Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics

Abstract : In this work we consider the numerical solution of large nonlinear eigenvalue problems that arise in thermoacoustic simulations involved in the stability analysis of large combustion devices. We briefly introduce the physical modeling that leads to a non-linear eigenvalue problem that is solved using a nonlinear fixed point iteration scheme. Each step of this nonlinear method requires the solution of a complex non-Hermitian linear eigenvalue problem. We review a set of state of the art eigensolvers and discuss strategies to recycle spectral informations from one nonlinear step to the next. More precisely, we consider the Implicitly Restarted Arnoldi method, the Krylov-Schur solver and its block-variant as well as the subspace iteration method with Chebyshev acceleration. On a small test example we study the relevance of the different approaches and illustrate on a large industrial test case the performance of the parallel solvers best suited to recycle spectral information.
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Numerical Linear Algebra with Applications, Wiley, 2015, 22 (6), pp.1039-1058. 〈10.1002/nla.1995〉
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Pablo Salas, Luc Giraud, Yousef Saad, Stéphane Moreau. Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics. Numerical Linear Algebra with Applications, Wiley, 2015, 22 (6), pp.1039-1058. 〈10.1002/nla.1995〉. 〈hal-01238263〉

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