A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations

H. Ben Dhia; Ludovic Chamoin; J. Tinsley Oden; Serge Prudhomme

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A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations

机译：基于最优控制的原子与连续体耦合仿真的新型自适应建模策略

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摘要

A new adaptive method based on an optimal control approach is proposed for adaptive modeling of an atomic-to-continuum coupling method constructed from the Arlequin framework. The coupling method provides for an approximation of the solution to a fully atomic model in which errors may arise due to the misplacement of the overlap region. The objective is thus to determine, a posteriori, the best position of this overlap region. More precisely, the problem is to find the optimal size of the atomic region that one needs to consider in the coupled formulation in order to accurately estimate predefined quantities of interest. In this new adaptive process, the position of the overlapping domain between the two models is conveniently parameterized and iteratively determined by searching for the optimal parameters. The performance of the method is demonstrated on one-dimensional and two-dimensional test problems. In particular, it is observed that the approach yields better convergence with respect to quantities of interest when compared to a classical adaptive approach based on a posteriori estimates of the modeling

机译：提出了一种基于最优控制方法的自适应方法，用于基于Arlequin框架的原子-连续体耦合方法的自适应建模。耦合方法提供了对完全原子模型的近似解，其中由于重叠区域的错位可能会产生误差。因此，目的是确定后验，该重叠区域的最佳位置。更确切地说，问题在于找到在耦合公式中需要考虑的原子区域的最佳尺寸，以便准确地估计预定的目标量。在这种新的自适应过程中，可以方便地对两个模型之间的重叠域位置进行参数化，并通过搜索最佳参数来迭代确定。在一维和二维测试问题上证明了该方法的性能。特别是，与基于模型后验估计的经典自适应方法相比，该方法在感兴趣的量方面具有更好的收敛性

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2011年第40期|p.2675-2696|共22页
作者
H. Ben Dhia; Ludovic Chamoin; J. Tinsley Oden; Serge Prudhomme;
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作者单位

Laboratoire de Mecanique des Sols, Structures et Materiaux (MSSMat), Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France;

Laboratoire de Mecanique et Technologie (LMT-Cachan), Ecole Normale Superieure de Cachan, 61, Avenue du President Wilson, 94235 Cachan Cedex, France;

Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station, C0200, Austin, TX 78712, USA;

Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station, C0200, Austin, TX 78712, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
modeling error; arlequin method; goal-oriented error estimation; adaptive modeling; optimal control;

机译：建模误差;穿衣法;目标导向误差估计;自适应建模;最优控制;

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A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations

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