Abstract
We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova-type model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 407-415 |
| Number of pages | 9 |
| Journal | International Journal for Multiscale Computational Engineering |
| Volume | 5 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2007 |
Keywords
- A posteriori
- Atomistic-continuum
- Defect
- Dislocation
- Error estimation
- Frenkel-Kontorova
- Goal-oriented
- Quasicontinuum