A unified fast multipole boundary element method for acoustic scattering from objects near a fluid–fluid interface

The unified fast multipole boundary element method (FMBEM) has been adapted to treat acoustic scattering from an elastic inclusion located near to (or embedded on) the interface between two semi-infinite fluid half-spaces. The parallel broadband Helmholtz FMBEM is used to model each fluid domain, while the elastic inclusion is modelled using either the finite element method, or an analogous elastodynamic FMBEM. The boundary integral equation for each fluid half-space is formulated to account for the transmission and reflection of the incident acoustic field from the planar surface of the interface, and so only the scattered field from the elastic inclusion and/or localised surface scattering features on the interface surface are evaluated. In the absence of specialised methods to absorb the outgoing waves, the scattered field will reflect from the edge of the truncated boundary element mesh representing the fluid-fluid interface. Numerical examples demonstrate that the resulting errors can be minimised when the truncated mesh is made a few times larger than the scattering feature. The boundary-only discretisation of the truncated fluid-fluid interface, O(N log N) computational cost of the FMBEM, and simplified truncation of the boundary mesh yield a computationally efficient model for fully three-dimensional analysis for this type of problem configuration.