Review: Automatic Model Reduction for Transient Simulation of MEMS‐based Devices

Abstract

Abstract The rapid development of MEMS‐based devices requires 3D time‐dependent simulations for coupled physical domains (thermal, mechanical, electrical, etc.). This in turn requires the solution of high‐dimensional ordinary differential equations (ODEs) that result from space discretization of the device. However, instead of a “brute force” approach to integrate a large system of ODEs, one can use modern mathematical methods to reduce the system's dimension. The goal of the present paper is to review them from an engineering perspective. It is shown that in many cases important for practice the order of ODEs can be reduced by several orders of magnitude almost without sacrificing precision.