Computing and Visualization in Science

, Volume 12, Issue 1, pp 23–35 | Cite as

Reduced basis methods for Stokes equations in domains with non-affine parameter dependence

Regular article

Abstract

In this paper we deal with reduced basis techniques applied to Stokes equations. We consider domains with different shape, parametrized by affine and non-affine maps with respect to a reference domain. The proposed method is ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. An “empirical”, stable and inexpensive interpolation procedure has permitted to replace non-affine coefficient functions with an expansion which leads to a computational decomposition between the off-line (parameter independent) stage for reduced basis generation and the on-line (parameter dependent) approximation stage based on Galerkin projection, used to find a new solution for a new set of parameters by a combination of previously computed stored solutions. As in the affine case this computational decomposition leads us to preserve reduced basis properties: rapid and accurate convergence and computational economies. The applications and results are based on parametrized geometries describing domains with curved walls, for example a stenosed channel and a bypass configuration. This method is well suited to treat also problems in fixed domain with non-affine parameters dependence expressing varying physical coefficients.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Modelling and Scientific Computing (CMCS), Institute of Analysis and Scientific Computing (IACS)EPFL, École Polytechnique Fédérale de LausanneLausanneSwitzerland

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