Collaborative Research: Fast Simulation of Complex MEMS Structures with the Boundary Element, Finite Element and Fast Multipole Methods

合作研究：用边界元、有限元和快速多极方法快速模拟复杂MEMS结构Subrata Mukherjee和Yijun Liu 2005年9月1日-2008年8月31日摘要微机电系统（MEMS）在各种工业中有着广泛的重要应用。这里关注的是MEMS，其由具有微米量级的横截面和数十至数百微米量级的长度的薄梁和/或板的阵列组成。本项目主要研究此类系统在电驱动（包括阻尼）作用下的动力学特性，并对包括机械场、电场和流场在内的全耦合问题进行模拟。有限元法将主要用于模拟结构，而最近提出的新的边界元法将用于模拟外部电场和流体场。该项目的一个关键特点是实施快速多极方法，在不牺牲精度的情况下非常有效地模拟MEMS的大规模模型。该项目有望成为MEMS仿真的重大突破。这项研究的结果将迅速纳入康奈尔大学和辛辛那提大学的研究生课程，并在科学期刊、会议和网站上传播。一个关于快速多极方法的研讨会，由N。计划于2006年在洛杉矶举行的第七届世界计算力学大会期间进行。奖学金将提供给美国的研究生参加这个研讨会。

Collaborative Research : Fast Simulation of Complex MEMS Structures with the Boundary Element, Finite Element and Fast Multipole MethodsSubrata Mukherjee and Yijun LiuSeptember 1, 2005 - August 31, 2008AbstractMicro-electro-mechanical systems (MEMS) enjoy a wide range of important applications in a variety of industries. MEMS, that consist of arrays of thin beams and/or plates, with cross-sections in the order of microns and lengths in the order of tens to hundreds of microns, are of concern here. Dynamics of such systems under electrical actuation, including damping, is of interest to this project.Simulations of fully-coupled problems, that include mechanical, electrical and fluidic fields, will be carried out in this project. The Finite Element Method will be primarily used to model the structure, while a recently proposed novel Boundary Element Method will be used to model the exterior electrical and fluid fields. A key feature of this project is the implementation of the Fast Multipole Method to simulate large-scale models of MEMS very efficiently without sacrificing accuracy. This project is expected to be a major breakthrough for MEMS simulation. Findings from this research will be rapidly incorporated into graduate courses at Cornell and Cincinnati, and disseminated in scientific journals, conferences and websites. A workshop on Fast Multipole Methods, led by Professor N. Nishimura of Kyoto University, is planned during the Seventh World Congress on Computational Mechanics in Los Angeles in 2006. Fellowships will be provided to US graduate students for their participation in this workshop.