Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Steadystate behavior of large water distribution systems: Algebraic multigrid method for the fast solution of the linear step
: Zecchin, Aaron
 Journal of water resources planning and management 138 (2012), Nr.6, S.639650 ISSN: 07339496 ISSN: 19435452 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
 linear systems; multigrid; water distribution systems; Newton 
Abstract
The Newtonbased global gradient algorithm (GGA) (also known as the Todini and Pilati method) is a widely used method for computing the steadystate solution of the hydraulic variables within a water distribution system (WDS). The Newtonbased computation involves solving a linear system of equations arising from the Jacobian of the WDS equations. This step is the most computationally expensive process within the GGA, particularly for large networks involving up to O(105) variables. An increasingly popular solver for large linear systems of the Mmatrix class is the algebraic multigrid (AMG) method, a hierarchicalbased method that uses a sequence of smaller dimensional systems to approximate the original system. This paper studies the application of AMG to the steadystate solution of WDSs through its incorporation as the linear solver within the GGA. The form of the Jacobian within the GGA is proved to be an Mmatrix (under specific criteria on the pipe resistance functions), and thus able to be solved using AMG. A new interpretation of the Jacobian from the GGA is derived, enabling physically based interpretations of the AMG's automatically created hierarchy. Finally, extensive numerical studies are undertaken where it is seen that AMG outperforms the sparse Cholesky method with node reordering (the solver used in EPANET2), incomplete LU factorization (ILU), and PARDISO, which are standard iterative and direct sparse linear solvers.