Experimental insight into the domain decomposition method for a finite element method code

Abstract

The use of Domain Decomposition Methods (DDM) for a Finite Element Method (FEM) framework was a hot topic in the past decade, leading to very powerful results in terms of scalability and widening the problems that could be full-wave simulated with the FEM, [1–3]. However, despite the promising results shown in these references, it seems not to be a widespread use of the DDM in commercial FEM softwares or publications, whereas the common research topics (adaptivity, higher-order basis functions, different element shapes) in FEM have not been explored together with DDM. In this communication, we share experimental details with different non-overlapping DDM within FEM. We explore the use of different finite element shapes with up to fourth-order basis functions. We propose a propagation problem through a rectangular waveguide as a benchmark, and we show the different implementation choices available and their impact in the performance of the code.