论文标题
关于均匀计算的耦合方法的一些评论
Some remarks on a coupling method for the practical computation of homogenized coefficients
论文作者
论文摘要
我们在[Cottereau，iJnme 2013]中最初引入的计算方法进行数值研究并改进，该方法旨在评估由高度振动系数建模的介质的有效系数。这种计算方法基于Arlequin型耦合。它结合了对介质（由振荡系数建模）的原始细规描述与有效描述（由恒定系数建模），并在有效培养基的系数上优化了使用纯均质介质的实际异质介质的响应。我们在这里提出了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。代表性的数值结果证明了与原始方法相比，我们的方法的附加值。
We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medium modelled by a highly oscillatory coefficient. This computational approach is based on a Arlequin type coupling. It combines the original fine-scale description of the medium (modelled by an oscillatory coefficient) with an effective description (modelled 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.
