Mon, 03/27/2023 - 4:00pm Tue, 03/28/2023 - 4:00pm Wed, 03/29/2023 - 4:00pm Miller Learning Center Room 0150 and Boyd Research and Education Center Room 0328 Dr. Chi-Wang Shu Applied Mathematics Brown University Personal Website 2023 Cantrell Lecture Speaker is Dr. Chi-Wang Shu from Brown University Dr. Chi-Wang Shu is the Theodore B. Stowell University Professor of Applied Mathematics at Brown University. He is known for his research in the fields of computational fluid dynamics, numerical solutions of conservation laws and Hamilton–Jacobi type equations. Shu has been listed as an ISI Highly Cited Author in Mathematics by the ISI Web of Knowledge. He received his Ph.D degree from the University of California at Los Angeles in 1986. He has been a full professor at Brown University since 1996. He received the following honors and rewards: He is the 2021 recipient of the John von Neumann Lecture Prize, the highest honor and flagship lecture of Society for Industrial and Applied Mathematics (SIAM). The prize recognizes his fundamental contributions to the numerical solution of partial differential equations: "His work on finite difference essentially non-oscillatory (ENO) methods, weighted ENO (WENO) methods, finite element discontinuous Galerkin methods, and spectral methods has had a major impact on scientific computing." The Association for Women in Mathematics has included him in the 2020 class of AWM Fellows for "his exceptional dedication and contribution to mentoring, supporting, and advancing women in the mathematical sciences; for his incredible role in supervising many women Ph.D.s, bringing them into the world of research to which he has made fundamental contributions, and nurturing their professional success". In 2012 he became a fellow of the American Mathematical Society. In 2009, he was selected as one of the first 183 Fellows of the Society for Industrial and Applied Mathematics (SIAM). Lecture 1 March 27th @ 4pm- Miller Learning Center Room 0150For General Audience Mathematics in Scientific Computing Scientific computing is a relatively new research area,which arose because of the advances in computer resources.It addresses the critical issue of the development, analysis and application of algorithms for solving problems in engineering and applied sciences. Mathematics plays a central role in the development of scientific computing, and is responsible for the success of computer simulation together with the increase of computer powers. In this talk I will give an introduction to scientific computing and use several examples to demonstrate the role mathematics is playing in its development. Lecture 2 March 28th @ 4pm- Boyd Research and Education Center Room 328Of interest to graduate students from both applied and pure math High order numerical methods for hyperbolic equationsHyperbolic equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities. In this talk we will survey several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference and finite volume methods, discontinuous Galerkin finite element methods, and spectral methods. We will discuss essential ingredients, properties and relative advantages of each method, and provide comparisons among these methods. Recent development and applications of these methods will also be discussed. Lecture 3 March 29th @ 4pm- Boyd Research and Education Center Room 328 Discontinuous Galerkin Method for Convection Dominated Partial Differential Equations Discontinuous Galerkin (DG) method is a finite element method with features from high resolution finite difference and finite volume schemes such as approximate Riemann solvers and nonlinear limiters. It was originally designed for solving hyperbolic conservation laws but has been generalized later to solve higher order convection dominated partial differential equations (PDEs) such as convection diffusion equations and convection dispersion equations. The DG method has been widely applied, in areas such as computational fluid dynamics, computational electromagnetism, and semiconductor device simulations, just to name a few. In this talk we will give a general survey of the DG method, emphasizing its designing principles and main ingredients. We will also describe some of the recent developments in DG methods.