SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page B761-B791, January 2020.
In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [C. Rodrigo, X. Hu, P. Ohm, J. Adler, F. Gaspar, and L. Zikatanov, Comput. Methods Appl. Mech. Engrg., 341 (2018), pp. 467--484]. The discretization is proved to be well-posed with respect to the physical and discretization parameters and thus provides a framework to develop preconditioners that are robust with respect to such parameters as well. We construct both norm-equivalent (diagonal) and field-of-value-equivalent (triangular) preconditioners for both the stabilized discretization and a perturbation of the stabilized discretization, which leads to a smaller overall problem after static condensation. Numerical tests for both two- and three-dimensional problems confirm the robustness of the block preconditioners with respect to the physical and discretization parameters.

中文翻译：

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多孔弹性方程新稳定化的鲁棒预处理器

SIAM科学计算杂志，第42卷，第3期，第B761-B791页，2020年1月。
在本文中，我们提出了块预处理器，用于稳定在[C. C.]中开发的多孔弹性方程的离散化。Rodrigo，X.Hu，P.Ohm，J.Adler，F.Gaspar和L.Zikatanov，计算 方法应用。机甲 Engrg。，341（2018），第467--484页]。事实证明，离散化相对于物理参数和离散化参数具有良好的定位性，因此提供了一个框架，可以开发对此类参数也很稳定的预处理器。对于稳定的离散化和稳定的离散化的扰动，我们都构造了等价的对角线（对角线）和值相等的值（三角形）预处理器，这导致静态凝聚后的整体问题较小。