Solving systems of elastic bar structures by preconditioned conjugate gradient method

For solving systems of linear equations derived from structural analysis by conjugate gradient method, a new efficient incomplete factorization preconditioning was published by Saint-Georges et al. [1]. Here we present an algorithm for finding a starting point for the ordering applied in [1] based on which a variant of the “spiral ordering” due to Duff et al. [2] for an undirected connected graph is formed. We test the solvers in [1] and some of its variants when different orderings are applied and for each ordering, some incomplete factorization preconditioners are prepared. In the comparison of the considered solvers, a remarkable reduction in the number of iterations was found by the presented variant of the spiral ordering with IC(0) preconditioner, when systems from elastic bar structures with 3D beam elements were solved. © 1999 Elsevier Science Ltd. All rights reserved.