Colloquium: "Analysis and computation of nonlocal models"

Speaker: Xiaochuan Tian, University of Texas at Austin

Abstract: Nonlocal models, often appear as integro-differential equations, have been widely introduced recently as mathematical descriptions of different phenomena in physics, biology and material sciences. While nonlocal models show their effectiveness in modeling a number of processes, they also come with increased difficulty in analysis and computation. In the first part of this talk, I will discuss robust discretizations of nonlocal diffusion and nonlocal mechanics models featured with a horizon parameter which characterizes the nonlocal interaction length. In particular, I will present an abstract mathematical framework that can be used to identify asymptotically compatible schemes for nonlocal variational problems which give convergent schemes insensitive to parameter changing. In the second part of talk, I will discuss multiscale modeling techniques so as to improve the computational efficiency of using nonlocal models. A seamless local-nonlocal coupling method based on the heterogeneous localization of nonlocal interactions will be discussed. This also motivates the development of new mathematical results -- for instance, a new trace theorem that extends the classical results will be presented.

Host: Renato Feres

Tea will be served @ 3:30 in room 200.