Two-level Schwarz methods for hybridizable discontinuous Galerkin methods - Lu, Peipei; Rupp, Andreas; Kanschat, Guido (Journal of scientific computing, 2023)
In this paper, we propose two-level domain decomposition methods for hybridizable discontinuous Galerkin discretizations including hybridized local discontinuous Galerkin, Raviart-Thomas, and Brezzi-Douglas-Marini finite elements for Poisson’s equation. We study the additive Schwarz method as a preconditioner and the multiplicative method as an iterative solver. In our algorithm, the same discretization scheme is defined on the coarse mesh. In particular, we use the injection operator developed in [13] and prove that the condition number of the preconditioned system only depends on the fraction between coarse and fine mesh sizes and the overlap width. Numerical experiments underline our analytical findings.