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Constructing the Adaptive Algorithms for Solving Multi-Wave Problems

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors improve the numerical method of calculating multi-wave models to increase the speed and monotonize (reduce the oscillations of numerical calculations) the numerical solution of problems of multi-wave dynamics for lengthy systems such as space tethers tens of kilometers long; pipelines in air and in liquid; underwater towed systems; airlifts 5 to 10 km long for the extraction of minerals from the bottom of the oceans, etc. The method is based on the decomposition of the numerical algorithm by wave types and wave velocities. It is shown that due to quantization in calculating longitudinal and transverse waves, it is possible to achieve a further increase in the computation speed compared to the wave factorization algorithm and compared to solving the full system of equations, without reducing the range of sustainable calculation. The final increase in the productivity of the program code is at least 50 to 200% when performing calculations, depending on the required accuracy and options for the decomposition of multi-wave models. This modification of the wave factorization method is relevant in solving the problems of controlling a distributed system, operative analysis of transient motion modes, etc., where the pace of calculations is critically important. A comparative evaluation of the accuracy of the full algorithm, the of wave factorization method, and of the decomposition by wave types and wave velocities has been carried out. Comparative analysis of the calculated data showed the monotonicity of the numerical solution profile on the basis of factorized algorithms, their lower sensitivity to errors in the initial data. A finite-difference scheme factorized by perturbation directions and wave types with variable dispersion-diffusion properties is constructed.

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Authors and Affiliations

  1. State Enterprise “State Research Institute of Building Constructions,” Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Iu. Kaliukh

  2. Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. Lebid

Authors
  1. Iu. Kaliukh
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  2. O. Lebid
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Correspondence to Iu. Kaliukh.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 106–117.

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Kaliukh, I., Lebid, O. Constructing the Adaptive Algorithms for Solving Multi-Wave Problems. Cybern Syst Anal 57, 938–949 (2021). https://doi.org/10.1007/s10559-021-00419-w

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  • DOI: https://doi.org/10.1007/s10559-021-00419-w

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