Recent advances in domain decomposition methods for large-scale saddle point problems

Abstract

Scalability of parallel solvers for problems with high heterogeneities relies on adaptive coarse spaces built from generalized eigenvalue problems in the subdomains. The corresponding theory is powerful and flexible but the development of an efficient parallel implementation is challenging. We report here on recent advances in adaptive coarse spaces and on their open source implementations in domain specific languages such as FreeFem, focusing on a new domain decomposition for saddle point formulations with some numerical tests.

Keywords

• High performance computing
• Saddle point problem
• Domain decomposition methods
• Nearly incompressible elasticity
• Multilevel methods