  A material that exhibits Willis coupling has constitutive equations that
couple the pressure-strain and momentum-velocity relationships. This coupling
arises from subwavelength asymmetry and non-locality in heterogeneous media.
This paper considers the problem of the scattering of a plane wave by a
cylinder exhibiting Willis coupling using both analytical and numerical
approaches. First, a perturbation method is used to describe the influence of
Willis coupling on the scattered field to a first-order approximation. A
higher-order analysis of the scattering based on generalized impedances is then
derived. Finally, a finite element method-based numerical scheme for
calculating the the scattered field is presented. These three analyses are
compared and show strong agreement for low to moderate levels of Willis
coupling.
