This paper considers the vectorization and parallelization of the "particle-particle" method used to take into account interactions between objects in the mathematical modeling of physical processes, using the example of taking into account the space charge when calculating the dynamics of charged particles. Comparison and estimation of time costs are carried out (as a test problem, the expansion of a multicomponent ion beam during one nanosecond with a step of Δt = 10-12 s was considered), taking into account the acceleration due to vectorization and parallelization between processor cores. It is concluded that the results of the work clearly demonstrate that the vectorization of computations can significantly speed up the computation time, and the explicit replacement of scalar operations with vector ones makes it possible to obtain additional speed-up in comparison with the use of automatic optimization of the program code. Key words: parallel computations, "particle-particle" method, vectorization of computations, numerical modeling, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model.

Keywords: parallel computations, particle-particle method, vectorization of computations, numerical simulation, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model

the article describes a variant of setting sequential algorithms in the form of bipartite graphs by further defining them, which makes it possible to work with algorithms using graph theory methods in the future. Two forms of the task are considered: modular and functional-predicative. The possibility of setting the algorithm in table-predicate form is shown. It is concluded that in addition to the generally accepted methods of setting the algorithm, it can be set in matrix-predicate or table-predicate form, which allows using methods of matrix theory and methods of predicate theory when working with algorithms. setting the algorithm in matrix-predicate form avoids isomorphism when performing algebraic and set-theoretic operations on it.; setting algorithms in matrix-predicate form allows you to perform almost any operations on them

Keywords: graph-algorithm scheme, sequential algorithm, predicative block, functional block, pre-definition, bipartite graph, table-predicative form, graph theory, isomorphism

The article shows the possibility of describing complex objects with parallel functioning components in the form of structures built on the basis of neural networks. The neural network is represented by an operator matrix, that is, a formal description that gives a universal way to solve many non-standard control problems. Matrix apparatus is shown to significantly improve the efficiency of the method compared to previously known. It is concluded that the representation of the neural network by the operator matrix provides a universal way to solve the problems of transport and information flows management; neuron-like systems based on such representation of the neuron are able to catch complex nonlinear relationships, self-improvement, learning in the process of use. Their use provides ample opportunities for finding and implementing effective solutions to the problems of management and control of flows

Keywords: graph, parallelism, transport and information flow, neural network, synaptic weight, predicate, activation function, operator matrix, neuron, complex systems