A Class of New Parallel Hybrid Algebraic Multilevel Iterations (Journal of Computational Mathematics, 2021)
For the large sparse system of linear equations with symmetric positive definite block coefficient matrix resulted from suitable finite element discretization of the second-order self-adjoint elliptic boundary value problem, by making use of the algebraic multilevel iteration technique and the blocked preconditioning strategy, we construct preconditioning matrices having parallel computing function for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iteration methods for solving this kind of system of linear equations. Theoretical analyses show that, besides much suitable for implementing on the high-speed parallel multiprocessor systems, these new methods are optimal-order methods. That is to say, their convergence rates are independent of both the sizes and the levels of the constructed matrix sequence, and the computational workloads are bounded by linear functions in the order number of the considered system of linear equations, respectively.