主 题: Recent development in Scientific Computing: Recent development in Scientific Computing
报告人: Franco Brezzi (Istituto Universitario di Studi Superiori, IUSS)
时 间: 2016-12-09 11:00 - 12:00
地 点: 英杰交流中心月光厅
After a short presentation of Scientific Computing, of its problems and its typical results, we recall some fundamental equations ruling the mathematical representation of most “real-life” problems. Going more into details, we consider their “Variational Formulation”, and the Ritz-Galerkin approach for the computation of an approximate solution. Further into details, we present the approximations based on a decomposition of the computational domain into “elements” (that is, tiny pieces of the domain: more and smaller pieces for a more accurate result). Among them we concentrate on the approximations based on decompositions made of elements of more complicated geometries, instead of the commonly used simplexes and boxes (in two dimensions: triangles and quadrilaterals). We discuss pros and cons of these choices, the theoretical and practical difficulties, and the expectations that made the subject so popular in the very last years. At the final level of detail, we present the Virtual Element Method, introduced about three years ago, and discuss some of its main features.
Franco Brezzi works on the theoretical bases of Scientific Computing, in particular in Numerical Methods for Partial Differential Equations, where he has made fundamental contributions to Mixed Finite Element Methods, Mimetic Finite Differences, or Virtual Elements of problems related to Structural Mechanics, Fluid Mechanics, and Electro-Magnetics, including algorithms and theories. He was awarded the Gauss-Newton gold medal of the International Association for Computational Mechanics of the World Congress of Computational Mechanics in 2004, SIAM von Neumann award in 2009, and the Leonhard Euler Medal and the Ritz-Galerkin Medal of the European Community on Computational Methods in Applied Science in 2014 and 2016, respectively. Franco Brezzi was an Invited Plenary Speaker at the ICM in 2014 in Seoul, and an Invited Speaker at the ICM in 1986 in Berkeley. He had been President of the Italian Mathematical Union from 2006 to 2012, and is currently Vice President of the European Mathematical Society. Also he is a member of the European Academy of Sciences, and a fellow of the International Association of Computational Mechanics and of the Society for Industrial and Applied Mathematics.