MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices
J. Lienemann, D. Billger, E.B. Rudnyi, A. Greiner and J.G. Korvink
IMTEK, Albert Ludwig University, DE
Keywords: model order reduction, Arnoldi process, compact modeling, second order differential equations, butterfly gyroscope
Modeling and simulation of the behavior of a system consisting of many single devices is an essential requirement for the reduction of design cycles in the development of microsystem applications. Analytic solutions for the describing partial differential equations of each component are only available for simple geometries. For complex geometries, either approximations or numerical methods can be used. However, the numerical treatment of the PDEs of thousands of interconnected single devices with each exhibiting a complex behavior is almost impossible without reduction of the order of unknowns to a lower-dimensional system. We present a fully automatic method to generate a compact model of second-order linear systems based on the Arnoldi process, and provide an example of successfull model order reduction to a gyroscope. In addition, we list other examples of where model order reduction with the Arnoldi method was or can be successfully applied to.
Nanotech 2004 Conference Technical Program Abstract