A structural analysis of field/circuit coupled problems based on a generalised circuit element

  • Idoia Cortes GarciaEmail author
  • Herbert De Gersem
  • Sebastian Schöps
Original Paper


In some applications, there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations describing the circuit (modified nodal analysis) which yields a system of differential algebraic equations (DAEs). This paper deals with the differential index analysis of such coupled systems. For that, a new generalised inductance–like element is defined. The index of the DAEs obtained from a circuit containing such an element is then related to the topological characteristics of the circuit’s underlying graph. Field/circuit coupling is performed when circuits are simulated containing elements described by Maxwell’s equations. The index of such systems with two different types of magnetoquasistatic formulations (A* and T-Ω) is then deduced by showing that the spatial discretisations in both cases lead to an inductance-like element.


Differential algebraic equations Differential index Modified nodal analysis Eddy currents T-omega formulation 


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We thank Prof. Caren Tischendorf for the fruitful discussions.


This work has been supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of CE at TU Darmstadt and DFG Grant SCHO1562/1-2.


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Authors and Affiliations

  1. 1.Technische Universität DarmstadtDarmstadtGermany

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