Computational geometry has until very recently had little impact upon the numerical solution of partial differential equations. The purpose of this talk is to explore Isogeometric Analysis, in which NURBS (Non-Uniform Rational B-Splines) and T-Splines are employed to construct exact geometric models [1,2] of complex domains. I will review recent progress toward developing integrated Computer Aided Design (CAD)/Finite Element Analysis (FEA) procedures that do not involve traditional mesh generation and geometry clean-up steps, that is, the CAD file is directly utilized as the analysis input file. I will summarize some of the mathematical developments within Isogeometric Analysis that confirm the superior accuracy and robustness of spline-based approximations compared with traditional FEA. I will present sample applications to problems of solids, structures and fluids.
Thomas J.R. Hughes holds B.E. and M.E. degrees in Mechanical Engineering from Pratt Institute and an M.S. in Mathematics and Ph.D. in Engineering Science from the University of California at Berkeley. He taught at Berkeley, Caltech and Stanford before joining the University of Texas at Austin. At Stanford he served as Chairman of the Division of Applied Mechanics, Chairman of the Department of Mechanical Engineering, Chairman of the Division of Mechanics and Computation, and occupied the Mary and Gordon Crary Family Chair of Engineering. At the University of Texas at Austin he is Professor of Aerospace Engineering and Engineering Mechanics and occupies the Computational and Applied Mathematics Chair III.
Dr. Hughes is a fellow of the American Academy of Mechanics (AAM), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the U.S. Association for Computational Mechanics (USACM), the International Association for Computational Mechanics (IACM), the Society of Industrial and Applied Mathematics (SIAM), and the American Association for the Advancement of Science (AAAS). He is co-editor of the international journal Computer Methods in Applied Mechanics and Engineering, a founder and past President of USACM and IACM, past Chairman of the Applied Mechanics Division of ASME, and past Chairman of the U.S. National Committee on Theoretical and Applied Mechanics (USNC/TAM).