dr. Marta D'Elia's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Speaker: Dr Marta D'Elia
Affiliation: Optimization and Uncertainty Quantification Department, 
Sandia National Laboratories, NM.
Title:  "Optimization-based coupling of local and nonlocal models"

Abstract:
Nonlocal models are used in many scientific and engineering applications 
where the material dynamics depends on the microstructure. This work 
presents an optimization-based method for the coupling of local and 
nonlocal continuum models; the coupling aims to combine the 
computational efficiency of partial differential equations with the 
accuracy of nonlocal models. The need for local-to-nonlocal couplings is 
especially acute when the size of the computational domain is such that 
the nonlocal solution becomes prohibitively expensive to compute, yet 
the nonlocal model is required to accurately resolve small scale 
features such as crack tips or dislocations that can affect the global 
material behavior.
We formulate the coupling as a control problem where the states are the 
solutions of the nonlocal and local equations, the objective is to 
minimize their mismatch on the overlap of the local and nonlocal 
domains, and the controls are the nonlocal volume constraint and the 
local boundary condition. We provide a mathematical and numerical 
analysis of the method in the context of nonlocal diffusion models. 
Numerical examples in one dimension illustrate the theoretical 
properties of the approach and provide the basis for realistic simulations.

Venue: SISSA, Friday 15 May at 11:00 in lecture room 133