Two-level algebraic domain decomposition preconditioners using Jacobi–Schwarz smoother and adaptive coarse grid corrections

We investigate two-level preconditioners on the extended linear system arising from the domain decomposition method. The additive Schwarz method is used as a smoother, and the coarse grid space is constructed by using the Ritz vectors obtained in the Arnoldi process. The coarse grid space can be improved adaptively as the Ritz vectors become a better approximation of the eigenvectors. Numerical tests on the model problem demonstrate the efficiency.