Recent advances in computational methods for microsystems Alberto Corigliano 1,a , Martino Dossi 1,b and Stefano Mariani 1,c 1 Department of Civil and Environmental Engineering, Politecnico di Milano Piazza L. da Vinci 32, 20133 Milano, Italy a alberto.corigliano@polimi.it, b dossi@stru.polimi.it, c stefano.mariani@polimi.it Keywords: MEMS; Electro-mechanical problem; Finite element method; Domain decomposition; Proper orthogonal decomposition. Abstract. An algorithm, which combines the use of Domain Decomposition and Model Order Reduction methods based on Proper Orthogonal Decomposition, is proposed. The algorithm allows for the efficient handling of electro-mechanical coupled problems in MEMS, with a strong reduction of computing time with respect to standard monolithic or staggered solution strategies. Examples of coupled electro-mechanical problems, concerning a vibrating beam subject to variable electrostatic forces, are presented and discussed. Introduction Microsystems, or Micro Electro Mechanical Systems (MEMS), (see e.g. [1]) are complex devices in which the design phase strongly depends on modeling and simulations. Due to the combination of multi-physics and multi-scale problems in MEMS, the computational burden can become extremely high or prohibitive for realistic models. The attempt to find efficient techniques for the simulation of complex problems in MEMS has fostered research in many directions. One of these directions, also explored in the present paper, is the use of Domain Decomposition (DD) and/or Model Order Reduction (MOR) methods to drastically reduce the computing time and to efficiently exploit possibilities offered by large scale and parallel computing. Recent attempts to combine the use of DD and MOR techniques in various contexts can be found e.g. in [2,3,4]. The goal of this paper is to show how the combination of a DD technique with a reduced order model obtained with the Proper Orthogonal Decomposition (POD) [5,6] can give rise to an algorithm which efficiently solves the electro-mechanical coupled problem [7,8,9], which is one of the typical ones for MEMS found e.g. in capacitive sensors or actuators. The proposed approach is part of a wider research activity which aims at obtaining realistic modeling and simulation techniques with computing times compatible with the design phases. Starting from the DD techniques formulated in [10,11] for structural dynamics, the Authors already proposed in [12] an original DD approach for the solution of the coupled electro-mechanical problem. Subsequently, the Authors proposed in [13] a combination of DD and POD conceived for the solution of coupled problems in MEMS. The present paper contains a further advancement with respect to [13], which consists in a different way to impose continuity between the initially de- coupled domains and in various strategies for the application of POD to the mechanical part of the solution domain. The proposed technique is one step further in the formulation of a general DD- POD approach which allows for the simulation of highly non-linear coupled problems, in the presence of irreversible material behaviors like e.g. plasticity and fracture. The paper is organized as follows: the electro-mechanical coupled problem is first formulated, together with its semi-discretized version; subsequently the DD, the POD techniques and the way in which they are here coupled are briefly discussed; numerical results concerning a vibrating beam under the action of variable electrostatic forces are discussed; final remarks conclude the paper. Formulation of the electro-mechanical problem With reference to Fig. 1, we focus on a two-dimensional domain Ω composed by an electrical part Ω  and a mechanical part Ω  , separated by the interface Γ. The outer boundary of Ω is divided Advanced Materials Research Vol. 745 (2013) pp 13-25 © (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.745.13 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 87.8.43.218-16/05/13,00:01:51)