Flexural or membrane-coupled or capillary gravity wave scattering by a
submerged or a piercing vertical porous barrier is analytically studied
based on a connection that involves the solution potentials and few
auxiliary potentials. The problems for the auxiliary potentials are
relatively easy to handle for their solutions. The original problem is
decomposed into two scattering or radiation problems of this type. The
solution wave potential is determined in terms of those resolved wave
potentials. Numerical results for the explicitly obtained scattering
quantities are also presented.