%0 Journal Article %T Efficient methods for computing spectral projectors for linearized hydrodynamic equations %+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS) %A Hechme, Grace %A Nechepurenko, Yuri %A Sadkane, Miloud %< avec comité de lecture %@ 1064-8275 %J SIAM Journal on Scientific Computing %I Society for Industrial and Applied Mathematics %V 31 %N 1 %P 667-686 %8 2008-12 %D 2008 %R 10.1137/050648122Journal articles %X 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. %G English %L hal-00976777 %U https://ensta-paris.hal.science/hal-00976777 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2