SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1273-A1304, January 2021.
We numerically investigate and improve upon a computational approach originally introduced in [R. Cottereau, Internat. J. Numer. Methods Engrg., 95 (2013), pp. 71--90] which aims at evaluating the effective coefficient of a medium modeled by a highly oscillatory coefficient. This computational approach is based on an Arlequin-type coupling. It combines the original fine-scale description of the medium (modeled by an oscillatory coefficient) with an effective description (modeled by a constant coefficient) and optimizes upon the coefficient of the effective medium to best fit the response of the actual heterogeneous medium using a purely homogeneous medium. We present here a mathematical formalization of the approach along with various improvements of the algorithms in order to obtain a procedure as efficient as possible. Representative numerical results demonstrate the added value of our approach in comparison to the original approach.

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关于均质系数实际计算的耦合方法的几点评论

SIAM科学计算杂志，第43卷，第2期，第A1273-A1304页，2021年1月。
我们在数值上研究和改进了最初在[R. Internat的Cottereau。J.纳默尔 Methods Engrg。，95（2013），pp。71--90]，其目的是评估以高振荡系数为模型的介质的有效系数。这种计算方法基于Arlequin型耦合。它将原始的精细描述（由振荡系数建模）与有效的描述（由常数系数建模）相结合，并根据有效介质的系数进行优化，以最佳拟合实际异质介质的响应。纯均质的介质。我们在这里介绍该方法的数学形式化以及算法的各种改进，以便获得尽可能高效的过程。