As the performance of modern computers keeps increasing, it is important to develop and implement efficient numerical software to take full advantage of their power. The first difficult problem is the parallelization of algorithms. In this lecture, we will discuss domain decomposition methods, which are one of the dominant paradigms in contemporary simulations of large-scale partial differential equations (PDE). The second challenge is the actual implementation of these methods: we use FreeFem++ to solve PDEs through generalized Galerkin methods.   We present a parallel implementation in FreeFem++ of scalable two-level domain decomposition methods. The performance of our code is illustrated by computing highly heterogeneous problems on large clusters.

This is a joint work with P. Jolivet and F. Nataf.