Parameter preserving model order reduction for MEMS applications

Model order reduction techniques are known to work reliably for finite-element-type simulations of MEMS devices. These techniques can tremendously shorten computational times for transient and harmonic analysis. However, standard model reduction techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved for the reduced model. However, design cycles often involve parameter modification, which should remain possible also in the reduced model. In this paper we demonstrate a novel parametrization method to numerically construct highly accurate parametric ODE systems based on a small number of systems with different parameter settings. This method is demonstrated to parameterize the geometry of a model of a micro-gyroscope, where the relative error introduced by the parametrization lies in the region of 10. We also present recent developments on semi-automatic order reduction methods that can preserve scalar parameters or functions during the reduction process. The first approach is based on a multivariate Padé-type expansion. The second approach is a coupling of the balanced truncation method for model order reduction of (deterministic) linear, time-invariant systems with interpolation. The approach is quite flexible in allowing the use of numerous interpolation techniques like polynomial, Hermite, rational, sinc, and spline interpolation. As technical examples we investigate a micro anemometer as well as the gyroscope. Speedup factors of 20 to 80 could be achieved, whilst retaining up to 6 parameters, and keeping typical relative errors below 1%.