Face-based Selection of Corners in 3D Substructuring

TL;DR

This paper introduces a new heuristic algorithm for selecting corners in 3D substructuring, improving robustness and parallelism in BDDC methods for structural analysis.

Contribution

A novel heuristic algorithm for corner selection in 3D substructuring that enhances robustness and parallel processing capabilities.

Findings

Demonstrated improved robustness on engineering problems

Achieved better parallelism in corner selection

Outperformed previous methods in structural analysis cases

Abstract

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.