Speaker: 杜强教授 (Prof. Qiang Du, Penn State University)

Time: 2013年9月16日下午4点至5点

Venue: 北京国际数学研究中心78号院77201

Abstract: Nonlocality is ubiquitous in nature. While PDEs have been used as effective models of many physical processes, nonlocal models and nonlocal balanced laws are also attracting more and more attention as possible alternatives to treat anomalous process and singular behavior. In this talk, we discuss some nonlocal models and a new nonlocal calculus framework as the axiomatic basis for systematic formulations, analysis and approximations of nonlocal models. The latter offers striking analogies and strong connections between local and nonlocal balance laws and it also provides a continuum description of many discrete operators developed for graphs and networks. The notion of asymptotically compatible discretizations will be introduced which gives convergent approximations in the nonlocal setting and converge asymptotically to the local limit as both the measure of nonlocality and the mesh size are taking to zero. This leads to robust numerical approaches for solving multiscale models with spatially varying degrees of nonlocality and length scales.