Analysis of an optimization-based atomistic-to-continuum coupling method for point defects

Journal Article · Sun Nov 15 23:00:00 EST 2015 · Mathematical Modelling and Numerical Analysis

DOI:https://doi.org/10.1051/m2an/2015023· OSTI ID:1313073

Olson, Derek ^[1]; Shapeev, Alexander V. ^[2]; Bochev, Pavel B. ^[3]; Luskin, Mitchell ^[1]

---

1. Univ. of Minnesota, Minneapolis, MN (United States)
2. Skolkovo Institute of Science and Technology, Skolkovo (Russia)
3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, we formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1313073
• Report Number(s): SAND--2014-18401J; PII: m2an141103
• Journal Information: Mathematical Modelling and Numerical Analysis, Journal Name: Mathematical Modelling and Numerical Analysis Journal Issue: 1 Vol. 50; ISSN 0764-583X
• Publisher: EDP Sciences
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
atomic lattice
atomistic-to-continuum coupling
constrained optimization
point defect