A CLASS OF NEW HYBRID ALGEBRAIC MULTILEVEL PRECONDITIONING METHODS

A class of new hybrid algebraic multilevel. preconditioning methods is presented for solving the large sparse systems of linear equations wi th 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-dimens ional problem domains, and their relative condition numbers are estima ted to be bounded uniformly, independent of the numbers of both the le vels and the nodes. (C) Elsevier Science Inc., 1997.