University of Notre Dame College of Engineering
C-SWARM | Center for Shock Wave-processing of Advanced Reactive Materials


Center for Shock Wave-processing of Advanced Reactive Materials



Room 117 I/J, Cushing Hall

Computational and Mathematical Aspects of
Nonlocal Models

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 (local) 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 several nonlocal models and discuss the impact of nonlocality upon their computational structure, reviewing discretization techniques, solution methods, and conditioning results. I’ll also highlight recent results from the numerical analysis of nonlocal models, including some non-intuitive results caused by the interplay of multiple length scales.

Michael Parks is the manager of the Computational Mathematics department in the Center for Computing Research at Sandia National Laboratories in Albuquerque, New Mexico. He holds a Ph.D. in computer science from the University of Illinois at Urbana-Champaign, an M.S. in computer science and B.S. degrees in physics and computer science from Virginia Tech. He is an associate editor for the SIAM Journal on Numerical Analysis the Elsevier journal Applied Mathematics and Computation, as well as the newly created Springer Journal of Peridynamics and Nonlocal Modeling. His research interests include numerical analysis, scientific computing, nonlocal models, multiscale mathematics, numerical linear algebra, linear solvers, and domain decomposition methods.


Featured People

Mr. Michael SkrochDr. Michael L. Parks

Computer Science
Research Institute,
Sandia National Laboratory