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A reduced order approach for the embedded shifted boundary FEM and a heat exchange system on parametrized geometries. (English) Zbl 1442.65376

Fehr, Jörg (ed.) et al., IUTAM symposium on model order reduction of coupled systems. MORCOS 2018. Proceedings of the IUTAM symposium, Stuttgart, Germany, May 22–25, 2018. Cham: Springer. IUTAM Bookser. 36, 111-125 (2020).
Summary: 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 in [A. Main and G. Scovazzi, J. Comput. Phys. 372, 972–995 (2018; Zbl 1415.76457)]. 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.
For the entire collection see [Zbl 1425.93009].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
80A19 Diffusive and convective heat and mass transfer, heat flow
35K05 Heat equation

Citations:

Zbl 1415.76457

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References:

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