In this work, we propose a novel block preconditioner, labeled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear equations originating from flow simulations in porous media. The flow model is discretized blending the Mixed hybrid finite element method for Darcy's equation with the Finite volume scheme for the mass conservation. The EDFA preconditioner is characterized by two features: the exploitation of the system matrix decoupling factors to recast the Schur complement and their inexact fully-parallel computation by means of restriction operators. We introduce two adaptive techniques aimed at building the restriction operators according to the properties of the system at hand. The proposed block preconditioner has been tested through extensive experimentation on both synthetic and real-case applications, pointing out its robustness and computational efficiency.

在这项工作中，我们提出了一种新的块预处理器，标记为显式解耦因子近似 (EDFA)，以加速 Krylov 子空间求解器的收敛，该求解器用于解决源自多孔介质流动模拟的非对称线性方程组序列。流动模型是离散混合达西方程的混合混合有限元方法与质量守恒的有限体积方案。EDFA 预处理器具有两个特点：利用系统矩阵解耦因子来重铸 Schur 补码，以及它们通过限制算子进行不精确的全并行计算。我们介绍了两种自适应技术，旨在根据手头系统的特性构建限制算子。