PDAEs in refined electrical network modeling

Abstract

Modeling with partial differential-algebraic equations is a natural and universal approach valid for various applications with coupled subsystems. This contribution summarizes the state of such models in the simulation of electric circuits; that is, we place known facts and techniques into an overall context. In fact, we mainly discuss the modeling and analysis aspects of several important settings. In the modeling context, we embed the network equations into the context of Maxwell's equations and address the three main types of coupling: modeling with subsystems of the same type, refined models, and multiphysics. In the analysis context, we address the existence of solutions for these complex systems as well as structural properties as the DAE index (after spatial semidiscretization). For the numerical simulations, we give results for the cosimulation technique (also referred to as dynamic iteration), which is a standard method for coupled systems.