@article {2021,
	title = {Hierarchical model reduction techniques for flow modeling in a parametrized setting},
	journal = {Multiscale Modeling and Simulation},
	volume = {19},
	year = {2021},
	pages = {267-293},
	abstract = {<p>In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.</p>},
	doi = {10.1137/19M1285330},
	author = {Matteo Zancanaro and F. Ballarin and Simona Perotto and Gianluigi Rozza}
}
@article {ZancanaroMrosekStabileOthmerRozza2021,
	title = {Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters},
	journal = {Fluids},
	volume = {6},
	number = {8},
	year = {2021},
	pages = {296},
	publisher = {MDPI AG},
	doi = {10.3390/fluids6080296},
	url = {https://doi.org/10.3390/fluids6080296},
	author = {Matteo Zancanaro and Markus Mrosek and Giovanni Stabile and Carsten Othmer and Gianluigi Rozza}
}
@article {2020,
	title = {Efficient Geometrical parametrization for finite-volume based reduced order methods},
	journal = {International Journal for Numerical Methods in Engineering},
	volume = {121},
	year = {2020},
	pages = {2655-2682},
	abstract = {<p>In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier{\textendash}Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level</p>},
	doi = {10.1002/nme.6324},
	url = {https://arxiv.org/abs/1901.06373},
	author = {Giovanni Stabile and Matteo Zancanaro and Gianluigi Rozza}
}
