A class of network optimization methods for planar grid generation

The grid generation problem considers the question of the computation of a grid Q over a given domain Ω from the knowledge of Q on the boundary ∂Ω. It is usually given in terms of the computation of the grid vertices belonging to the interior of Ω, that in the direct optimization formulation are computed as the minimizer of a particular minimization problem. In this paper the grid generation problem is reformulated as a network optimization problem on a particular graph, that is a nonlinear minimum cost flow problem, where in place of the standard Euclidean vector norm is proposed the use of the well-known vector p-norm, where p⩾1. Some results coming from our numerical experience on the examples proposed in the Rogue's Gallery of Grids are reported.