Learning Overlap Optimization for Domain Decomposition Methods

The finite element method is a numerical simulation technique for solving partial differential equations. Domain decomposition provides a means for parallelizing the expensive simulation with modern computing architecture. Choosing the sub-domains for domain decomposition is a non-trivial task, and in this paper we show how this can be addressed with machine learning. Our method starts with a baseline decomposition, from which we learn tailored sub-domain overlaps from localized neighborhoods. An evaluation of 527 partial differential equations shows that our learned solutions improve the baseline decomposition with high consistency and by a statistically significant margin.