Последние новости
Поздравляем с Днём Победы!
08.05.2026
Полезные ссылки
Сообщение о землетрясении
Если Вы ощутили землетрясение, пожалуйста, сообщите о нёмAn Analysis of the Computational Complexity and Efficiency of Various Algorithms for Solving a Nonlinear Model of Radon Volumetric Activity with a Fractional Derivative of a Variable Order
- Federal State Budget Research Institution Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences
Abstract
The article presents a study of the computational complexity and efficiency of various
parallel algorithms that implement the numerical solution of the equation in the hereditary
α(t)-model of radon volumetric activity (RVA) in a storage chamber. As a test example,
a problem based on such a model is solved, which is a Cauchy problem for a nonlinear
fractional differential equation with a Gerasimov–Caputo derivative of a variable order
and variable coefficients. Such equations arise in problems of modeling anomalous RVA
variations. Anomalous RVA can be considered one of the short-term precursors to earth-
quakes as an indicator of geological processes. However, the mechanisms of such anomalies
are still poorly understood, and direct observations are impossible. This determines the
importance of such mathematical modeling tasks and, therefore, of effective algorithms
for their solution. This subsequently allows us to move on to inverse problems based on
RVA data, where it is important to choose the most suitable algorithm for solving the direct
problem in terms of computational resource costs. An analysis and an evaluation of various
algorithms are based on data on the average time taken to solve a test problem in a series
of computational experiments. To analyze effectiveness, the acceleration, efficiency, and
cost of algorithms are determined, and the efficiency of CPU thread loading is evaluated.
The results show that parallel algorithms demonstrate a significant increase in calculation
speed compared to sequential analogs; hybrid parallel CPU–GPU algorithms provide a
significant performance advantage when solving computationally complex problems, and
it is possible to determine the optimal number of CPU threads for calculations. For se-
quential and parallel algorithms implementing numerical solutions, asymptotic complexity
estimates are given, showing that, for most of the proposed algorithm implementations, the
complexity tends to be n2 in terms of both computation time and memory consumption.
Tverdyi D. An Analysis of the Computational Complexity and Efficiency of Various Algorithms for Solving a Nonlinear Model of Radon Volumetric Activity With a Fractional Derivative of a Variable Order. Computation. 2025. Т. 13. № 11. С. 1-29. DOI: 10.3390/computation13110252
