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 applications: the stress analysis of a thin shell structure, and that of a three-dimensional structure modelled by solid elements. These comparisons suggest that for topologically two-dimensional problems, sparse solvers are e ective when the number of processors is relatively small. They also suggest that for three-dimensional applications, scalable domain decomposition methods such as FETI deliver a superior performance on both sequential and parallel hardware con gurations.