A Rigorous Finite-Element Domain Decomposition Method for   Electromagnetic Near Field Simulations
  Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an accurate modeling of complicated geometrical features. However, from a numerical point of view solving the arising system of linear equations is very demanding even for medium sized 3D domains. In numerics, a domain decomposition method is a commonly used strategy to overcome this problem. Within this approach the overall computational domain is split up into smaller domains and interface conditions are used to assure continuity of the electromagnetic field. Unfortunately, standard implementations of the domain decomposition method as developed for electrostatic problems are not appropriate for wave propagation problems. In an earlier paper we therefore proposed a domain decomposition method adapted to electromagnetic field wave propagation problems. In this paper we apply this method to 3D mask simulation. 
L. Zschiedrich, S. Burger, A. Sch\"adle, F. Schmidt