01868nas a2200181   4500008004100000245012100041210006900162260003800231520122900269100002701498700002201525700001901547700002401566700002101590700001601611700002201627856003701649       2020                        eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and  bSpringer International Publishing3 a<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>1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aAtallah, Nabib1 aScovazzi, Guglielmo1 aRozza, Gianluigi1 aFehr, Jörg1 aHaasdonk, Bernard  uhttps://arxiv.org/abs/1807.07753