  We use the Method of Difference Potentials (MDP) to solve a non-overlapping
domain decomposition formulation of the Helmholtz equation. The MDP reduces the
Helmholtz equation on each subdomain to a Calderon's boundary equation with
projection on its boundary. The unknowns for the Calderon's equation are the
Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered
by applying their respective Calderon's equations to the same data at the
common interface. Solutions on individual subdomains are computed concurrently
using a straightforward direct solver. We provide numerical examples
demonstrating that our method is insensitive to interior cross-points and mixed
boundary conditions, as well as large jumps in the wavenumber for transmission
problems, which are known to be problematic for many other Domain Decomposition
Methods.
