On a robust multilevel method applied for solving large-scale linear elasticity problems

The paper discusses an iterative scheme for solving large‐scale three‐dimensional linear elasticity problems, discretized on a tensor product of two‐dimensional and one‐dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black‐box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd.