Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 50. no. 1. P. 149 – 168. ISSN 2079-6641

INFORMATION AND COMPUTING TECHNOLOGIES
https://doi.org/10.26117/2079-6641-2025-50-1-149-168
Research Article
Full text in Russian
MSC 68W10; 65Y20; 26A33

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Analysis of Efficiency of the Hybrid Parallel Algorithm for Numerical Solution of the Cauchy Problem for Hereditary Models of Radon Volumetric Activity in FEVO Software Complex

D. A. Tverdyi^{\ast}

Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Paratunka village, Mirnaya str., 7, Russia

Abstract. The article presents a investigation of the computational efficiency of a hybrid parallel algorithm
implementing a nonlocal implicit finite-difference scheme (IFDS) for the numerical solution of the problem of radon volume activity dynamics (RVA). In particular, we solve the Cauchy problem for a nonlinear equation with fractional variable order derivative of Gerasimov-Caputo type (hereditary α(t)-model) to describe the anomalous RVA dynamics in the storage chamber, which can be a precursor to strong earthquakes. Tools for data analysis and modeling of RVA dynamics are implemented in the FEVO software complex. Also in the FEVO software complex, taking into account the known observed data of the AAR, by the method of unconditional Levenberg-Marquardt optimization, the solution of inverse problems for the identification of the parameters of hereditary α(t)-models is implemented, which requires multiple solutions within the framework of the direct problem, which in turn determines the importance of developing parallel algorithms for their solution. The parallel algorithm was implemented in C language because of its speed and versatility in working with memory, which is important when organizing calculations on CPU (using OpenMP API) together with GPU (using CUDA API). The efficiency of the algorithm was analyzed as a series of 10 computational experiments on a personal computer, consisting in solving a test case based on the hereditary α(t)-model of RVA. Further, the acceleration, efficiency and cost of the algorithm are determined, and the efficiency of CPU thread utilization is evaluated. The efficiency analysis tools are implemented in FEVO. From the analysis we can conclude that the hybrid parallel IFDS algorithm shows a speedup of 9-12 times compared to the fastest sequential implementation.

Key words: parallel computing, CUDA, OpenMP, C, memory effect, hereditary, time nonlocality, fractional derivatives, dynamic systems, nonlinearity, implicit finite-difference schemes.

Received: 10.03.2025; Revised: 01.04.2025; Accepted: 03.04.2025; First online: 18.04.2025

For citation. Tverdyi D. A. Analysis of efficiency of the hybrid parallel algorithm for numerical solution of the Cauchy problem for hereditary models of radon volumetric activity in FEVO software complex. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 50: 1, 149-168. EDN: ZVMJVG. https://doi.org/10.26117/2079-6641-2025-50-1-149-168.

Funding. The research was funded by a grant from the Russian Science Foundation, project number 23-71-01050, which can be found at https://rscf.ru/project/23-71-01050/

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for the submission of the final version of the article for publication.

^{\ast}Correspondence: E-mail: tverdyi@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Tverdyi D. A., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Tverdyi Dmitrii Alexsandrovich – PhD (Phys. & Math.), Researcher, Electromagnetic Radiation Laboratory, Institute of Cosmophysical Research and Radio Wave Propagation, FEB RAS, Paratunka village, Russia, ORCID 0000-0001-6983-5258.

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