVermolen, Fred, J1 aVuik, Cornelis  uhttps://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/1912267602309nas a2200313   4500008004100000020001400041245013100055210006900186260001500255300001000270490000800280520128800288653003401576653002201610653001701632653002101649653002601670653001701696653003301713653003601746653002601782100001801808700001701826700002401843700002001867700002501887700002101912856006201933       2020                        eng d  a2040-793900aReduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation0 aReduced order methods for parametric optimal flow control in cor  c2020/05/27  ae33670 vn/a3 a<p>Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.</p>10acoronary artery bypass grafts10adata assimilation10aflow control10aGalerkin methods10ahemodynamics modeling10aOptimization10apatient-specific simulations10aProper orthogonal decomposition10areduced order methods1 aZainib, Zakia1 aBallarin, F.1 aFremes, Stephen, E.1 aTriverio, Piero1 aJiménez-Juan, Laura1 aRozza, Gianluigi  uhttps://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R