  Adjoint methods enable the accurate calculation of the sensitivities of a
quantity of interest. The sensitivity is obtained by solving the adjoint
system, which can be derived by continuous or discrete adjoint strategies. In
acoustic wave propagation, continuous and discrete adjoint methods have been
developed to compute the eigenvalue sensitivity to design parameters and
passive devices (Aguilar, J. G. et al, 2017, J. Computational Physics, vol.
341, 163-181). In this short communication, it is shown that the continuous and
discrete adjoint characteristic decompositions, and Riemann invariants, are
connected by a similarity transformation. The results are shown in the Laplace
domain. The adjoint characteristic decomposition is applied to a
one-dimensional acoustic resonator, which contains a monopole source of sound.
The proposed framework provides the foundation to tackle larger acoustic
networks with a discrete adjoint approach, opening up new possibilities for
adjoint-based design of problems that can be solved by the method of
characteristics.
