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Numerical Analysis

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Numerical Analysis

Numerical Analysis

MATH 4073

Ying Wang, Department of Mathematics

Mathematical models for modern applied sciences and engineering often consist of ordinary and partial differential equations. In most cases these problems do not have a simple explicit solution and can only be solved numerically. The construction and the accuracy of the numerical computation become vitally important. This Presidential Dream Course will expose the students to the subject through rigorous mathematical approaches.

The topics will include (but not be limited to) numerical linear algebra, single-step, multi-step, explicit and implicit numerical integrators for ordinary differential equations, and numerical methods for hyperbolic conservation laws. The focus of this course will be on the consistency, stability and convergence analysis. Students will have the opportunities to hear the state of the art of the subject from the world-class guest speakers.

Public Lecture Series

The Department of Mathematics presents a public lecture series in conjunction with the Presidential Dream Course. Presentations are free and open to the public. For information or accommodation to events on the basis of disability, please contact the department of Mathematics at 405-325-6711.

Numerical Computation on Curved Surfaces

Colin Macdonald

Tuesday, August 28, 2018
Physical Sciences Building Room 201
View Lecture Flyer [PDF]

Colin Macdonald, Ph.D.
Mathematics Department, University of British Columbia

Despite the appearance sometimes given in textbooks, not all differential equations are posed on straight lines and rectangles. This talk will introduce some easy-to-use techniques for computing numerical solutions to partial differential equations posed on curved surfaces and other general domains. One application is modelling animal coat pattern formation using reaction-diffusion equations. We'll also look at some other examples such as curve evolution, bulk-surface coupling, point clouds, visual effects, image processing, and mesh generation. A brief software demo will show how you can apply these techniques to your own problems.

Data Integration in Multiscale Simulations

Yalchin Efendiev

Friday, September 21, 2018
3:30pm - 4:30pm
Physical Sciences Building Room 108
View Lecture Flyer [PDF]

Yalchin Efendiev, Ph.D.
Ewing-Mobil Chair in Computational Science,
Professor of Mathematics,
Director of Institute for Scientific Computation (ISC), Texas A&M University

Yalchin Efendiev obtained his Ph.D. degree from Caltech in 1999. He came to Texas A&M University as an Assistant Professor in 2001, moving up to Associate Professor in 2005 and Full Professor in 2008. He is now the Director of Institute for Scientific Computation and the Mobil Chair in Computational Science of Texas A&M. He is the Principal Editor of Journal of Computational and Applied Mathematics and serves in the editorial boards of several other journals. He is an AMS Fellow, a keynote speaker at the Annual Meeting of International Porous Media Society in 2015, and a 45-minute invited speaker at the International Congress of Mathematicians at Seoul in 2014.

Mathematics in Scientific Computing

Chi-Wang Shu

Monday, October 8, 2018
5:30pm - 6:30pm
Nielsen Hall Room 270
View Lecture Flyer [PDF]

Chi-Wang Shu, Ph.D.
Theodore B. Stowell University Professor of Applied Mathematics, Brown University

Chi-Wang Shu obtained his B.S. degree from the University of Science and Technology of China in 1982 and his Ph.D. degree from the University of California at Los Angeles in 1986. He came to Brown University as an Assistant Professor in 1987, moving up to Associate Professor in 1992 and Full Professor in 1996. He was the Chair of the Division of Applied Mathematics between 1999 and 2005, and is now the Theodore B. Stowell University Professor of Applied Mathematics. His research interest includes high order finite difference, finite element and spectral methods for solving hyperbolic and other convection dominated partial differential equations, with applications to areas such as computational fluid dynamics, semi-conductor device simulations and computational cosmology. He served as the Managing Editor of Mathematics of Computation between 2002 and 2012, is now the Chief Editor of Journal of Scientific Computing and serves in the editorial boards of several other journals. His honors include the First Feng Kang Prize of Scientific Computing in 1995 and the SIAM/ACM Prize in Computational Science and Engineering in 2007. He is a SIAM Fellow and an AMS Fellow, and an invited speaker at the International Congress of Mathematicians at Seoul in 2014.

Consistent Coupling of Nonlocal Diffusion (Applied Math Seminar)

Xingjie Li

Friday, October 30, 2018
2:30pm - 3:30pm
Physical Sciences Building Room 323
View Lecture Flyer [PDF]

Xingjie Li, Assistant Professor
University of North Carolina at Charlotte

Dr. Xingjie Li is a tenure-track assistant professor at University of North Carolina at Charlotte. Her research lies in the area of applied and computational mathematics, focusing on multiscale modeling and structure-preserving schemes. She has built interdisciplinary collaborations with mathematicians, physicists and engineers in many application problems.