DifferentialAlgebraic Equation
Index analysis
Electromagnetic Device
Electric Circuit
Topological index calculation of DAEs in coupled electromagnetic field/circuit simulation
Lennart Jansen
Jansen
Lennart
Journal of computational and applied mathematics, 201301, 19
Lennart Jansen
Preprint series:
Journal of computational and applied mathematics, 201301, 19
MSC 2000
 34A09 Implicit equations, differentialalgebraic 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 differentialalgebraic 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 semiexplicit system of differentialalgebraic 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.
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