Numerical Analysis of Nonlinear PDAEs: A Coupled Systems Approach and its Application to Circuit Simulation

Lennart Jansen , Michael Matthes

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), Preprint Nr. 13 - 10, 32

MSC 2000

35K90 Abstract parabolic evolution equations

34A09 Implicit equations, differential-algebraic equations

Abstract
Applications like electrical circuits including electromagnetic devices, semiconductor devices or thermal elements, and water or gas transportation networks give rise to a mix of partial differential equations and differential-algebraic equations. Such a mix is called a partial differential-algebraic equation (PDAE). In this paper we investigate a prototype for nonlinear coupled PDAE systems. The objectives are to prove the global existence and uniqueness of a solution, the convergence of Galerkin equations and a perturbation result for this prototype class. Regarding the applications we consider the simulation of electric circuits including thermal resistors. With a new decoupling technique we are able to reformulate the MNA equations up to index 2 such that we can apply the results of the prototype.