A semi-explicit formulation of a coupled electromagnetic field/circuit problem

The demand of combining circuit simulation directly with complex device models to refine critical circuit parts becomes more and more important, since the classical circuit simulation can no longer supply sufficiently accurate results. The simulation of such coupled problems leads to large systems and therefore to high computing times. We consider a set of differential–algebraic equations, which arise from an electric circuit modeled by the modified nodal analysis coupled with electromagnetic devices. While the normal circuit elements are zero dimensional elements the electromagnetic devices are given by a three dimensional model. Therefore the number of variables can easily go beyond millions, if we refine the spatial discretization. We analyze the structure of the discretized coupled system and present a way to transform it into a semi-explicit system of differential–algebraic equations. In the process we make use of a new decoupling method for DAEs which results from a mix of the Strangeness Index and the Tractability Index. This remodeling allows us to prove a global unique solvability result for the coupled circuit/field problem and it is also a crucial step if we want to apply model order reduction techniques or semi-explicit solvers.