The Network-Max-P-Regions model
ABSTRACT This paper introduces a new p-regions model called the Network-Max-P-Regions (NMPR) model. The NMPR is a regionalization model that aims to aggregate n areas into the maximum number of regions (max-p) that satisfy a threshold constraint and to minimize the heterogeneity while taking into account the influence of a street network. The exact formulation of the NMPR is presented, and a heuristic solution is proposed to effectively compute the near-optimized partitions in several simulation datasets and a case study in Wuhan, China.
This paper considers corona discharge problems with multiple conductors, such as those appearing in some electrostatic precipitators. A common precise condition is identified in which the previous approaches proposed in the literature fail. For dealing with these conditions, a novel, stabilized, and regularized formulation of the problem is proposed. Moreover, a Newton–Raphson scheme is defined for iteratively solving a nonstandard Petrov–Galerkin finite-element discretization of the problem. The presented approach is validated on a benchmark for which an analytical solution is known and its applicability to problems of industrial relevance is shown.