Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver

In this paper, we prove that the Algebraic A-FETI method corresponds to one particular instance of the original one-level FETI method. We also report on performance comparisons on an Origin 2000 between the one- and two-level FETI methods and an optimized sparse solver, for two industrial applicatio ns: the stress analysis of a thin shell structure, and that of a three-dime nsional structure modelled by solid elements. These comparisons suggest tha t for topologically two-dimensional problems, sparse solvers are effective when the number of processors is relatively small. They also suggest that f or three-dimensional applications, scalable domain decomposition methods su ch as FETI deliver a superior performance on both sequential and parallel h ardware configurations. Copyright (C) 1999 John Wiley & Sons, Ltd.