David Witman, Max Gunzburger, Janet Peterson


Reduced Order Modeling Applied to Non-Local Problems


Nonlocal theories refer to a set of concepts and methods that can be used in lieu or in combination of currently existing techniques used to solve differential equations. Peridynamics is a class of methods contained within these nonlocal theories that was developed in order to accurately model discontinuities in certain applications like fracture dynamics. These nonlocal methods rely on what is commonly referred to as a horizon, or radius in which surrounding particles interact with one another.