Name
Title | ||
|---|---|---|
Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel-Kontorova Model |
Abstract | ||
|---|---|---|
We propose and analyze a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method. Based on this error estimator, we develop an algorithm which adaptively determines the atomistic and continuum regions to compute a quantity of interest to within a given tolerance. We apply the algorithm to the computation of the structure of a crystallographic defect described by a Frenkel-Kontorova model and present the results of numerical experiments. The numerical results show that our method gives an efficient estimate of the error and that our atomistic-continuum adaptivity algorithm computes the quantity of interest to within a given tolerance with a nearly minimal atomistic region. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/070688559 | MULTISCALE MODELING & SIMULATION |
Keywords | Field | DocType |
error estimation,a posteriori,goal-oriented,atomistic-continuum modeling,quasicontinuum,Frenkel-Kontorova model,dislocation,defect | Crystallographic defect,Mathematical optimization,A priori and a posteriori,Continuum (design consultancy),Dislocation,Frenkel–Kontorova model,Mathematics,Computation,Estimator | Journal |
Volume | Issue | ISSN |
7 | 1 | 1540-3459 |
Citations | PageRank | References |
7 | 1.27 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Arndt | 1 | 7 | 1.27 |
| Mitchell Luskin | 2 | 124 | 23.89 |