An Algebraic Multilevel Iteration Method for Finite Element Matrices∗

To solve a sparse linear system of equations resulting from the finite element approximation of elliptic self-adjoint second order boundary value problems an algebraic multilevel iteration method is presented. The new method can be considered as an extension of methods, which have been defined by Axelsson and Eijkhout [4] for nine-point matrices and later generalized by Axelsson and Neytcheva [6] for the Stieltjes matrices, to a wider class of sparse symmetric positive-definite matrices. The rate of convergence and the computational complexity of the method are analyzed. Experimental results on some standard test problems are presented and discussed.