On the initial estimate of interface forces in FETI methods

TL;DR

This paper introduces a new initialization strategy for FETI methods that improves their efficiency in heterogeneous structures by better estimating interface forces, making FETI comparable to BDD in performance.

Contribution

A novel approach for splitting interface forces in FETI methods is proposed, enhancing initial estimates and restoring efficiency in challenging heterogeneous problems.

Findings

FETI's poor performance is linked to initial interface stress estimates.

The new initialization strategy significantly reduces FETI iterations.

FETI with the new strategy matches BDD efficiency in tested cases.

Abstract

The Balanced Domain Decomposition (BDD) method and the Finite Element Tearing and Interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities, FETI requires a large number of iterations to compute the solution compared to BDD. In this paper, the origin of the bad efficiency of FETI in these particular cases is traced back to poor initial estimates of the interface stresses. To improve the estimation of interface forces a novel strategy for splitting interface forces between neighboring substructures is proposed. The additional computational cost incurred is not significant. This yields a new initialization for the FETI method and restores numerical efficiency which makes FETI comparable to BDD even for problems where FETI was performing poorly. Various simple test problems are presented to discuss the efficiency of the proposed strategy and to illustrate the so-obtained numerical equivalence between the BDD and FETI solvers.