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Accession Number:
ADA616287
Title:
A New Certification Framework for the Port Reduced Static Condensation Reduced Basis Element Method
Descriptive Note:
Journal article preprint
Corporate Author:
MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MECHANICAL ENGINEERING
Report Date:
2014-09-04
Pagination or Media Count:
38.0
Abstract:
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 interfacesports 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 et al. 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.
Distribution Statement:
APPROVED FOR PUBLIC RELEASE
