Lie Algebraic Methods as Mathematical Models for High Performance Computing Using the Multi-agent Approach

In this paper we discuss some problems of the construction of mathematical models of dynamic processes to effectively carry out computational experiments using high performance computing systems (both parallel and distributed). The suggested approach is based on the Lie algebraic approach and the multi-agents paradigm. The Lie algebraic tools demonstrated high effectiveness in dynamical systems modeling. A matrix presentation for dynamical systems propagation allows to implement a modular representation of the objects of study as well as the corresponding operations. Moreover, the matrix formalism is based upon the multi-agent paradigm for modeling and control of complex systems for physical facilities. The corresponding codes are realized both in symbolic and numerical forms.