A comparison of solvers for quadratic eigenvalue problems from combustion

Claude Sensiau (1) , Franck Nicoud (2) , Martin van Gijzen (3) , J.W. van Leeuwen (3)

1 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 TU Delft - Delft University of Technology

Two iterative subspace methods (Arnoldi and Jacobi-Davidson) are compared for solving typical quadratic eigenvalue problems arising when studying combustion instabilities. An academic, representative test case is presented with associated analytical solution. The efficiency of the iterative methods is studied in terms of running time when 1-10 eigenpairs are sought for, the computational domain being discretized with 500-32000-node finite element meshes. The sensitivity of the methods to the dimension of the search subspace is also investigated.

Mots clés: quadratic eigenvalue problems; subspace methods; combustion instabilities

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Analyse numérique [math.NA]

Claude Sensiau, Franck Nicoud, Martin van Gijzen, J.W. van Leeuwen. A comparison of solvers for quadratic eigenvalue problems from combustion. International Journal for Numerical Methods in Fluids, 2008, 56 (8), pp.1481-1487. ⟨10.1002/fld.1691⟩. ⟨hal-00820759⟩