Abstract : The quest for more efficient and accurate computational electromagnetics (CEM) techniques has been vital in the design of modern engineering. The main motivation of this work lays in a simple yet crucial observation of most real-world electromagnetic problems. They all exhibit certain degrees of redundancies, locally and/or globally. Take for example a vehicle: its geometry is symmetric with respect to a mid-plane; for an antenna array or frequency selective surface the redundancies are more obvious since all elements are identical. In our group, we have recently developed a novel approach for analyzing electrically large, geometrically complicated structures that involve complex materials, by systematically exploiting local or global mirror, translational or rotational symmetries in the geometry.The approach is based on the domain decomposition (DD) methodology tailored specifically for electromagnetic wave problems. Although DDM has been popular in the applied mathematics community for solving Poisson equations, it is not directly applicable to wave propagation problems. In particular, I shall discuss three major ingredients which enable the DDM for solving large electromagnetic problems.1.Cement Technique: The cement technique allows for non-matching grids across sub-domain boundaries. The feature makes the DDM a practical tool and mitigates the need for conformal meshes in numerical computations;2.Converging Transmission Conditions: For solving large electromagnetic problems, it is usually beneficial to solve it through iterative process. The DDM can be viewed as a preconditioning strategy for solving the resulting large matrix equations. However, it will be shown in the talk, the convergence in the DDM process strongly depends on the choice of the transmission condition through which the information between sub-domains are interchanged;3.Finite Element Tearing and Interconnecting (FETI) Algorithm: For large electromagnetic problems, which involve large number of repeating blocks, the FETI algorithm provides a very appealing solution strategy. The FETI algorithm aims to compute the transfer functions of the building blocks within DDM explicitly, thus, eliminates matrix solution process during the DDM iterations. The FETI algorithm potentially plays a significant role in future design and optimization of electromagnetic devices.The power of the developed DDM will be demonstrated through a number of large electromagnetic problems, involving upto billions of finite element unknowns, and its variants such as domain decomposition finite elements / boundary elements method (DD-FE-BEM), and a modeling procedure for industrial applications.

Biography :Jin-Fa Lee received the B.S. degree from National Taiwan University, in 1982 and the M.S. and Ph.D. degrees from Carnegie-Mellon University in 1986 and 1989, respectively, all in electrical engineering. From 1988 to 1990, he was with ANSOFT Corp., where he developed several CAD/CAE finite element programs for modeling three-dimensional microwave and millimeter-wave circuits. From 1990 to 1991, he was a post-doctoral fellow at the University of Illinois at Urbana-Champaign. From 1991 to 2000, he was with Department of Electrical and Computer Engineering, Worcester Polytechnic Institute. Currently, he is a Professor at Electro Science Lab., Dept. of Electrical Engineering, Ohio State University. Prof. Lee becomes an IEEE Fellow on year 2005. His students won the 4th place in student paper contest in IEEE APS/URSI 2004, and 3rd place in IEEE APS/URSI 2005.Professor Lee research interests mainly focus on numerical methods and their applications to computational electromagnetics. Current research projects include: analyses of numerical methods, fast finite element methods, fast integral equation methods, hybrid methods, three-dimensional mesh generation, domain decomposition methods, cement finite elements, and finite element tearing and interconnecting methods.

Prof. Jin-Fa LeeProf. Jin-Fa Lee Dept. of Electrical Engineering, Ohio State UniversityDept. of Electrical Engineering, Ohio State University

Date : Dec. 7, 2005, 13:30Date : Dec. 7, 2005, 13:30 Place : Place : 博理館博理館 R101R101