Proceedings of IMECE 2009 ASME International Mechanical Engineering Congress and Exposition November 13-November 19, 2009 Lake Buena Vista, Florida, USA IMECE2009-10525 1 Copyright © 2009 by ASME FAST HARMONIC MEMS SIMULATION WITH ARNOLDI MODEL ORDER REDUCTION David Binion and Xiaolin Chen Mechanical Engineering School of Engineering and Computer Science Washington State University Vancouver Vancouver, WA 98686 ABSTRACT Recent years has witnessed a large increase in the use of vibrating Micro-Electro-Mechanical-Systems (MEMS) especially in the expanding wireless telecommunication industry. In particular, the use of microresonators to generate or filter signals has facilitated a reduction in the size of many popular cell phones. Advances in microfabrication have increased the ability to create complex MEMS devices. Finite Element Analysis (FEA) has widely been used in the design of these devices. To obtain accurate simulations of complex MEMS devices, a dense FEA mesh is required resulting in computationally demanding simulation models. Arnoldi Model Order Reduction has been investigated and implemented to improve the computational efficiency of MEMS simulations. Using ANSYS, a popular FEA program, a micro resonator model was created. With Arnoldi, a Krylov subspace was extracted from the model and the model was projected onto the subspace reducing the model size. A harmonic simulation over normal operating frequencies was performed on the reduced model and compared with a simulation of the original model. It was found that the computational time was drastically reduced through the use of Arnoldi while achieving similar accuracy as compared to the original model. INTRODUCTION Recent years has seen a large increase in the use of vibrating Micro-Electro-Mechanical-Systems (MEMS) especially in the expanding wireless telecommunication industry. In particular, micromechanical resonators have displayed the ability to achieve high quality factors with low power consumption which along with their small size has made them attractive options for use as signal generators or signal filters [1,2]. The increase in their use has led to focused research in the design and modeling of microresonators [1-4]. Finite Element Analysis (FEA) has widely been used to model microresonators. Detailed solutions obtained through FEA describe the resonators harmonic response over its operating frequency. However, harmonic simulation of electromechanical devices through FEA must account for the interactions between two physics domains which can be computationally expensive. In addition, micromachining advances has allowed the creation of increasingly complex MEMS structures. Fine FEA discretizations are required to accurately simulate these complex devices which place additional demands on CPU and computer memory resources. Model Order Reduction (MOR) techniques [5-12] have been shown to be an effective method for alleviating the computational demands of MEMS simulations. MOR is a process that reduces the dimension of a system of Ordinary Differential Equations (ODEs) obtained from FEA discretization. The reduced system is then used to simulate the full scale model behavior. To achieve accurate reduced model simulations, essential full scale model characteristics must be maintained; namely the input/output behavior [9]. The Arnoldi algorithm [13] is a MOR technique that has shown the ability to maintain these characteristics while reducing computational demands. Reduced models produced via Arnoldi are generated based on a specific operating frequency. J. Lienemann et. al. [7] demonstrated MOR for a reduced model of a micro-mechanical gyroscope. Harmonic simulation was performed over a wide range of operating