@conference { 20.500.11767_123375,
	title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences},
	booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019},
	volume = {139},
	year = {2021},
	pages = {841{\textendash}850},
	publisher = {Springer},
	organization = {Springer},
	isbn = {978-3-030-55873-4},
	doi = {10.1007/978-3-030-55874-1_83},
	url = {https://arxiv.org/abs/1912.07886},
	author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza}
}
@conference {2021,
	title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences},
	booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019},
	year = {2021},
	month = {2021//},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {<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>},
	isbn = {978-3-030-55874-1},
	doi = {https://doi.org/10.1007/978-3-030-55874-1_83},
	url = {https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676},
	author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza},
	editor = {Fred J Vermolen and Cornelis Vuik}
}
@article {2020,
	title = {Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation},
	journal = {International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng},
	volume = {n/a},
	year = {2020},
	month = {2020/05/27},
	pages = {e3367},
	abstract = {<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>},
	keywords = {coronary artery bypass grafts, data assimilation, flow control, Galerkin methods, hemodynamics modeling, Optimization, patient-specific simulations, Proper orthogonal decomposition, reduced order methods},
	isbn = {2040-7939},
	doi = {https://doi.org/10.1002/cnm.3367},
	url = {https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R},
	author = {Zakia Zainib and F. Ballarin and Stephen E. Fremes and Piero Triverio and Laura Jim{\'e}nez-Juan and Gianluigi Rozza}
}
