A class of new hybrid algebraic multilevel preconditioning methods, Original Research Article

A class of new hybrid algebraic multilevel preconditioning methods is presented for solving the large sparse systems of linear equations with symmetric positive definite coefficient matrices resulting from the discretization of many second-order elliptic boundary-value problems by the finite-element method. The new preconditioners are shown to be of optimal orders of complexities for two-dimensional and three-dimensional problem domains, and their relative condition numbers are estimated to be bounded uniformly, independent of the numbers of both the levels and the nodes.