  The balancing domain decomposition methods (BDDC) are originally introduced
for symmetric positive definite systems and have been extended to the
nonsymmetric positive definite system from the linear finite element
discretization of advection-diffusion equations. In this paper, the convergence
of the GMRES method is analyzed for the BDDC preconditioned linear system from
advection-diffusion equations with the hybridizable discontinuous Galerkin
(HDG) discretization. Compared to the finite element discretizations, several
additional norms for the numerical trace have to be used and the equivalence
between the bilinear forms and norms needs to be established. For large
viscosity, if the subdomain size is small enough, the number of iterations is
independent of the number of subdomains and depends only slightly on the
sudomain problem size. The convergence deteriorates when the viscosity
decreases. These results are similar to those with the finite element
discretizations. Moreover, the effects of the additional primal constraints
used in the BDDC algorithms are more significant with the higher degree HDG
discretizations. The results of two two-dimensional examples are provided to
confirm our theory.
