Multi‐level iterative technique and aggregation concept with semi‐analytical preconditioning for solving boundary‐value problems

Abstract

Abstract Some iterative multi‐level approaches for solving large‐scale finite‐element elliptic problems are proposed. It is suggested that these approaches be used in combination with an aggregation technique. On the basis of the aggregation concept a new efficient preconditioning procedure in the inner iterative scheme of the algorithm is developed. This procedure is derived from the fundamental solution of a corresponding elliptic problem. The efficiency of the approaches is demonstrated by numerical examples.