Application of Multi-Grid Method for Solving System of Linear Equations in Hydraulic Analysis of Pipe Networks

آب و خاک

Article 6, Volume 28, Issue 1, March 2014, Pages 61-71   

Document Type: Research Article

DOI: 10.22067/jsw.v0i0.35756

Authors

N. Moosavian^* ; M.R. Jaefarzadeh

Abstract

The gradient-based algorithms are widely used for hydraulic analysis of pipe networks. Solving system of linear equations has the most computational cost in the gradient-based methods particularly for large networks with more than hundreds of variables. The Jacobian matrix form in the gradient-based methods is square and banded. Elements of this matrix are function of flow rate and hydraulic resistance of pipe. The sparse Cholesky method with node reordering is commonly applied for solving system of linear equations in the EPANET and WATERGEMS softwares. As an alternative, the Jacobian matrix can be solved using the Multi-Grid method. This paper studies the application of pre-conditioner methods such as AMG-CG and AGMG for solving the Jacobian matrix and compares its results with other iterative and direct solvers. According to the results, AGMG demonstrates better performance than AMG-CG in all studied cases and it is the best method for solving system of linear equations in hydraulic analysis of huge pipe networks.

Keywords

Pipe networks; Hydraulic analysis; Multi-Grid method