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 linear solution and a pure advective transport solution with different right‐hand sides. The new solver was compared with other preconditioned iterative methods, the MODFLOW's GMG solver, and direct sparse solvers. Test problems include two‐ and three‐dimensional benchmarks spanning homogeneous and highly heterogeneous and anisotropic formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. The algebraic multigrid preconditioner efficiency was preserved for the three dimensional heterogeneous and anisotropic problem unlike for the MODFLOW's GMG solver. 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 Péclet 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 its routine application to large geological models. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning would remain competitive for the class of nonlinear and/or transient problems.

中文翻译：

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用代数多重网格预处理求解地下水流和运输模型。

已经设计了用代数多重网格进行预处理的迭代求解器，作为一种优化技术，可以加快大型稀疏线性系统的响应速度。在这项工作中，该技术是在双重轮廓方法的框架中实现的。这涉及单个地下水流线性解和具有不同右侧的纯对流输运解。将新的求解器与其他预处理的迭代方法，MODFLOW的GMG求解器和直接稀疏求解器进行了比较。测试问题包括二维和三维基准，这些基准涵盖了均匀，高度非均质和各向异性的地层。对于地下水流动问题，使用代数多重网格预处理可将数值解的速度提高一到两个数量级。与MODFLOW的GMG求解器不同，对于三维异质性和各向异性问题，代数多网格预处理器的效率得以保留。相反，稀疏的直接求解器对于纯对流运输过程（例如向前行进时间模拟）最有效。因此，对于更一般的对流扩散输运方程，最佳的稀疏求解器可能与佩克利数有关。当配备了最好的求解器时，通过双重描绘方法处理数百万个网格块仅需几秒钟。这为常规应用于大型地质模型铺平了道路。本文对代数多重网格预处理在非线性和/或瞬态问题中保持竞争力的策略和条件提供了实用的提示。