Component-wise algebraic multigrid preconditioning for the iterative solution of stress analysis problems from microfabrication technology

A methodology for preconditioning discrete stress analysis systems using ro bust scalar algebraic multi-grid (AMG) solvers is evaluated in the context of problems that arise in microfabrication technology. The principle idea i s to apply an AMG solver in a segregated way to the series of scalar block matrix problems corresponding to different displacement vector components, thus yielding a block diagonal AMG preconditioner. We study the component-w ise AMG preconditioning in the context of the space decomposition and subsp ace correction framework [1]. The subspace problems are solved approximatel y by the scalar AMG solver and the subspace correction is performed either in block diagonal (block Jacobi) or lower triangular (block Gauss-Seidel) f ashion. In our test examples we use fully unstructured grids of different s izes. The numerical experiments show robust and efficient convergence of th e Krylov iterative methods with component-wise AMG preconditioning for both 2D and 3D problems. Copyright (C) 2001 John Wiley & Sons, Ltd.