Y. J. Liu 1 Mechanical Engineering, University of Cincinnati, 598 Rhodes Hall, 2600 Clifton Avenue, Cincinnati, OH 45221-0072, e-mail: yijun.liu@uc.edu S. Mukherjee Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 e-mail: sm85@cornell.edu N. Nishimura Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501 Japan, e-mail: nchml@i.kyoto-u.ac.jp M. Schanz Institute of Applied Mechanics, Graz University of Technology, Technikerstr. 4, A-8010 Graz, Austria, e-mail: m.schanz@tugraz.at W. Ye Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong, China, e-mail: mewye@ust.hk A. Sutradhar Department of Surgery and Department of Mechanical Engineering, The Ohio State University, 915 Olentangy River Road, Suite 2100, Columbus, OH 43212 e-mail: Alok.Sutradhar@osumc.edu E. Pan Department of Civil Engineering, The University of Akron, ASEC Room 534, Akron, OH 44325-3905 e-mail: pan2@uakron.edu N. A. Dumont Pontifical Catholic University of Rio de Janeiro, 22451-900 Brazil e-mail: dumont@puc-rio.br A. Frangi Department of Structural Engineering, Politecnico of Milano, P.za L. da Vinci 32, 20133 Milano, Italy, e-mail: attilio.frangi@polimi.it A. Saez Department of Continuum Mechanics and Structural Analysis, University of Seville, Camino de los Descubrimientos s/n, Seville, E-41092, Spain, e-mail: andres@us.es Recent Advances and Emerging Applications of the Boundary Element Method Sponsored by the U.S. National Science Foundation, a workshop on the boundary ele- ment method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This pa- per was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green’s functions, symmetric Galerkin formulations, bound- ary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for stu- dents, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review. [DOI: 10.1115/1.4005491] 1 Corresponding author. Manuscript received May 25, 2011; final manuscript received December 12, 2011; published online March 30, 2012. Transmitted by Editor: J. N. Reddy. Applied Mechanics Reviews MAY 2011, Vol. 64 / 031001-1 Copyright V C 2011 by ASME Downloaded 21 Apr 2012 to 131.175.24.250. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm