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Numerical methods based on solving the Riemann problem of the decay of an arbitrary discontinuity are extremely demanding of computational resources. Applying the data of numerical methods to modern computational grids requires the use of a supercomputer. Among the various tools for improving the performance of supercomputer applications, we can emphasize the vectorization of program code. The AVX-512 instruction set has a number of unique features allowing to apply vectorization to the Riemann solver software context, which results in a significant acceleration of the solver.

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