一种高效的空空间近似牛顿方法用于水分配网络的水力模拟
An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
AI总结：
本文提出一种高效的近似牛顿方法，通过部分更新管道摩擦水头损失计算来更高效可靠地求解线性系统，利用空空间基生成方案获得稀疏且良态的空空间基，减少更新集大小。
摘要：
空空间牛顿算法在解决水力分析中出现的非线性方程时效率较高。本文提出并评估了一种近似牛顿方法，该方法依赖于部分更新网络管道的摩擦水头损失计算，以更高效且可靠地求解线性系统。研究了更新集参数以提出合适值。分析了不同的空空间基生成方案，选择产生稀疏且良态的空空间基的方法，从而减少更新集大小。通过在空空间中求解稀疏对称正定系统，使用稀疏Cholesky分解因子化，计算牛顿步。通过利用空空间系统矩阵的恒定结构，在Cholesky分解中使用单次符号因子化多次，从而降低线性求解的计算成本。算法和分析通过中等至大型水网络模型进行验证。
英文摘要：
Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.
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