Structural-Algebraic Remodeling of Coupled Dynamical Systems*

Lena Scholz, Andreas Steinbrecher
The automated modeling of multi-physical dynam-ical systems is usually realized by the coupling of different subsystems via certain interface or coupling conditions. This approach results in large-scale high-index differential-algebraic equations (DAEs). Since the direct numerical simulation of these kinds of systems leads to instabilities and possibly non-convergence of the numerical methods a regularization or remodeling of the system is required. In many simulation environments a kind of
more » ... ments a kind of structural analysis based on the sparsity pattern of the system is used to determine the index and a reduced system model. However, this approach is not reliable for certain problem classes, in particular not for coupled systems of DAEs. We will present a new approach for the remodeling of coupled dynamical systems that combines the structural analysis, in particular the Signature Method [9], with classical algebraic regularization techniques. This allows to handle so-called structurally singular systems and also enables a proper treatment of redundancies or inconsistencies in the system.