Time-Stepping via Complementarity

Abstract

In this chapter, the numerical time integration methods for switched electronic circuits are described with a focus on the event-capturing time-stepping schemes based on the complementarity theory. After briefly introducing the strengths and weaknesses of various simulation approaches (hybrid, regularised and non-smooth), the mathematical nature of solutions for dynamical complementarity systems are discussed in view of numerical time-integration. Then the formulation of the time-stepping methods via complementarity will be described. For each class of solutions, a suitable method is provided, and its properties are illustrated on simple electrical circuits. Some implementation details are then explained. Especially, the complementarity solvers that are used at each time-step are described recalling the main families of available solvers. Some insights on the software implementation are also given. Finally, numerical applications and examples on more realistic circuits are considered. We will mainly focus on the architecture of a direct current–direct current (DC–DC) buck power converter.