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Performance Analysis of the χMD Matrix Solver Package for MODFLOW-USG
Ground Water ( IF 2.0 ) Pub Date : 2021-05-12 , DOI: 10.1111/gwat.13110
Motomu Ibaraki 1 , Yiding Zhang 2 , Richard G. Niswonger 3 , Sorab Panday 4
Affiliation  

The χMD matrix solver package is incorporated into USGS groundwater modeling software, such as MODFLOW-NWT, MODFLOW-USG, and MT3D. The solver is used to solve matrices assembled through numerical discretization of the groundwater flow equation, and solute transport equations. χMD has demonstrated its higher robustness, faster execution speed, and more efficient memory usage compared to the existing solvers for many types of groundwater flow problems. χMD uses preconditioned iterative Krylov-subspace methods and consists of preconditioning and acceleration modules. Because the solver package uses a variety of preconditioning features including level-based incomplete lower-upper (ILU) factorization method with a drop tolerance scheme, users must choose optimal preconditioning parameters to improve execution speed and robustness. In order to examine how the preconditioning parameters, ILU factorization level, and drop tolerance values affect the overall performance of the matrix solver, we evaluated five different groundwater model applications using MODFLOW-USG that include different numerical complexities. For those five cases, the number of discretization nodes varied from 10,000 cells to 730,300 cells. From the analysis, we found that the preconditioning parameters greatly affect execution times and memory usage of the preconditioning and acceleration procedures. In addition, a combination of the ILU level between five to seven and the drop tolerance value between 10−2 and 10−3 usually resulted in shorter overall execution time. Our study suggests that the users can elicit higher performance and robustness of the χMD matrix solver using this combination of the parameters and enhance computational efficiency of solving groundwater and solute transport problems.

中文翻译:

MODFLOW-USG χMD 矩阵求解器包的性能分析

χMD 矩阵求解器包被整合到 USGS 地下水建模软件中,例如 MODFLOW-NWT、MODFLOW-USG 和 MT3D。求解器用于求解通过地下水流动方程和溶质运移方程的数值离散化组合而成的矩阵。与现有的多种地下水流动问题求解器相比,χMD 已证明其具有更高的鲁棒性、更快的执行速度和更有效的内存使用。χMD 使用预处理迭代 Krylov 子空间方法,由预处理和加速模块组成。由于求解器包使用了多种预处理功能,包括基于级别的不完全下上层 (ILU) 分解方法和容差方案,因此用户必须选择最佳的预处理参数以提高执行速度和鲁棒性。为了检查预处理参数、ILU 分解级别和下降容差值如何影响矩阵求解器的整体性能,我们使用 MODFLOW-USG 评估了五种不同的地下水模型应用程序,其中包括不同的数值复杂性。对于这五种情况,离散化节点的数量从 10,000 个单元格到 730,300 个单元格不等。通过分析,我们发现预处理参数极大地影响了预处理和加速程序的执行时间和内存使用。此外,ILU 级别介于 5 到 7 之间,跌落公差值介于 10 之间 我们使用 MODFLOW-USG 评估了五种不同的地下水模型应用程序,其中包括不同的数值复杂性。对于这五种情况,离散化节点的数量从 10,000 个单元格到 730,300 个单元格不等。通过分析,我们发现预处理参数极大地影响了预处理和加速程序的执行时间和内存使用。此外,ILU 级别介于 5 到 7 之间,跌落公差值介于 10 之间 我们使用 MODFLOW-USG 评估了五种不同的地下水模型应用程序,其中包括不同的数值复杂性。对于这五种情况,离散化节点的数量从 10,000 个单元格到 730,300 个单元格不等。通过分析,我们发现预处理参数极大地影响了预处理和加速程序的执行时间和内存使用。此外,ILU 级别介于 5 到 7 之间,跌落公差值介于 10 之间-2和 10 -3通常会缩短整体执行时间。我们的研究表明,用户可以使用这种参数组合来获得 χMD 矩阵求解器的更高性能和鲁棒性,并提高解决地下水和溶质运移问题的计算效率。
更新日期:2021-05-12
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