The proposed project is concerned with the development, analysis and applications of numerical simulation tools to a number of problems in computational sciences, in particular, in computational physics and computational material sciences. It is a continuation of PI's past research work in this area that has contributed to the modeling, analysis, and computation of various problems in superconductivity, Bose-Einstein condensation, and phase transitions in binary and multicomponent alloys.
In the proposed work, while building upon the past progress, the PI will take on new initiatives in the study of some interesting physical problems at various time and spatial scales and in the design of new algorithms and efficient solvers which can then be used to understand experimental phenomena and the underlying physical and material properties. The proposed works are to be carried out in the following aspects: to develop or refine mathematical models for the underlying physical problems, so to enlarge the range of validity of such models; to analyze these models in order to gain further understanding of their properties and of their solutions; to develop, analyze, and implement algorithms, in particular, parallel and adaptive algorithms, for the numerical simulation of these models; and to use our algorithms and codes, together with physicists and material scientists, to study some interesting phenomena in physics and material sciences, including the further studies on the quantized vortices in superconductors and Bose-Einstein condensates, on the effects of fluctuation and on the validity and the extension of mezoscopic phenomenological models. While we will focus on developing innovative mathematical theory and computational algorithms, comparisons with the physical experiments will also be made whenever possible.
