Efficiency Study of the “Black-Box” Component Decomposition Preconditioning for Discrete Stress Analysis Problems

Abstract

Abstract. Efficiency of the preconditioning methodology for an iterative solution of discrete stress analysis problems is studied in this article. The preconditioning strategy is based on space decomposition and subspace correction framework. The principle idea is to decompose a global discrete system into a sequence of scalar subproblems, corresponding to the different Cartesian coordinates of the displacement vector. The scalar subproblems can be treated by a host of direct and iterative techniques, however we restrict ourselves to a "black-box" application of the direct sparse solvers and the scalar algebraic multigrid (AMG) method. The subspace correction is performed in either block diagonal or block lower triangular fashion. The efficiency and potential limitations of the proposed preconditioning methodology are studied on stress analysis for 2D and 3D model problems from microfabrication technology.

Modelling 3D semi-deformable tubes in real time

“…Replacing the direct solver by an iterative Krylov method [21] preconditioned by the algebraic multigrid (AMG) [23] can be an alternative. However, our experience in the context of FE modelling of linear elasticity problems is that real benefits of an iterative solver become obvious when discrete problem size exceeds 10 4 degrees of freedom [15]. Thus, direct solution methods seem to be optimal in this context.…”

HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D

“…For the example tested here, relatively high iteration counts can be attributed to a stretched domain. It is known that multigrid gradually loses its effectiveness when the domain/grid dimension in one or more coordinate directions is much larger than in the remaining directions (see [46]). † † One possible way of alleviating this problem is to limit the number of coarse levels, so that on the coarsest level the size of the system is greater than 1 (in our experiments, we coarsen to a single point).…”