The Coupling of Discrete Electromagnetism and the Boundary-Element Method for the Simulation of Accelerator Magnets

The theory of discrete electromagnetism (DEM) is quickly gaining ground in the computational electromagnetism community. It reflects in an unprecedented clarity the topological and geometrical properties of the phenomena of electromagnetism. The structural analogies of the Finite Element Method (FEM) and DEM formulations has attracted many researchers' attention over the past years. In this thesis we will show that FEM is indeed another DEM formulation. To this end we introduce a boundary term and transfer matrices in DEM, both of which find their analogue in a FEM equation system. As an alternative to the Galerkin-Hodge operator used in FEM we propose a geometrically defined Hodge operator on simplicial cells, thus presenting a solely geometrically and topologically defined variant of DEM formulations. The coupling of DEM with a Boundary Element Method (BEM) has proven to combine the advantages of both methods. The resulting DEM-BEM algorithm is found to be suited for the simulation of accelerator magnets: non-linear and conductive material is discretized for a DEM formulation whereas the superconductive coils are considered at the highest accuracy in a BEM formulation. The goal of this thesis is the implementation of a DEM-BEM coupling with the Whitney-form based Galerkin-Hodge operator being used in the DEM formulation.