There are some problems of accelerator simulation (for example, computer design of new accelerator projects, optimization of working machines and quasi-real time accelerator control) which demand high performance computing using parallel and distributed computer systems. In particular, usage of computer clusters set is perspective for this purpose. In this reports we develop the approach suggested in our previous works. This approach is based on several levels of process of parallel and distributed computing. The structured physical and mathematical description of a beam evolution behavior (including space charge forces) allows to distribute calculations on several computing clusters with parallel computing inside each structural block. Computer algebra tools play the great role in such approach. Indeed, on the one hand, the used matrix formalism for Lie algebraic methods admits the symbolic computations and storage of the results in corresponding databases. On the other hand, the possibilities of visual 2D- and 3D-presentation allows to analyze the studied effects more carefully and intuitive. Multivariate description of beam evolution, space charge forces, and optimization procedures permits to compute various representative models simultaneously on different clusters.