@conference {2020,
	title = {A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries},
	booktitle = {IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22{\textendash}25, 2018},
	year = {2020},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	abstract = {<p>A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.</p>},
	doi = {10.1007/978-3-030-21013-7_8},
	url = {https://arxiv.org/abs/1807.07753},
	author = {Efthymios N Karatzas and Giovanni Stabile and Nabib Atallah and Guglielmo Scovazzi and Gianluigi Rozza},
	editor = {Fehr, J{\"o}rg and Bernard Haasdonk}
}
@article {2018,
	title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models},
	journal = {Journal of Scientific Computing},
	volume = {74},
	year = {2018},
	pages = {197-219},
	doi = {10.1007/s10915-017-0430-y},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114\&doi=10.1007\%2fs10915-017-0430-y\&partnerID=40\&md5=023ef0bb95713f4442d1fa374c92a964},
	author = {Immanuel Martini and Bernard Haasdonk and Gianluigi Rozza}
}
@article {2015,
	title = {Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system},
	journal = {Advances in Computational Mathematics},
	volume = {special issue for MoRePaS 2012},
	year = {2015},
	abstract = {<p>The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.</p>},
	keywords = {Domain decomposition, Error estimation, Non-coercive problem, Porous medium equation, Reduced basis method, Stokes flow},
	issn = {1019-7168},
	doi = {     10.1007/s10444-014-9396-6},
	author = {Immanuel Martini and Gianluigi Rozza and Bernard Haasdonk}
}
