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 robust scalar algebraic multigrid (AMG) solvers is evaluated in the context of problems that arise in microfabrication technology. The principle idea is 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‐wise AMG preconditioning in the context of the space decomposition and subspace correction framework [1]. The subspace problems are solved approximately by the scalar AMG solver and the subspace correction is performed either in block diagonal (block Jacobi) or lower triangular (block Gauss–Seidel) fashion. In our test examples we use fully unstructured grids of different sizes. The numerical experiments show robust and efficient convergence of the Krylov iterative methods with component‐wise AMG preconditioning for both 2D and 3D problems. Copyright © 2001 John Wiley & Sons, Ltd.