Nonlocal models such as peridynamics and fractional equations can capture effects that classical partial differential equations fail to capture. These effects include multiscale behavior, discontinuities in the solutions such as cracks, and anomalous behavior such as super- and sub-diffusion. For this reason, they provide an improved predictive capability for a large class of engineering and scientific applications including fracture mechanics, subsurface flow, turbulence, and image processing, to mention a few.
However, the improved accuracy of nonlocal formulations comes at the price of modeling and computational challenges that may hinder the usability of these models. Challenges include the nontrivial prescription of nonlocal boundary conditions, the unresolved treatment of nonlocal interfaces, the identification of model parameters, often sparse and subject to noise, and the incredibly high computational cost.
In this talk I will first introduce nonlocal models and describe a recently developed nonlocal calculus for their analysis. Then, I will discuss simulation challenges and describe in detail how we are addressing some of them at Sandia National Labs.
21/09/2020
BIO
Dr. Marta D'Elia obtained her bachelor and master degree in Mathematical Engineering at Politecnico of Milano under the supervision of Prof. Quarteroni (Dec 2007). She obtained her PhD in Applied Mathematics at Emory University under the supervision of Prof. Veneziani (Dec 2011). Here, she worked on optimal control and data assimilation in CFD for cardiovascular applications. She was a postdoctoral fellow from Jan 2012 to Jan 2014 at Florida State University where she worked with Prof. Gunzburger on optimization for nonlocal and fractional models. In February 2014 she joined Sandia National Laboratories, where she works now as a Member of the Technical Staff in the Computational Science and Analysis group at the California site. Her interests include nonlocal modeling and simulation, optimization and optimal control, and scientific machine learning.