INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2005; 64:528–546 Published online 8 June 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1383 Analysing microwave devices using a symmetric coupling of finite and boundary elements Seung-Cheol Lee ∗, †, ‖ , Marinos N. Vouvakis ‡, ‖ , Kezhong Zhao § and Jin-Fa Lee ¶ ElectroScience Laboratory, Electrical Engineering Department, The Ohio State University, U.S.A. SUMMARY This paper presents a symmetric coupling between the finite element and boundary element methods for analysing open microwave devices. The proposed finite element boundary element (FEBE) method is based on the E-field vector Helmholtz equation. Second-order hierarchical Curl-conforming vector finite elements over tetrahedrons are used to discretize the interior region. The boundary element (BE) truncation surface is discretized with the second-order divergence-conforming surface elements with triangular support. The symmetry of the BE part is restored through the application of the Calderon-projector. Moreover, the BE computations are accelerated using a single level QR algorithm. This reduces both memory and computational time. The resulted symmetric system of equations is solved with a very efficient preconditioned conjugate gradient (PCCG) method with a p-multiplicative Schwarz (pMUS) preconditioner. Copyright  2005 John Wiley & Sons, Ltd. 1. INTRODUCTION Microwave devices have been successfully analysed by various numerical methods [1–4]. Among them, the finite element method (FEM) may be the most suitable due to its abil- ity to model complex geometric and material features. On the other hand, FEM has been proven ineffective in dealing with unbounded geometries. Several methods have been proposed to overcome this problem, by enforcing an appropriate boundary condition on a truncation surface. The most popular methods to accomplish this are the absorbing boundary condition ∗ Correspondence to: Seung-Cheol Lee, ElectroScience Laboratory, Electrical Engineering Department, The Ohio State University, 1320, Kinnear Road, Columbus, OH 43212-1191, U.S.A. † E-mail: lee.1802@osu.edu ‡ E-mail: vouvakis.1@osu.edu § E-mail: zhao.74@osu.edu ¶ E-mail: lee.1863@osu.edu ‖ Ansoft Fellow. Contract/grant sponsor: Ansoft Corp. Contract/grant sponsor: National University of Singapore Received 30 April 2004 Revised 8 March 2005 Copyright  2005 John Wiley & Sons, Ltd. Accepted 12 March 2005