Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics

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 nonlinear 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 information from one nonlinear step to the next. More precisely, we consider the Jacobi-Davidson algorithm, the Implicitly Restarted Arnoldi method, the Krylov-Schur solver and its block-variant, and 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 for large-scale thermoacoustic stability analysis.