Immanuel Martini (Universität Stuttgart): Certified Reduced Basis Approximation for Heterogeneously Coupled Parametrized Flow Problems

Donnerstag, 02.07.2015 14:00 im Raum SRZ 205
Mathematik und Informatik

A critical issue in Reduced Basis methods for domain decomposition problems is to find functions that approximate the traces of the detailed solutions on the interface. There have been several efforts including an eigenvalue decomposition [Huynh et al., 2013], “empirical” basis functions [Eftang and Patera, 2013] and “fourier” interface functions [Iapichino, 2012]. We present a framework for the coupled Stokes-Darcy system [Martini et al., 2014], that treats the approximation on the interface as a black box. In this way, we can treat heterogeneous domain decomposition problems as opposed to previous works. Numerical results demonstrate the flexibility of the method with respect to the number of interface basis functions and show that our approach yields an efficient and accurate approximation if few global “detailed” solutions are computed in the offline-phase. We also observe, that the a-posteriori error estimation can be problematic when dealing with heterogeneous problems. We also present a model order reduction approach for parametrized laminar flow problems including viscous boundary layers. The viscous effects are captured by a Navier-Stokes model in the vicinity of the boundary layer, whereas a potential model is used in the outer region [Schenk and Hebeker, 1993]. Here, we avoid the more involved ansatz of posing localized, decoupled problems on the subdomains and apply the existing theory and algorithms for reduced basis approximation of non-coercive and nonlinear partial differential equations [Veroy and Patera, 2005] [Manzoni, 2012].

Angelegt am Mittwoch, 24.06.2015 13:37 von cgiet_01
Geändert am Montag, 29.06.2015 14:04 von wuebbel
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