用本构关系误差证明计算均匀化中基于投影的降阶模型
Certification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
摘要：
在本文中，我们提出了上，下误差界技术降阶建模应用于随机复合材料的计算均匀化。上界依赖于构造应力场的降阶模型。在确保减小的应力满足有限元意义上的平衡时，获得期望的边界特性。通过定义位移的分层富集降阶模型来获得下界。我们表明，通过调整相应降阶模型的参数，可以无缝控制两个误差估计的锐度。
英文摘要：
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model.
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