Efficient Time Integration of Nonlinear Partial Differential Equations by Means of Rosenbrock Methods

We avoid as as much as possible the order reduction of Rosenbrock methods when they are applied to nonlinear partial differential equations by means of a similar technique to the one used previously by us for the linear case. For this we use a suitable choice of boundary values for the internal stages. The main difference from the linear case comes from the difficulty to calculate those boundary values exactly in terms of data. In any case, the implementation is cheap and simple since, at each stage, just some additional terms concerning those boundary values and not the whole grid must be added to what would be the standard method of lines.

Evaluating Rosenbrock Methods for Usage in Real-Time Simulation of Multibody Models

The upward trend in the usage of sensors and intelligent systems in mechanical systems is requiring the continuing growth in hardware-in-the-loop (HIL) testing in theautomotive industry. This trend in turn is requiring that more sophisticated multibody system models (MBS) be incorporated into hardware-in-the-loop design and testing phases. Running sophisticated multibody models consisting of a large number of bodies and a variety of compliant elements is a challenging on a HIL system. The models must be detailed enough to give realistic results yet run fast enough to meet strict turnaround times of the HIL system. This paper will explore the use of a Rosenbrock method in a real-time environment and compare its performance and accuracy to other integrators in particular to a Backward Difference Formula (BDF) that is restricted in order and number of iterations.