Solving knife-edge scattering problems using singular boundary elements

A multidomain boundary element method (BEM) is employed to study the scattering of time-harmonic acoustic waves by knife-edge structures in an acoustic field. Analysis shows that singularities exist in such structures, and that the behavior of the acoustic pressure and its derivative near a knife edge resembles that of the displacement and stress near a crack tip in an elastic body. Singular elements are employed to model the behavior on the part of the boundary in the vicinity of the singularity. The advantage of the singular elements is seen through several numerical examples involving mufflerlike structures containing baffles and one with a knife-edge scattering in full space. For a given level of mesh refinement, both the nearfield and farfield solutions are improved with the introduction of singular elements.