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 precon ditioning was published by Saint-Georges et al. [1]. Here we present an alg orithm for finding a starting point for the ordering applied in [1] based o n which a variant of the "spiral ordering" due to Duff et al. [2] for an un directed connected graph is formed. We test the solvers in [1] and some of its variants when different orderings are applied and for each ordering, so me incomplete factorization preconditioners are prepared. In the comparison of the considered solvers, a remarkable reduction in the number of iterati ons was found by the presented Variant of the spiral ordering with IC(0) pr econditioner, when systems from elastic bar structures with 3D beam element s were solved. (C) 1999 Elsevier Science Ltd. All rights reserved.