A subspace iteration eigensolver based on Cauchy integrals for vibroacoustic problems in unbounded domains

Despite the potential and the increasing popularity of the boundary element method (BEM), modal analyses based on BEM are not yet put into engineering practice, mainly due to the lack of efficient solvers for the underlying nonlinear eigenvalue problem (EVP). In this article, we review a subspace iteration method based on FEAST for the solution of vibroacoustic EVPs involving the finite element method (FEM) and BEM. The subspace is obtained by applying a spectral projector and is computed by contour integration, whereas the contour is also used to subsequently solve the projected EVP by rational approximation. The computation of the projection matrices is addressed by two approaches. In the case of heavy fluid loading, we solve the underlying coupled linear systems by an iterative block Krylov method. In the case of light fluid loading, we exploit the fact that the coupled system admits accurate model order reduction solely based on the structural subsystem. Applications to a spherical shell and to a musical bell indicate that only a few contour points are required for an accurate solution without inducing spurious eigenvalues. The results are compared with those of a contour integral method and illustrate the efficiency of the proposed eigensolver.