  Stokes-Dirac structures are infinite-dimensional Dirac structures defined in
terms of differential forms on a smooth manifold with boundary. These Dirac
structures lay down a geometric framework for the formulation of Hamiltonian
systems with a nonzero boundary energy flow. Simplicial triangulation of the
underlaying manifold leads to the so-called simplicial Dirac structures,
discrete analogues of Stokes-Dirac structures, and thus provides a natural
framework for deriving finite-dimensional port-Hamiltonian systems that emulate
their infinite-dimensional counterparts. The port-Hamiltonian systems defined
with respect to Stokes-Dirac and simplicial Dirac structures exhibit gauge and
a discrete gauge symmetry, respectively. In this paper, employing Poisson
reduction we offer a unified technique for the symmetry reduction of a
generalized canonical infinite-dimensional Dirac structure to the Poisson
structure associated with Stokes-Dirac structures and of a fine-dimensional
Dirac structure to simplicial Dirac structures. We demonstrate this Poisson
scheme on a physical example of the vibrating string.
