This work is directed to the creation of new modern computer technologies and methods of parallel programming for the raise of efficiency of solving fundamental scientific and applied problems in gravitational gas dynamics connected with great amount of computations. The main attention is given to theoretical questions and their practical application for decomposing and parallelizing the methods and algorithms of solving complicated integro-differential systems of equations. Various ways of parallelization specified by peculiarities of decomposition of the whole problem under study into a series of simultaneously solved subproblems (the decompositions according to physico-mathematical processes, computational geometry regions, computing technologies, and main input parameters) are considered. The degree of their efficiency is analyzed to formulate an optimal approach to parallelization. Our theoretical results are used to implement a program package of new generation for solving space gas dynamics problems.

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