Parameter preserving model order reduction for MEMS applications

Model order reduction techniques are known to work reliably for finite element-type simulations of micro-electro-mechanical systems devices. These techniques can tremendously shorten computational times for transient and harmonic analyses. 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 article we demonstrate a novel parameterization method to numerically construct highly accurate parametric ordinary differential equation 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 parameterization lies in the region of . 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. Speed-up factors of 20--80 could be achieved, while retaining up to six parameters and keeping typical relative errors below 1%.