  Acoustic wave propagation through a homogeneous material embedded in an
unbounded medium can be formulated as a boundary integral equation and
accurately solved with the boundary element method. The computational
efficiency deteriorates at high frequencies due to the increase in mesh size
with a fixed number of elements per wavelength and also at high material
contrasts due to the ill-conditioning of the linear system. This study presents
the design of boundary element methods feasible for nonconforming surface
meshes at the material interface. The nonconforming algorithm allows for
independent grid generation, improves flexibility, and reduces the degrees of
freedom. It works for different boundary integral formulations for Helmholtz
transmission problems, operator preconditioning, and coupling with finite
element solvers. The extensive numerical benchmarks at canonical configurations
and an acoustic foam model confirm the significant improvements in
computational efficiency when employing the nonconforming grid coupling in the
boundary element method.
