A simple explicit-implicit finite element tearing and interconnecting transient analysis algorithm

Abstract

A simple explicit-implicit finite element tearing and interconnecting (FETI) algorithm (AFETI-EI algorithm) is presented for partitioned transient analysis of linear structural systems. The present algorithm employs two decompositions. First, the total system is partitioned via spatial or domain decomposition to obtain the governing equations of motions for each partitioned domain. Second, for each partitioned sub-system, the governing equations are modally decomposed into the rigid-body and deformational equations. The resulting rigid-body equations are integrated by an explicit integrator, for its stability is not affected by step-size restriction on account of zero-frequency contents (omega = 0). The modally decomposed partitioned deformation equations of motion are integrated by an unconditionally stable implicit integration algorithm. It is shown that the present AFETI-EI algorithm exhibits unconditional stability and that the resulting interface problem possesses the same solution matrix profile as the basic FETI static problems. The present simple dynamic algorithm, as expected, falls short of the performance of the FETI-DP but offers a similar performance of implicit two-level FETI-D algorithm with a much cheaper coarse solver; hence, its simplicity may offer relatively easy means for conducting parallel analysis of both static and dynamic problems by employing the same basic scalable FETI solver, especially for research-mode numerical experiments. Copyright (c) 2011 John Wiley & Sons, Ltd.