## Abstract

An adaptive approach to control modeling error in multiscale simulations that involve molecular and continuum scales is presented. The modeling error is defined as the difference between the solution of a reference particle model, which is considered intractable in practice, and the solution of a manageable multiscale surrogate problem based on the Arlequin framework. The method relies on computable error estimates of the modeling error in specific outputs of interest that require the solution of an adjoint problem. These are the so-called goal-oriented error estimates, which are used to adapt the surrogate model, i.e. to find the optimal configuration of the overlap region between the molecular and continuum models, in order to deliver approximations of quantities of interest within some preset accuracy. Performance of the adaptive strategy is demonstrated on two-dimensional numerical examples.

Original language | English (US) |
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Pages (from-to) | 1887-1901 |

Number of pages | 15 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 198 |

Issue number | 21-26 |

DOIs | |

State | Published - May 1 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:P.T. Bauman acknowledges the support of the DOE Computational Science Graduate Fellowship. H. Ben Dhia would like to thank the J.T. Oden Faculty Fellowship Research Program for the kind invitation to ICES in May 2008. Support of this work by DOE under contract DE-FG02-05ER25701 is gratefully acknowledged.

## Keywords

- A posteriori estimation
- Arlequin framework
- Atomic-to-continuum coupling methods
- Goal-oriented error estimation and adaptivity

## ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications