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

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.


Published in:
Computing and Visualization in Science, 12, 1, 23-35
Year:
2009
Note:
published online since November 2006
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 Record created 2007-04-24, last modified 2018-03-17

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