An Optimized Schwarz Algorithm for a Discontinuous Galerkin Method

It has been shown in [4] that block Jacobi iterates of a discretization obtained from hybridizable discontinuous Galerkin methods (HDG) can be viewed as non-overlapping Schwarz methods with Robin transmission condition. The Robin parameter is exactly the penalty parameter μ of the HDG method. There is a stability constraint on the penalty parameter and the usual choice of μ results in slow convergence of the Schwarz method. In this paper we show how to overcome this problem without changing μ.