Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis

Abstract

Abstract The inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GMRES it requires much smaller workspace while may converge considerably faster than BiCGStab. The effectiveness of the proposed methods is illustrated with matrix pencils of order up to 3.1 ⋅ 106 arising in the temporal linear stability analysis of a typical hydrodinamic flow.