Plenary Lecture

Dual BEM since 1986

Professor Jeng-Tzong Chen
Life-time Distinguished Professor
Department of Harbor and River Engineering
National Taiwan Ocean University
2 Pei-Ning Road, Keelung, 202-24, Taiwan
Ε-mail: jtchen@mail.ntou.edu.tw

Abstract: In this talk, the development of dual BEM is reviewed since its appearance in 1986 by Hong and Chen. Roles of hypersigularity are also examined in the computational mechanics. A novel method using the SVD (singular value decomposition) for problems with degenerate boundaries was proposed without employing hypersingular formulation and subdomain approach in 2003. Some traps of BEM in engineering applications, degenerate scale, spurious eigenvalues and fictitious frequencies, are investigated. We provide a perspective on the nonuniqueness and its treatment, including degenerate boundary, degenerate scale, spurious eigensolution, fictitious frequency and corner problems as shown in Table 1, in the boundary integral formulation and boundary element method (BEM). All the nonuniqueness problems originate from the rank deficiency in the influence matrix. Both the Fredholm alternative theorem and SVD technique are employed to study the nonuniqueness problems. Based on the circulant properties and degenerate kernels as analytical tools for circular and annular cases, mathematical analysis can be done. Updating terms and updating documents of the SVD technique are utilized. The roles of right and left unitary vectors of SVD in BEM and their relations to true, spurious and fictitious modes are examined by using the Fredholm alternative theorem. Two methods, CHIEF and CHEEF techniques, for dealing with the nonuniqueness problems in BEM are proposed. Null-fields of nonuniqueness problems and the related works since 1984 are also addressed. Only key references of NTOU/MSV group are contained here.

Brief Biography of the Speaker:
Jeng-Tzong Chen, born in 1962, received a BS degree in Civil Engineering, an M.S. in Applied Mechanics, and a Ph.D. in Civil Engineering, respectively, in 1984, 1986 and 1994, from National Taiwan University, Taipei, Taiwan, R.O.C. He had worked as a research assistant in the Structural Division of the Department of Rocket and Missile System, Chung Shan Institute of Science and Technology, from 1986 to 1990. In 1994, he was invited to be an Associate Professor in the Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan, R.O.C. He was promoted to a full professor in 1998. Later in 2004, he was selected to be the Distinguished Professor. In 2007, he was selected as the Life-time Distinguished Professor. He is also the Professor of Department of Mechanical and Mechatronic Engineering of Taiwan Ocean University. His major interest is computational mechanics. He had derived the theory of dual integral equations for boundary value problems with degenerate boundary. Prof. Chen also developed four dual BEM programs for the BVPs of Laplace equation, Helmholtz equation, bi-Helmholtz and modified Helmhotlz equation and Navier equation. Recently, he also employed the null field integral equations to solve BVPs with circular boundaries including holes and inclusions. He wrote two books in Chinese on dual BEM and FEM using MSC/NASTRAN, respectively. He was ever invited to give plenaray and keynote lectures, e.g., twice in World Congress on Computational Mechanics (WCCM4 in Buenos Aries and WCCM5 in Vienna) and FEM/BEM 2003 in St. Petersburg, Russia. Also, he is the editor of Journal of the Chinese Institute of Civil and Hydraulic Engineering. He has been the Editor of Journal of Marine Science and Technology and the guest editor of J. Chinese Institute of Engineers. He won several times of Outstanding Research Awards from National Science Council, Taiwan. He also won the Wu, Ta-You Memorial Award in 2002. He is currently the member of editorial board of five international SCI journals. Until now, he has published more than 126 SCI papers on BEM and FEM in technical Journals. More than 615 papers are found to cite Chen’s work.. Boundary element method is one focus of Professor Chen's research interests. Others may be categorized into two areas. One is vibration and acoustics, and the other is computational mechanics.