  The finite element method (FEM) and the boundary element method (BEM) can
numerically solve the Helmholtz system for acoustic wave propagation. When an
object with heterogeneous wave speed or density is embedded in an unbounded
exterior medium, the coupled FEM-BEM algorithm promises to combine the
strengths of each technique. The FEM handles the heterogeneous regions while
the BEM models the homogeneous exterior. Even though standard FEM-BEM
algorithms are effective, they do require stabilisation at resonance
frequencies. One such approach is to add a regularisation term to the system of
equations. This algorithm is stable at all frequencies but also brings higher
computational costs. This study proposes a regulariser based on the on-surface
radiation conditions (OSRC). The OSRC operators are also used to precondition
the boundary integral operators and combined with incomplete LU factorisations
for the volumetric weak formulation. The proposed preconditioning strategy
improves the convergence of iterative linear solvers significantly, especially
at higher frequencies.
