Sensitivity analysis and adaptive multi-point multi-moment model order reduction in MEMS design

Abstract

We present a model order reduction algorithm for linear time-invariant descriptor systems of arbitrary derivative order that incorporates sensitivity analysis for network parameters in respect to design parameters. It is based on implicit moment matching via rational Krylov subspace methods with adaptive choice of expansion points and number of moments based on an error indicator. Additionally, we demonstrate how parametric reduced order models can be obtained at nearly no extra costs, such that parameter studies are extremely accelerated. The finite element model of a yaw rate sensor MEMS device has been chosen as a numerical example, but our method is also applicable to systems arising in modeling and simulation of electromagnetics, electrical circuits, machine tools, heat conduction and other phenomena

Physically-Based Reduced Order Modelling of a Uni-Axial Polysilicon MEMS Accelerometer

“…Typically, such procedures were centred around Lanczos or Arnoldi's methodologies, see e.g., [2–6]. When nonlinearities of the model are weak, adaptive procedures for the projection of the governing equations onto the reduced order space, within which the system is mathematically assumed to evolve, may prove sufficient [7]. Instead, when nonlinearities are strong, Taylor series expansions or piecewise-linearisations were shown to be necessary in [2,8] to attain accuracy.…”