UDC 533.6.013.42
1 State Enterprise “State Research Institute of Building Constructions,” Kyiv, Ukraine,
and Institute of Telecommunication and Global Information Space of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
 kalyukh2002@gmail.com
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2 Institute of Telecommunication and Global Information Space of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
o.g.lebid@gmail.com
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CONSTRUCTING THE ADAPTIVE ALGORITHMS FOR SOLVING
MULTI-WAVE PROBLEMS
Abstract. The authors improve the numerical method of calculating multiwave models to increase
the speed and monotony of the numerical solution of problems of multiwave dynamics for long systems
such as space communications of the length of tens of kilometers; pipelines in both air and liquid;
underwater towed systems; airlifts for the extraction of minerals from the bottom of the oceans of the length of 5 to 10 km, etc.
The method is based on the decomposition of the numerical algorithm by wave types and wave velocities.
The test analysis of the two-mode problem on acceleration of the towed long system allowed establishing
the ranges of its application. 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 50–200% when performing calculations,
depending on the required accuracy and options for the decomposition of multiwave 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 wave factorization method,
the decomposition algorithm 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 original data.
A finite-difference scheme factorization by perturbation directions and wave types with variable dispersion-diffusion properties is constructed.
Keywords: multiwave models, types and speed of waves, decomposition, algorithm, lengthy system.
FULL TEXT
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