Adaptive-Multilevel BDDC and its parallel implementation

TL;DR

This paper introduces an adaptive-multilevel BDDC method that enhances convergence and scalability for large engineering problems by adaptively selecting constraints and efficiently solving local eigenvalue problems.

Contribution

It combines adaptive and multilevel BDDC approaches with a new strategy for local eigenproblem solutions, improving convergence and scalability.

Findings

Effective detection of troublesome parts at each level

Improved convergence of the BDDC method

Good scalability on large problems and core counts

Abstract

We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.