Boichura M. Parameters identification of quasiideal fields with using numerical method of complex analysis

A topical scientific problem, which consists in the development of numerical complex analysis methods concerning the identification of parameters of quasiideal fields according to applied quasipotential tomography, which provides the possibility of optimal use of the set of experimental data, is solved on the basis of research conducted in the dissertation. Accordingly, a methodology (method and corresponding algorithms) of complex analysis of solving the applied quasipotential tomography problems which would assume (for each of the corresponding injections) a presence at the boundary of the domain only equipotential lines (with local velocity distributions or stream function values given at them) and stream lines (with known potential distributions at them) was developed. It is based on the ideas of applied quasipotential method for image reconstruction, according to which iterative solving of analysis and synthesis problems is reduced to use of numerical quasiconformal mapping and parametric identification methods, respectively. On this basis, corresponding algorithms for the key assumptions regarding the structure of the isotropic environment on a plane are specified (in particular, the form of minimizing functional is constructed, given the need to fulfill the condition of speed equality using data of both stream and quasipotential functions in the iterative process, at each injection), and the corresponding algorithms are extended to space. These ideas are reduced to the cases where there are several sections of application the quasipotentials and identification of parameters in an anisotropic medium. In the latter case, the minimizing functional is constructed taking into account the ideas of regularization, the necessity of fulfilling the corresponding generalizations of the Cauchy-Riemann conditions and the relationships between the characteristics of eigenvalues at each injection. The computer programs for solving image reconstruction problems under a series of key assumptions about the structure of the conductivity coefficient (tensor) as scalar functions of real variables using applied quasipotential tomographic data have been developed using corresponding algorithms. Comparative analysis of the results of numerical experiments, conducted using both the methods developed in the dissertation and the known methods, gives reason to conclude that obtained algorithms can be extended to cases of study the structure of specific objects and media (the movement of matter in which is carried out by similar laws), that take place, particularly, in hydrodynamics, geology, industry and medicine.