图拉普拉斯问题的多级谱粗化及其在油藏模拟中的应用
Multilevel spectral coarsening for graph Laplacian problems with application to reservoir simulation
摘要：
我们扩展以前开发的两级粗化程序的混合鞍点的形式写的图拉普拉斯问题的完全递归的多级情况下。由此产生的离散化层次结构产生了一个层次结构的升级模型，在这个意义上，他们提供了近似的自然规范（在混合设置）。这个属性使我们能够利用它们在三个应用程序：（i）作为一个准确的降阶模型，（ii）作为一个工具，在多级Monte Carlo模拟（在有限体积离散化的应用），和（iii）提供一个序列的非线性算子在FAS（全近似方案）求解非线性压力方程离散的保守两点通量近似。我们说明了潜在的建议多级技术在所有三个应用程序上的一些流行的基准问题，用于油藏模拟。
英文摘要：
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 FAS (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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
