@article {2021,
	title = {A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier{\textendash}Stokes problems},
	journal = {Computer \& Mathematics With Applications},
	year = {2021},
	month = {2021/08/12/},
	abstract = {<p>We focus on steady and unsteady Navier{\textendash}Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.</p>},
	keywords = {Cut Finite Element Method, Navier{\textendash}Stokes equations, Parameter{\textendash}dependent shape geometry, Reduced Order Models, Unfitted mesh},
	isbn = {0898-1221},
	url = {https://www.sciencedirect.com/science/article/pii/S0898122121002790},
	author = {Efthymios N Karatzas and Monica Nonino and F. Ballarin and Gianluigi Rozza}
}
