Application of the parallel BDDC preconditioner to the Stokes flow

TL;DR

This paper presents a parallel BDDC preconditioner implementation for Stokes flow problems, demonstrating its effectiveness and scalability in fluid dynamics simulations.

Contribution

It introduces a parallel BDDC method without explicit coarse problems, applied successfully to Stokes flow discretized by Taylor-Hood elements.

Findings

Effective parallel implementation using MUMPS solver

Successful application to multiple Stokes flow problems

BDDC shows promise for fluid dynamics simulations

Abstract

A parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method is described. It is based on formulation of BDDC with global matrices without explicit coarse problem. The implementation is based on the MUMPS parallel solver for computing the approximate inverse used for preconditioning. It is successfully applied to several problems of Stokes flow discretized by Taylor-Hood finite elements and BDDC is shown to be a promising method also for this class of problems.