TY - JOUR
T1 - A new certification framework for the port reduced static condensation reduced basis element method
AU - Smetana, Kathrin
N1 - Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In this paper we introduce a new certification framework for the port-reduced static condensation reduced basis element (PR-SCRBE) method, which has been developed for the simulation of large component based applications such as bridges or acoustic waveguides. In an offline computational stage we construct a library of interoperable parametrized reference components; in the subsequent online stage we instantiate and connect the components at the interfaces/ports to form a system of components. To compute a "truth" finite element approximation of the (say) coercive elliptic partial differential equation on the component based system we use a domain decomposition approach. For an efficient simulation we employ two different types of model reduction - a reduced basis (RB) approximation within the interior of the component (Huynh etal. 2013) and empirical port reduction (Eftang and Patera 2013) on the ports where the components connect.We demonstrate the well-posedness of the PR-SCRBE approximation and introduce a new certification framework. To assess the quality of the port reduction we use conservative fluxes. We adapt the standard estimators from RB methods to the SCRBE setting to derive an a posteriori error estimator for the RB-error contribution. In order to combine the a posteriori estimators for both error contributions and derive a rigorous a posteriori error estimator for PR-SCRBE we adapt techniques from multi-scale methods and component mode synthesis. Finally, we prove that the effectivity of the derived estimator can be bounded.We provide numerical experiments for heat conduction and linear elasticity to show that the derived a posteriori error estimator provides an effective estimator. Moreover we demonstrate the applicability of the introduced certification framework by analyzing the computational (online) costs.
AB - In this paper we introduce a new certification framework for the port-reduced static condensation reduced basis element (PR-SCRBE) method, which has been developed for the simulation of large component based applications such as bridges or acoustic waveguides. In an offline computational stage we construct a library of interoperable parametrized reference components; in the subsequent online stage we instantiate and connect the components at the interfaces/ports to form a system of components. To compute a "truth" finite element approximation of the (say) coercive elliptic partial differential equation on the component based system we use a domain decomposition approach. For an efficient simulation we employ two different types of model reduction - a reduced basis (RB) approximation within the interior of the component (Huynh etal. 2013) and empirical port reduction (Eftang and Patera 2013) on the ports where the components connect.We demonstrate the well-posedness of the PR-SCRBE approximation and introduce a new certification framework. To assess the quality of the port reduction we use conservative fluxes. We adapt the standard estimators from RB methods to the SCRBE setting to derive an a posteriori error estimator for the RB-error contribution. In order to combine the a posteriori estimators for both error contributions and derive a rigorous a posteriori error estimator for PR-SCRBE we adapt techniques from multi-scale methods and component mode synthesis. Finally, we prove that the effectivity of the derived estimator can be bounded.We provide numerical experiments for heat conduction and linear elasticity to show that the derived a posteriori error estimator provides an effective estimator. Moreover we demonstrate the applicability of the introduced certification framework by analyzing the computational (online) costs.
KW - A posteriori error estimation
KW - Domain decomposition
KW - Reduced basis methods
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U2 - 10.1016/j.cma.2014.09.020
DO - 10.1016/j.cma.2014.09.020
M3 - Article
AN - SCOPUS:84908377217
SN - 0045-7825
VL - 283
SP - 352
EP - 383
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -