SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page A2737-A2765, January 2021.
We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. We illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.

中文翻译：

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图拉普拉斯问题的多级光谱粗化与油藏模拟的应用

SIAM 科学计算杂志，第 43 卷，第 4 期，第 A2737-A2765 页，2021 年 1 月。
我们将先前开发的用于以混合鞍点形式编写的图拉普拉斯问题的两级粗化程序扩展到完全递归的多级情况。由此产生的离散化层次结构产生了放大模型的层次结构，因为它们提供了自然规范（在混合设置中）的近似值。这一特性使我们能够在三个应用中利用它们：(i) 作为精确的简化模型，(ii) 作为多级蒙特卡罗模拟中的工具（应用于有限体积离散化），以及 (iii) 用于提供一系列非线性用于求解由保守两点通量近似离散化的非线性压力方程的完全近似方案中的算子。