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  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|
|Number of pages||12|
|State||Published - 2014|
|Event||9th International Conference on Large-Scale Scientific Computations, LSSC 2013 - Sozopol, Bulgaria|
Duration: Jun 3 2013 → Jun 7 2013
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Other||9th International Conference on Large-Scale Scientific Computations, LSSC 2013|
|Period||6/3/13 → 6/7/13|
Bibliographical noteFunding 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.