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 such as Newton’s method or Krylov subspace methods. In this talk I explore two such approaches and new techniques to ensure accuracy, efficiency, and robustness. The first approach combines Newton and Schwarz in the context of a brittle fracture model, where I’ve added new backtracking to stabilize the Newton iterations. The second is a novel combination of Schwarz with Krylov subspace techniques.

Refreshments will be served preceding the talk, starting at 2:45.