We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. The proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

我们关注于由Biot的pooleeasticity方程的三场混合有限元逼近产生的线性系统的完全隐式解。目的是开发代数块预处理器，以通过Krylov子空间方法有效解决此类系统。在这项工作中，我们研究使用基于近似逆的技术解耦方程的本机系统，并获得与基于字段类型的未知数基于物理的划分有关的舒尔补码的显式稀疏近似。所提出的方法已在各种数值实验中进行了测试，包括涉及石油和岩土工程的实际应用。