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.
Highlights
Modeling with partial differential-algebraic equations is a natural and universal approach valid for various applications with coupled subsystems
The purpose of this work is to give an overview of PDAE techniques, which were developed in the field of electric circuit simulation, and stresses that PDAEs are an adequate modeling technique, not limited to electric circuits, which might enable and enhance simulation
In this paper we have given an overview of PDAE models in circuit simulation
Summary
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. We mainly discuss the modeling and analysis aspects of several important settings. We address the existence of solutions for these complex systems as well as structural properties as the DAE index (after spatial semidiscretization). We give results for the cosimulation technique ( referred to as dynamic iteration), which is a standard method for coupled systems
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