Applied Math Seminar: Integral equation modeling for anomalous diffusion and nonlocal mechanics

Seminar | May 10 | 11 a.m.-12 p.m. | 891 Evans Hall

 Max Gunzburger, Florida State University

 Department of Mathematics

We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. In particular, we discuss the recently developed asymptotically compatible families of discretization schemes. Brief forays into examples and extensions are made, including obstacle problems and wave problems.