Optimized Schwarz algorithms for DDFV discretizations

We introduce a new non-overlapping optimized Schwarz method for anisotropic diffusion problems.
This class of algorithms can take into account the underlying physical properties of the problem at hand
throught the transmission conditions. We present a discretization of the algorithm using discrete duality
finite volumes (DDFV for short), which are ideally suited for anisotropic problem on general meshes.
We present here the case of high order transmission conditions in the DDFV framework. We prove the
convergence of the algorithm for a large class of symmetric transmission operators, including the discrete
Ventcell operator. We also illustrate with numerical simulations that the use of high order transmission
conditions (the optimized Ventcell conditions) leads to more efficient algorithms than the use of first
order Robin transmission conditions, especially in case of strong anisotropic operators.