A Discontinuous Coarse Space (DCS) Algorithm for Cell Centered Finite Volume Based Domain Decomposition Methods: The DCS-RJMin Algorithm

摘要

In this paper, we have introduced a new discontinuous coarse space algorithm, the DCS-RJMin, which is suitable for cell-centered finite volume discretizations. The coarse space greatly improves numerical convergence. It would be of great interest to study which is the optimal low-dimensional subspace of all piecewise discontinuous piecewise harmonic functions. Future work also includes the development of a possible alternative to a coarse space in order to get scalability: "Piecewise Krylov Methods" where the same minimization problem than the one used in DCS-RJMin is used but where the coarse space is made of piecewise (per subdomain) differences between consecutive one-level iterates.