The RSRR method for solving large-scale nonlinear eigenvalue problems in boundary element method

The last few decades have witnessed significant advances in the boundary element (BE) based industrial product design and analysis. However, it is so far still challenging to solve the large-scale nonlinear eigenvalue problems (NEPs) that lie in the heart of the BE based structural and acoustic modal analyses. The challenge stems from the particular structure of the BE matrices, including the asymmetry which requires special attention in developing NEP solvers, the dense population which causes a high computational complexity, and the nonlinearity in frequency which poses a further restriction to the solvers. This paper aims to overcome the above challenge by using the recently developed resolvent sampling based Rayleigh-Ritz method (RSRR), combined with the fast boundary element method (BEM). Technical and numerical schemes to facilitate the practical application and reduce the computational cost are proposed and studied. Two benchmarks and an industrial-size rocket fairing model are provided to show the ease to use, good accuracy and computational efficiency of the proposed method.