Abstract
In this paper, we propose a multiscale coupling approach to perform Monte-Carlo simulations on systems described at the atomic scale and subjected to random phenomena. The method is based on the Arlequin framework, developed to date for deterministic models involving coupling a region of interest described at a particle scale with a coarser model (continuum model). The new method can result in a dramatic reduction in the number of degrees of freedom necessary to perform Monte-Carlo simulations on the fully atomistic structure. The focus here is on the construction of an equivalent stochastic continuum model and its coupling with a discrete particle model through a stochastic version of the Arlequin method. Concepts from the Stochastic Finite Element Method, such as the Karhünen-Loeve expansion and Polynomial Chaos, are extended to multiscale problems so that Monte-Carlo simulations are only performed locally in subregions of the domain occupied by particles. Preliminary results are given for a 1D structure with harmonic interatomic potentials.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3530-3546 |
| Number of pages | 17 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 197 |
| Issue number | 43-44 |
| DOIs | |
| State | Published - Aug 1 2008 |
| Externally published | Yes |
Bibliographical note
Funding Information:The authors benefited from helpful discussions with Raul Tempone from KTH, Sweden and Hachmi Ben Dhia from Ecole Centrale de Paris, France. The support of the Department of Energy within the multiscale mathematics program under contract DE-FG02-05ER25701 is gratefully acknowledged.
Keywords
- Arlequin method
- Particle model
- Polynomial Chaos
- Stochastic PDE's
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications