Control of industrial air pollution using domain decomposition methods and parallel optimization algorithms

Abstract

Air-pollution is one of the most critical ecological and public health challenges of the 21st century. Its pre-emptive, passive, and reactive control is a fundamental aspect of environmental management, that is aimed at minimising the release of harmful substances and their impact on human health and natural systems. An effective pollution control strategy involves the scientific modelling of the pollution dispersion so as to either prevent pollutants from being emitted or mitigate the effects after their release in specified areas of interest. One mathematical framework suitable for this purpose, includes the solution of partial differential equations in order to accurately simulate the physical phenomenon in question. By coupling this model with an optimisation scheme, it is possible to design targeted interventions, such as the real-time adjustment of emission rates, the optimal placement of industrial facilities, and other related countermeasures. These actions can guarantee that the concentration of a pollutant will be within specified safe margins inside the regions of interest. The main objectives of this thesis are to propose an accurate mathematical model that describes the dispersion of air-pollutants in a wide range of scenarios, and implement it successfully within an appropriate parallel optimisation scheme, while evaluating its convergence under specific assumptions. The formulation of an optimisation methodology under those requirements, will result in a large-scale numerical problems with different properties depending on the application parameters, and with various limitations regarding their numerical solution. In an attempt to overcome them, this thesis examines the use of PDE-constrained optimisation methods in combination with parallel techniques so as to achieve the minimisation of the air-pollutants’ effects along with the distribution of the computational burden. More specifically, it will provide insight on the implementation of the augmented Lagrangian technique with the use of a Newton method in the formulation of a robust and accurate optimisation framework. In addition, emphasis will be given in the utilisation of parallel algorithms based on domain decomposition methodologies (DDM) in order to produce faster results, improve scalability, and allow the time-sensitive regulation of the pollutants’ emission rate.