An Assessment of Some Preconditioning Techniques in Shell Problems

Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear systems in many areas of scienti®c computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a signi®cant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available. However, in the analysis of thin shells the situation is not so transparent. It is well known that the sti€ness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitive with direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. # 1998 John Wiley & Sons, Ltd.