Automated multi-level substructuring (AMLS) for electromagnetics

We present an algebraic setting of an automated multi-level substructuring (AMLS) method for electromagnetic Maxwell eigenproblem solution. To our knowledge it is novel, and it involves a non-trivial generalisation of the corresponding method for elastodynamics and acoustics. In comparison to the AMLS method for elliptic problems the electromagnetic stiffness matrix is singular, it has a large kernel of gradients of H1H1-conforming shape functions. This difficulty was overcome by confining the method to solenoidal fields only.The goal of AMLS is to achieve a high level of dimensional reduction inexpensively, using multi-level modal substructuring, enabling reliable solution of huge response problems, without compromising the accuracy of the quantity of interest.As proof of concept we present simple numerical experiments on rectangular domains verifying a correct implementation of a truly multi-level version of the generalised algorithm. For real life applications the algorithm need to be equipped with, automated nested mesh dissection and an algorithm for automatic subdomain eigenspace truncation. Finally, the algorithm needs to be tuned and parallelised.