Probabilistic Domain Decomposition: an out-of-the-box approach to beat Amdahl's law in PDEs

Francisco Bernal
Department of Mathematics
Technical University of Lisbon
Lisbon, Portugal


In this talk, I will introduce the method of probabilistic domain decomposition (PDD). PDD is a novel approach designed to circunvent the limit to scalability inherent in state-of-the-art domain decomposition methods, which are required to tackle the large PDEs arising in applications. The mathematics of PDD are those of stochastic processes rather than matrix algebra, while the main underlying ideas are conceptually simple. I will focus on a multigrid-like version of PDD, in which previous information about the solution (in the form of rougher approximations) is incorporated via variance reduction with the goal of speeding up the simulation. One or two numerical examples will be worked out.