Algebraic multiscale (AMS) is a recent development for the construction of efficient linear solvers in reservoir simulations. It employs upscaling ideas to coarsen the respective linear system and provides a high amount of inherent parallelism. However, it has the drawback that it can so far only be applied to scalar problems, e.g., a pressure sub-problem. Moreover, AMS relies on the availability of information on the physics and the grid to construct a two-level scheme. Generalizing the AMS approach to overcome these limitations requires substantial efforts and is not straightforward. To exploit the benefits of AMS, however, we integrate its core ideas in an algebraic multigrid (AMG) method. Thus, all results and techniques from the well-established AMG are directly available in conjunction with (core ingredients of) AMS. This holds regarding multilevel usage as well as the independence of geometric and physical information. But it also holds for the System-AMG approach that allows us to consider additional thermal and mechanical unknowns.

中文翻译：

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代数多尺度到代数多重网格的推广

代数多尺度（AMS）是在油藏模拟中构建有效线性求解器的最新进展。它采用了放大的思想来粗化各个线性系统，并提供了大量的固有并行度。但是，它的缺点是到目前为止它只能应用于标量问题，例如压力子问题。此外，AMS依靠物理和网格上信息的可用性来构建两级方案。推广AMS方法以克服这些局限性需要大量的努力，而且并非一帆风顺。但是，为了利用AMS的好处，我们将其核心思想整合到了代数多重网格（AMG）方法中。因此，成熟的AMG的所有结果和技术都可以直接与AMS（的核心成分）结合使用。这适用于多层次使用以及几何和物理信息的独立性。但是它也适用于System-AMG方法，该方法使我们可以考虑其他未知的热和机械问题。