Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow solve and a pure advective transport solve with different right-hand sides. The new solver was compared with traditional preconditioned iterative methods and direct sparse solvers on several two- and three-dimensional benchmark problems spanning homogeneous and heterogeneous formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be P\'eclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for routine time-consuming tasks such as sensitivity analysis. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning for the class of nonlinear and/or transient problems would remain competitive.

中文翻译：

---

用代数多重网格预处理求解地下水流和输运模型

代数多重网格预处理的迭代求解器已被设计为加速大型稀疏线性系统响应的最佳技术。在这项工作中，该技术是在双重描绘方法的框架中实现的。这涉及单个地下水流求解和具有不同右侧的纯对流传输求解。在跨越同质和非均质地层的几个二维和三维基准问题上，将新求解器与传统的预处理迭代方法和直接稀疏求解器进行了比较。对于地下水流问题，使用代数多重网格预处理可以将数值求解速度提高一到两个数量级。相反，稀疏直接求解器对于纯平流传输过程（例如前向旅行时间模拟）是最有效的。因此，对于更一般的对流-弥散传输方程的最佳稀疏求解器很可能与 P\'eclet 数有关。配备最好的求解器后，通过双重描绘方法处理数百万个网格块只需几秒钟。这为灵敏度分析等日常耗时任务铺平了道路。这篇论文给出了一些策略和条件的实用提示，在这些策略和条件下，非线性和/或瞬态问题类别的代数多重网格预处理将保持竞争力。配备最好的求解器后，通过双重描绘方法处理数百万个网格块只需几秒钟。这为灵敏度分析等日常耗时任务铺平了道路。这篇论文给出了一些策略和条件的实用提示，在这些策略和条件下，非线性和/或瞬态问题类别的代数多重网格预处理将保持竞争力。配备最好的求解器后，通过双重描绘方法处理数百万个网格块只需几秒钟。这为灵敏度分析等日常耗时任务铺平了道路。这篇论文给出了一些策略和条件的实用提示，在这些策略和条件下，非线性和/或瞬态问题类别的代数多重网格预处理将保持竞争力。