This paper introduces a new algorithm to increase the simulation performance of algebraic equation systems by encapsulating function calls.This avoids unnecessary evaluations of function calls and leads to positive structural effects, such as code motion.To enable the reader to reconstruct the algorithm, all four phases of the algorithm are described in detail and the complexity of them is analyzed.The overall complexity for practical models is O(n), where n is the number of equations.It is shown that the algorithm significantly decreases the simulation time for a wide range of physical based models.

Common tearing methods try to find static tearing variables. This means that selected tearing variables are used for the entire simulation, which also means that all inner equations are used for the entire simulation. Hence, the tearing method sets up the tearing system in a way, that there are no restrictions on the domain of the inner equations. In general, this leads to bigger tearing sets. This paper presents an extension of common tearing methods that generates another tearing set in addition. The additional set has fewer tearing variables, which means that it should be more efficient in general. However, the additional set has some restrictions on its domain of definition. That is why common approaches would not even create it and why it may not be used for the entire simulation. Hence, its domain needs to be analysed during simulation to validate if the smaller set is defined on the current domain. If that is the case the smaller set is used for the calculation, otherwise the original set is used. This paper shows how this additional tearing set can be generated. It is also demonstrated how the domain can be monitored during runtime in order to make the switching process efficient. Results using a prototype implementation in OpenModelica are analysed to show the benefits of this method.

This paper is concerned with the tearing method according to François Cellier. Tearing is used to reduce the dimension of algebraic loops, which inevitably arise in the modelling of scientific systems using differential-algebraic equations, as far as possible to achieve an efficient simulation. However, the original tearing method according to Cellier is not suitable for the application in practice, since restrictions on the solvability of equations for variables, and other features, which appear in reality, are not considered. In this work, different changes to the method are introduced and tested, which make it possible to use Cellier Tearing in practice. In addition, the modeller can influence the selection of tearing variables. Modifications of the integrated heuristic are presented, whose efficiency is statistically evaluated at the end of this work. With these changes and the new heuristics, Cellier's method becomes a very suitable way to optimize the efficiency of simulation in practice.

A method for testing the operability of a built-up in a test vehicle driver assistance system, which operates information supplied in response to sensors that detect a test of in the environment, driving test vehicle traveling target vehicle, in particular a engaging in the longitudinal or transverse guidance of the motor vehicle driver assistance system wherein the test vehicle (2) controls the operation of the target vehicle (3) for selectively performing at least a defined driving maneuver by the administration of control signals via a wireless communication link at least partially.