Recent advances on domain decomposition finite element methods

This paper gives a birds eye view of the most recent algebraic acceleration and memory reduction techniques used in the finite element domain decomposition solution of electrodynamic boundary value problems arising in radiation, scattering and signal integrity applications. The presentation will focus on techniques that reliably deliver robust computational improvements and are resilient on plethora of realistic industrial grade models. These state-of-the-art techniques will be broadly grouped and presented into three categories: iterative solution preconditioning, low-rank randomized approximations, and direct solutions. The methodologies herein are rather general and can be adopted to other variational solutions of second order partial differential equation boundary value problems.