Abstract
The time dependent systems of equations obtained in most simulation settings of this work are systems of differential algebraic equations. These systems can be classified according to their index. Systems with higher index require special numerical treatment. Therefore, when dealing with (coupled) systems of differential algebraic equations, a priori knowledge about their index allows to properly handle their simulation. This chapter presents three generalised elements definitions as well as the index analysis of the system of equations arising from circuits (modified nodal analysis) containing the generalised elements. For each one of the definitions, examples arising from different approximations of Maxwell’s equations are given.
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Cortes Garcia, I. (2021). Structural Analysis of the Coupled Systems. In: Mathematical Analysis and Simulation of Field Models in Accelerator Circuits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-63273-1_4
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