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We use the Method of Difference Potentials (MDP) to solve a non-overlappingdomain decomposition formulation of the Helmholtz equation. The MDP reduces theHelmholtz equation on each subdomain to a Calderon's boundary equation withprojection on its boundary. The unknowns for the Calderon's equation are theDirichlet and Neumann data. Coupling between neighboring subdomains is renderedby applying their respective Calderon's equations to the same data at thecommon interface. Solutions on individual subdomains are computed concurrentlyusing a straightforward direct solver. We provide numerical examplesdemonstrating that our method is insensitive to interior cross-points and mixedboundary conditions, as well as large jumps in the wavenumber for transmissionproblems, which are known to be problematic for many other Domain DecompositionMethods.

Non-iterative domain decomposition for the Helmholtz equation using the method of difference potentials