Computational algorithms and applied mathematical software for high and ultra-high performance systems. Educational aspect

The article discusses algorithms and methods of numerical modeling on high-performance computing systems of massive parallelism, ensuring the efficient use of general-purpose processors and graphics accelerators. Using the example of the interaction of the Computational Mathematics and Cybernetics Department of Moscow State University and the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, the article emphasizes the high role of training personnel for the development of supercomputer technologies and solving complex fundamental and applied problems with their help. The article discusses the possibilities of solving such diverse problems, based on fundamental research, as reducing the amount of calculations in the study of continuum mechanics problems and ensuring the possibility of performing fault-tolerant calculations. It is noted that it is necessary to maintain and strengthen the training of highly qualified personnel with fundamental training to solve interdisciplinary problems in the interests of maintaining the competitiveness of key science-intensive industries.