Many sequential mathematical optimization methods
and simulation-based heuristics for optimal control and
design of water distribution networks rely on a large number
of hydraulic simulations. In this paper, we propose an efficient
inexact subspace Newton method for hydraulic analysis of water
distribution networks. By using sparse and well-conditioned
fundamental null space bases, we solve the nonlinear system
of hydraulic equations in a lower-dimensional kernel space of
the network incidence matrix. In the inexact framework, the
Newton steps are determined by solving the Newton equations
only approximately using an iterative linear solver. Since large
water network models are inherently badly scaled, a Jacobian
regularization is employed to improve the condition number of
these linear systems and guarantee positive definiteness. After
presenting a convergence analysis of the regularised inexact
Newton method, we use the conjugate gradient (CG) method
to solve the sparse reduced Newton linear systems. Since CG
is not effective without good preconditioners, we propose tailored
constraint preconditioners that are computationally cheap
because they are based only on invariant properties of the null
space linear systems and do not change with flows and pressures.
The preconditioners are shown to improve the distribution of
eigenvalues of the linear systems and so enable a more efficient
use of the CG solver. Since contiguous Newton iterates can have
similar solutions, each CG call is warm-started with the solution
for a previous Newton iterate to accelerate its convergence rate.
Operational network models are used to show the efficacy of
the proposed preconditioners and the warm-starting strategy in
reducing computational effort.