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Inverse contaminant fluid flow problems using boundary element methods

Domenii publicaţii > Matematica + Tipuri publicaţii > Tezã de doctorat (nepublicatã)

Autori: Alexandru Rap

Editorial: University of Leeds, UK, 2005.

Rezumat:

The purpose of this thesis is to develop some necessary techniques to solve inverse contaminant fluid flow problems related with water pollution. In general the water pollution phenomenon is mathematically modelled by the convection-diffusion equation and, in particular, the water pollution source identification problem leads to the need to solve ill-posed inverse problems related with this equation. Recently, inverse problems have become more and more important in various fields of science and technology, and have certainly been one of the fastest growing areas in research.

The work presented in this thesis proposes some powerful and reliable numerical techniques for solving mathematical problems that arise from two types of situations that occur in water pollution. The first situation refers to cases when due to either physical impossibility, or simply inconvenience, one cannot take measurements of the pollutant concentration on some hostile parts of the boundary of the region that has been polluted. The problem in these cases requires the identification of the pollutant concentrations on those inaccessible parts, provided that some extra measurements can be taken on the accessible boundary. The second situation refers to cases when concentration measurements can be taken over the entire boundary of the polluted region and the unknown locations and strengths of a number of pollution point sources are sought. The mathematical modelling of these two situations leads to the need of solving two different inverse problems for the convection-diffusion equation, namely the Cauchy and the inverse source problems, respectively.

The main achievement of this thesis is that it brings together the two very interesting and important practical problems of water pollution described above and two very powerful numerical methods, namely the Boundary Element Method and the Dual Reciprocity Boundary Element Method.

The accuracy and convergence of the numerical techniques proposed in this thesis are illustrated by comparing the numerical and the analytical solutions for several test examples. The stability of the numerical solutions is investigated by introducing random noise into the input data.

Cuvinte cheie: Inverse problems, Boundary element method, Dual reciprocity boundary element method, Water pollution, Tikhonov regularisation, Iterative sequential quadratic programming