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

Malak Diab and Caren Tischendorf

Splitting Methods for Linear Circuit DAEs of Index 1. 

Abstract: 

Operator Splitting is a powerful method for numerical investigation of

complex models. This method was successfully used for ordinary and partial differential

equations (ODEs and PDEs) [10]. In constrained dynamical problems as electric

circuits or energy transport networks, differential-algebraic equations (DAEs)

arise [12]. The constraints prevent a simple transfer of operator splitting from ODEs

to DAEs. Here, we present an approach for splitting linear circuit DAEs of index

1 [6] based on a topological decoupling of the circuit that is modeled by loop and

cutset equations. Finally, we present convergence results for the proposed DAE operator

splitting.

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2021-08

8 pp.