Abstract
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in [17] for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.
| Original language | English (US) |
|---|---|
| Title of host publication | Large-Scale Scientific Computing - 9th International Conference, LSSC 2013, Revised Selected Papers |
| Publisher | Springer Verlag |
| Pages | 33-44 |
| Number of pages | 12 |
| ISBN (Print) | 9783662438794 |
| DOIs | |
| State | Published - 2014 |
| Event | 9th International Conference on Large-Scale Scientific Computations, LSSC 2013 - Sozopol, Bulgaria Duration: Jun 3 2013 → Jun 7 2013 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 8353 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 9th International Conference on Large-Scale Scientific Computations, LSSC 2013 |
|---|---|
| Country/Territory | Bulgaria |
| City | Sozopol |
| Period | 6/3/13 → 6/7/13 |
Bibliographical note
Funding Information:DO was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. ML was supported in part by the NSF PIRE Grant OISE-0967140, DOE Award DE-SC0002085, and AFOSR Award FA9550-12-1-0187. AS was supported in part by the DOE Award DE-SC0002085 and AFOSR Award FA9550-12-1-0187.