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A Combined Structural-Algebraic Approach for the Regularization of Coupled Systems of DAEs

Scholz, Lena; Steinbrecher, Andreas

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

The automated modeling of multi-physical dynamical systems is usually realized by coupling different subsystems together 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 kind 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 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 we show that it is not suited for coupled systems of DAEs. We will present a new approach for the regularization of coupled dynamical systems that combines the structural analysis, in particular the Signature Method of Pryce, with classical algebraic regularization techniques and thus allows to handle so-called structurally singular systems and also enables a proper treatment of redundancies or inconsistencies in the system.