Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems

摘要

We propose and analyze overlapping two-level additive Schwarz preconditioners for the local discontinuous Galerkin discretization. We prove that the condition number of the preconditioned system is bounded by C[1 + (H/δ)], where H represents the coarse mesh size, 8 measures the overlap among the subdomains, and the constant C is independent of H, δ, the fine mesh size h and the number of subdomains Ns. Numerical results are presented showing the scalability of the method.