Топологічні аспекти моделювання паралельних обчислень при розв’язанні динамічних задач на базі інтерфейсу передачі повідомлень

Abstract

The article deals with the development, substantiation and research of analytical models of data transmission when solving complex multidimensional dynamic problems. Models of interprocessor exchange are obtained for computing systems with distributed memory and topological architectures: ring, 2D-torus, hypercube, etc. The application of double arithmetic based on the GMP-library and its effect on the temporal characteristics of parallel applications are considered. The dependence of the parallelism characteristics of numerical algorithms when using the streaming SIMD-extension is analyzed. The modern stage of development of computer and information technologies has one of its directions - the use of the idea of parallelism in order to reduce the time of solving multidimensional problems that have a high temporal complexity or are even NP-complete. Despite the significant increase in the productivity of existing parallel systems, reducing the cost of components for their construction, development and implementation of parallel methods remains the most difficult problem due to the lack of study of the internal structure of algorithms and their properties. Thus, the introduction of parallel computing requires not so much the mastering of parallel data processing as the development of parallel algorithms based on the parallelization of sequential ones or the construction of fundamentally new, more efficient parallel methods. That is why the analysis of existing parallel algorithms, studying the possibilities of improving their characteristics is an important, promising and practically demanded task. The purpose of the work is to increase the efficiency of solving complex multidimensional dynamic problems implemented on parallel architectures of distributed memory using the message passing interface (MPI) due to the reduction of communication time. Tasks of the work: firstly, it is the development of analytical models of multiple data transfer operations for different topologies of connection of processors, substantiation of the models and research of the quality of parallel calculations of various classes of numerical methods for cluster systems. The possibility and effectiveness of using double arithmetic (GMP-library) and its influence on the temporal characteristics of parallel implementation are separately investigated. Additionally, the paper analyzes the dependence of the parallelism characteristics of the methods on the use of Streaming SIMD-Extension (SSE). The scientific novelty of the field lies in the development and development of analytical models for processes of interprocessor exchange given by cluster systems, which allow to increase the efficiency of parallel implementations of numerical methods in rich dynamic tasks for a short period of time on a communication warehouse. The practical significance of the field is in the development of split models for the analysis of the efficiency of collective operations of multiple data transfer within the MPI interface, which is the current standard for software implementation of robots with shared memory. Possibility of arranging floating arithmetic based on the GMP library was added, which is especially important for the development of folding problems of dynamic problems with singularities.