Korenyak Y. Behavior of scalar fields on multiply connected riemann complicated form surfaces and their computer modeling

Plant of thesis a research is the expansion of a subject domain of R-functions method on asymmetric two-dimensional problems. The purpose of work is the development of R-functions theory design methods for creation of structural and computer models of physical fields on composite multiply connected Riemann surfaces of the complicated form and evaluation of their integrated characteristics; to development of effective algorithms and programs for the analysis of researched fields. Methods of researches is the design theory of R-functions; variational methods of a boundary value problems solution of mathematical physics; computing experiment, as a mode of a solution of nature-scientific problems by modes of mathematical modeling and calculus mathematics. The theoretical value of thesis consists in development of computer models adequate to physical fields, which allow investigating asymmetric fields on two-dimensional surfaces of the complicated form both creation of effective methods and algorithms of a research and prediction of physical fields in two-dimensional Riemannian space. The practical value of work consists in a construction of an adequate computer model and modes of the two-dimensional surfaces representation, that it is possible to use in systems of automated projection for a solution of mathematical physics various problems in case of symmetrical and asymmetric fields on composite surfaces with the help of R-functions method, development of gears with approachment to optimum distribution of a field on a surface, for example, for problems of an electrostatics. The techniques of a determination of integrated performances of fields for inhomogeneous surfaces are offered at an amount inclusions of heterogeneities greater two; rationalization of integrated characteristics of a field (determination of integrated performances, close to best values, of a field at a variation of the area boundaries). The introduction of basic outcomes of researches for use in educational process and conducting areas of a national economy, as electrotechnical and light industry, etc. is planned.