SIAM Southeastern Atlantic Section Conference

September 18-19, 2021

Mini-symposium (MS)

MS2:  Recent Developments in Nonlocal Continuum Modeling

Organizers: James Scott, University of Pittsburgh

                     Pablo Seleson, Oak Ridge National Laboratory

Abstract: The efficacy of nonlocal continuum models in describing behavior across a variety of applications, such as mechanics, diffusion, and image processing, has been demonstrated in recent years. The peridynamics continuum mechanics model, nonlocal diffusion equations, and fractional PDEs are some notable examples. A variety of recent developments will be presented at this mini-symposium, giving attendees a broad picture of the state-of-the-art of nonlocal continuum modeling. Topics will include advances in mathematical analysis of nonlocal models, innovations in numerical methods and computational implementations of nonlocal models, and new applications of nonlocal models to engineering and scientific problems.


Saturday, September 18, 10:00 AM – 12:00 PM: Part I of III

Room: Libry 3035

10:00 – 10:30 Robert Lipton, Louisiana State University, Nonlocal brittle fracture modeling with applied traction forces

10:30 – 11:00 Pablo Paul Stinga, Iowa State University, Regularity estimates for nonlocal space-time master equations

11:00 – 11:30 James Scott, University of Pittsburgh, Relaxation phenomena in the localized limits of nonlocal energies movtivated by bond-based peridynamics

11:30 – 12:00 Mitchell Sutton, University of Tennessee, One-side fractional diffusion equations and their finite element approximations


Saturday, September 18, 3:30 PM – 5:30 PM: Part II of III
Room: Libry 3035

3:30 – 4:00 William Oates, Florida State University, Overal equilibrilium in the coupling of peridynamics and classical continuum mechanics

4:00 – 4:30 Elaine Gorom, University of North Carolina at Charlotte, A symmetric force-based method for the atomistic-to-continuum coupling

4:30 – 5:00 Pablo Seleson, Oak Ridge National Laboratory, Overall equilibrium in the coupling of peridynamics and classical continuum mechanics

5:00 – 5:30 Xiaochuan Tian, UC San Diego, A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems


Sunday, September 19, 10:30 AM – 12:30 PM: Part III of III

Room: Libry 3035

10:30 – 11:00 Hong Wang, University of South Carolina, A fast numerical method for a state-based PD model

11:00 – 11:30 Marco Pasetto, Oak Ridge National Laboratory, Convergence studies in meshfree peridynamic wave and crack propagation

11:30 – 12:00 Isaac Lyngaas, Oak Ridge National Laboratory, An RBF quadrature rule approach for solving nonlocal continuum models

12:00 – 12:30 Biraj Dahal, Georgia Tech, The evolution of the peridynamics co-authorship network