Parallel implementation of Multilevel BDDC

TL;DR

This paper presents a parallel implementation of the multilevel BDDC method, which enhances scalability by recursively applying BDDC to solve large-scale linear elasticity and Stokes flow problems more efficiently.

Contribution

It introduces a detailed parallel implementation of the multilevel BDDC algorithm, improving scalability for large problems compared to standard BDDC.

Findings

Multilevel BDDC outperforms two-level BDDC in large-scale problems.

Parallel implementation enables efficient computation on complex engineering problems.

Recursion in BDDC enhances scalability and solution speed.

Abstract

In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method.