Geodesic
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. Fiziko-matematičeskie nauki, Tome 50 (2025) no. 1, pp. 149-168

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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 $\alpha$(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 $\alpha$(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 $\alpha$(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.
Keywords: parallel computing, CUDA, OpenMP, memory effect, hereditary, time nonlocality, fractional derivatives, dynamic systems, nonlinearity, implicit finite-difference schemes.
Mots-clés : C 
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     author = {D. A. Tvyordyj},
     title = {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},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {149--168},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a8/}
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D. A. Tvyordyj. 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. Fiziko-matematičeskie nauki, Tome 50 (2025) no. 1, pp. 149-168. http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a8/