Reducing sparse nonlinear eigenproblems by automated multi-level substructuring

The automated multi-level substructuring method (AMLS) was recently suggested as an alternative to iterative projection methods for computing eigenpairs of huge matrix eigenproblems in the context of structural engineering. Taking advantage of a substructuring on several levels the method constructs a projected problem of much smaller dimension which still yields satisfactory accuracy over a wide frequency range of interest. In this paper we generalise the AMLS method to certain classes of nonlinear eigenvalue problems which can be partitioned into an essential linear and positive definite pencil and a small residual. The efficiency of the method is demonstrated by numerical examples modeling damped vibrations of a structure with nonproportional damping, a gyroscopic eigenproblem, and a rational eigenproblem governing free vibrations of a fluid–solid structure.