Schwarz methods partition numerical domains to take advantage of parallelization in computing, while also acting as preconditioners. The domains may be partitioned physically into distinct regions, by field into distinct behaviours, and/or algebraically into distinct degrees of freedom. Schwarz methods tend to produce only linear convergence rates, and so should be combined with fast solvers […]

Many problems in engineering and biology necessitate solving the first passage time problem, which addresses questions such as the expected time for a Brownian particle in unbounded space to reach a target. I will present a boundary integral equation method for solving this mean first passage time with complex geometries of absorbing and reflecting bodies. […]