Applied Mathematics Seminar

Title:  Nonlocal Models and Peridynamics

Speaker: Speaker:  Michael Parks (Sandia National Laboratories)
http://www.sandia.gov/~mlparks/

Abstract: Nonlocal models are receiving increasing interest from scientific and engineering communities due to their ability to describe physical processes which are not well represented by PDE-based models. In particular, nonlocal models are useful in that they can resolve phenomena at multiple length scales, making them suitable models for multiscale processes. I will survey peridynamics, a nonlocal extension of classical continuum mechanics, as a representative nonlocal model. I will show several motivating examples and discuss the impact of nonlocality upon the computational structure of the model, reviewing discretization techniques, conditioning results, and solution methods. I’ll highlight recent results from the numerical analysis of peridynamics, including some non-intuitive results caused by the interplay of multiple length scales.