Network Approach and Di erential { Algebraic Systems inTechnical

In technological computer aided design (TCAD), advanced pre-processors generate the mathematical models automatically. Network approaches enable the handling of complex applications with several thousand or more equations. Since most network descriptions rely on redundant coordinates, the corresponding models lead to descriptor forms or diierential-algebraic equations. Such coupled systems of ordinary diierential and nonlinear constraint equations present speciic numerical and analytical diiculties which are characterized by the index. Studying typical examples from electric circuit simulation, multi-body system dynamics, charge cycle of combustine engines and chemical process simulation, we introduce the underlying network approach and classify arising models in terms of the index and structural properties. Hints on available commercial and public domain software packages and some performance studies are included in the presentation.