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Efficient methods for computing spectral projectors for linearized hydrodynamic equations

Grace Hechme 1 Yuri Nechepurenko Miloud Sadkane
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This paper presents efficient methods for computing the spectral projectors for hydrodynamic equations, linearized at a steady state and approximated with respect to space. The focus is on the spectral projectors corresponding to a given part of the finite spectrum. In the case when the size of the problem is not too large, a QR-based method is proposed and compared with the $QZ$ method. In the large scale case, two variants of the Jacobi-Davidson method, with a deflation procedure, are developed. In both cases, the computed spectral projectors can be used to construct low-order models suited for the context of hydrodynamic stability. Numerical results are reported.
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Grace Hechme, Yuri Nechepurenko, Miloud Sadkane. Efficient methods for computing spectral projectors for linearized hydrodynamic equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2008, 31 (1), pp.667-686. ⟨10.1137/050648122⟩. ⟨hal-00976777⟩



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