Application of aggregation multilevel iterative solver to problems of structural mechanics

Abstract

The application of aggregation multilevel iterative solver AMIS [2, 3] to the structural analysis of large-scale finite element problems is discussed. It is well-known that such problems usually are poorly conditioned and this leads to slow convergence of iterative methods [1]. The preconditioned conjugate gradient method with aggregation multilevel preconditioning is applied to solution the both: linear static problems and natural vibration ones. The effectiveness of several solution stages is considered: the creation of aggregation model, the application of sparse matrix technique to solution of the coarsest level problem, the smoothing algorithms and so on. The set of local rigid links are imposed to the given finite element model to decrease the number of degrees of freedom. The nodeby- node or element-by-element approaches are applied to obtain the reduced model on coarsest level. We try to keep as large number of equation on coarsest level as the computer resources permits it to do. The block sparse multifrontal solver [4] is applied to solve the coarsest level problem. The proper reordering method among multilevel reordering and multiple minimum degrees ones is chosen to reduce fill-inns. The several modifications of incomplete Cholesky factorization approaches are applied to smooth rapidly oscillating residuals after prolongation. The numerous numerical examples, taken from computational practice of SCAD Soft, illustrate the robustness and efficiency of proposed method.