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A Static Condensation Reduced Basis Element Approach for the Reynolds Lubrication Equation

Part of: Incompressible viscous fluids Partial differential equations, boundary value problems Elliptic equations and systems

Published online by Cambridge University Press:  05 December 2016

Eduard Bader ,
Martin A. Grepl  and
Siegfried Müller
Eduard Bader*
Affiliation:
Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany
Martin A. Grepl*
Affiliation:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
Siegfried Müller*
Affiliation:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
*
*Corresponding author. Email addresses:bader@aices.rwth-aachen.de (E. Bader), grepl@igpm.rwth-aachen.de (M. A. Grepl), mueller@igpm.rwth-aachen.de (S. Müller)
*Corresponding author. Email addresses:bader@aices.rwth-aachen.de (E. Bader), grepl@igpm.rwth-aachen.de (M. A. Grepl), mueller@igpm.rwth-aachen.de (S. Müller)
*Corresponding author. Email addresses:bader@aices.rwth-aachen.de (E. Bader), grepl@igpm.rwth-aachen.de (M. A. Grepl), mueller@igpm.rwth-aachen.de (S. Müller)
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Abstract

In this paper, we propose a Static Condensation Reduced Basis Element (SCRBE) approach for the Reynolds Lubrication Equation (RLE). The SCRBE method is a computational tool that allows to efficiently analyze parametrized structures which can be decomposed into a large number of similar components. Here, we extend the methodology to allow for a more general domain decomposition, a typical example being a checkerboard-pattern assembled from similar components. To this end, we extend the formulation and associated a posteriori error bound procedure. Our motivation comes from the analysis of the pressure distribution in plain journal bearings governed by the RLE. However, the SCRBE approach presented is not limited to bearings and the RLE, but directly extends to other component-based systems. We show numerical results for plain bearings to demonstrate the validity of the proposed approach.

Keywords

Reynolds lubrication equationstatic condensationdomain decompositionmodel order reductionreduced basis element methoda posteriori error estimation

MSC classification

Secondary: 76D08: Lubrication theory 35J25: Boundary value problems for second-order elliptic equations 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N55: Multigrid methods; domain decomposition
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 126 - 148
Copyright
Copyright © Global-Science Press 2016 

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