Iterative versus direct parallel substructuring methods in semiconductor device modelling

The numerical simulation of semiconductor devices is extremely demanding in term of computational time because it involves complex embedded numerical schemes. At the kernel of these schemes is the solution of very ill-conditioned large linear systems. In this paper, we present the various ingredients of some hybrid iterative schemes that play a central role in the robustness of those solvers when they are embedded in other numerical schemes. On a set of bidimensional unstructured mixed finite element problems representative of semiconductor simulation, we perform a fair and detailed comparison between parallel iterative and direct linear solution techniques. We show that iterative solvers can be robust enough to solve the very challenging linear systems that appear in those simulations.