Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 221-239, January 2020.
We establish a link between the decoupling constraint in a two-grid staggered solution algorithm for consolidation in heterogeneous porous media and the concepts of Voigt and Reuss bounds commonly encountered in the theory of computational homogenization of multiphase composites. Our analysis involves deriving bounds on a tuning parameter in the decoupling constraint for determining the speed and accuracy of the algorithm. An upper bound is obtained from theoretical convergence of the algorithm which leads to the fastest convergence. A lower bound is established by employing the concepts of Voigt and Reuss bounds. From these bounds, we conclude that there is a value for the tuning parameter between the bounds that gives the most accurate solution.

中文翻译：

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异质多孔介质中两网格交错固结中Voigt和Reuss界的对应和解耦约束

2020年1月，《多尺度建模与仿真》，第18卷，第1期，第221-239页。
我们在异质多孔介质固结的两网格交错求解算法中的解耦约束与多相复合材料计算均质化理论中经常遇到的Voigt和Reuss界的概念之间建立了联系。我们的分析涉及在去耦约束中推导调整参数的界限，以确定算法的速度和准确性。从算法的理论收敛获得上限，这导致最快的收敛。通过采用Voigt和Reuss界限的概念来确定下界。根据这些边界，我们得出结论，边界之间存在一个调整参数值，该值给出了最准确的解决方案。