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、有限元和快速多极子方法快速模拟复杂的MEMS结构Subrata Mukherjee和刘益军2005年9月1日至2008年8月31日摘要微电子机械系统(MEMS)在各种行业中有着广泛的重要应用。MEMS由薄束和/或板阵列组成，横截面在微米量级，长度在几十到几百微米量级，在这里是令人关注的。这类系统在电激励下的动力学，包括阻尼，是本项目的重要内容。在本项目中，将对包括机械、电气和流体场在内的全耦合问题进行模拟。有限元方法将主要用于对结构进行建模，而最近提出的一种新的边界元方法将用于对外部电场和流场进行建模。该项目的一个主要特点是实现了快速多极子方法，在不牺牲精度的情况下非常高效地模拟了大规模的MEMS模型。该项目有望成为MEMS模拟的重大突破。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。由京都大学N·西村教授领导的快速多极方法研讨会计划于2006年在洛杉矶举行的第七届世界计算力学大会期间举行。将为参加此次研讨会的美国研究生提供奖学金。

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.