Lena Scholz

DAEs in Applications

Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. By incorporating the special structure of the DAE systems arising in certain physical domains, the general approach for the regularization of DAEs can be efficiently adapted to the system structure. We will present the analysis and regularization approaches for DAEs arising in mechanical multibody systems, electrical circuit equations, and flow problems. In each of these cases the DAEs exhibit a certain structure that can be used for an efficient analysis and regularization. Moreover, we discuss the numerical treatment of hybrid DAE systems, that also occur frequently in industrial applications. For such systems, the framework of DAEs provides essential information for a robust numerical treatment.

The Signature Method for DAEs arising in the modeling of electrical circuits

Abstract We consider the Signature Method ( Σ -method) for the structural analysis of differential–algebraic equations (DAEs) that arise in the modeling and simulation of electrical circuits. Different formulations of the set of model equations are considered. We show that for some formulations the structural approach may fail for certain circuit topologies, while other formulations are better suited for a structural analysis. In particular, we show that for the branch-oriented model equations the Signature Method always succeeds with a structural index that corresponds to the differentiation index of the system. The results are illustrated by a number of examples.

A DERIVATIVE ARRAY APPROACH FOR LINEAR SECOND ORDER DIFFERENTIAL-ALGEBRAIC SYSTEMS ∗

We discuss the solution of linear second order differential-algebraic equations (DAEs) with variable coefficients. Since index reduction and order r for higher order, higher index differential-algebraic systems do not commute, appropriate index reduction methods for higher order DAEs are required. We present an index reduction method based on derivative arrays that allows to determine an equivalent second order system of lower index in a numerical computable way. For such an equivalent second order system, an appropriate order reduction method allows the formulation of a suitable first order DAE system of low index that has the same solution components as the original second order system.