Topological index calculation of DAEs in coupled electromagnetic field/circuit simulation

Lennart Jansen

Preprint series: Journal of computational and applied mathematics, 2013-01, 19

MSC 2000

34A09 Implicit equations, differential-algebraic equations

35Q60 Equations of electromagnetic theory and optics

Abstract
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. After this remodeling the electromagnetic part of the equation will be a system of ordinary differential equations with sparse matrices only. It will be shown that the topological index conditions for this coupled system are analogous to the conditions for an ordinary electric circuit.