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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2016-21

Jonas Pade und Caren Tischendorf


Waveform Relaxation: A Convergence Criterion for Differential-Algebraic Equations. 


Abstract: While waveform relaxation (also known as dynamic iteration or co- simulation) methods are known to converge for coupled systems of or- dinary differential equations (ODEs), they may suffer from instabilities for coupled differential-algebraic equations (DAEs). Several convergence criteria have been developed for index-1 DAEs. We present here a con- vergence criterion for a coupled system of an index-2 DAE with an ODE. The analysis is motivated by the wish to combine electromagnetic field simulation with circuit simulation in a stable manner. The spatially dis- cretized Maxwell equations in vector potential formulation with Lorenz gauging represent an ODE system. A lumped circuit model via the estab- lished modified nodal analysis is known to be a DAE system of index ≤ 2. Finally, we present sufficient network topological criteria to the coupling that are easy to check and that guarantee convergence.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), P-2016-21


15 pp.