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

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...

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Vydané v:	Computation Ročník 13; číslo 11; s. 252
Hlavný autor:	Tverdyi, Dmitrii
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.11.2025
Predmet:	algorithm efficiency Algorithms Analysis asymptotic complexity estimates Cauchy problems Complexity Derivatives Differential equations Earthquake prediction Earthquakes Effectiveness Efficiency Estimates finite difference schemes Fractals Fractional calculus fractional derivatives of variable order Geological processes Geology Geophysics Germany Inverse problems Iterative methods Mathematical analysis Modelling New York nonlinear parallel computing Radon Russia Seismology United States New York United States Germany Russia
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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 earthquakes 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 sequential 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.
AbstractList	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 earthquakes 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 sequential 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. 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 earthquakes 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 sequential 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 n[sup.2] in terms of both computation time and memory consumption.
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Cites_doi	10.1137/1.9781611971200 10.1007/s40314-020-01191-x 10.1137/1.9781611972344 10.35330/1991-6639-2023-6-116-83-94 10.1098/rspa.2019.0498 10.20944/preprints202406.1939.v1 10.1007/BFb0067700 10.1007/s11012-017-0652-y 10.1007/978-3-031-90546-9_11 10.1134/S2070048210020055 10.1007/978-3-642-18101-6 10.1016/j.jenvrad.2013.04.014 10.1615/JAutomatInfScien.v48.i10.10 10.1190/1.1441293 10.1097/00004032-199705000-00012 10.1145/321812.321815 10.1016/j.jenvrad.2023.107310 10.1515/fca-2017-0040 10.3390/fractalfract6010023 10.3390/math6020016 10.3390/math11040850 10.3390/w10091276 10.1007/b97553 10.1007/978-3-642-33911-0 10.3390/geosciences15010030 10.1007/978-3-031-18150-4 10.3390/math11153358 10.1007/s40314-019-0878-5
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References	Bohaienko (ref_36) 2020; 39 Patnaik (ref_19) 2020; 476 ref_13 ref_11 ref_10 Novozhenova (ref_21) 2017; 20 ref_18 ref_17 ref_16 ref_15 Watson (ref_31) 1978; Volume 630 Bogaenko (ref_34) 2016; 48 Huang (ref_7) 2024; 271 Tverdyi (ref_29) 2024; 47 ref_25 Caputo (ref_20) 2017; 52 ref_23 ref_22 Yasuoka (ref_1) 1997; 72 Brent (ref_42) 1974; 21 ref_28 ref_27 ref_26 Gibadullin (ref_30) 2025; Volume 500 Bohaienko (ref_35) 2019; 38 ref_33 Tverdyi (ref_12) 2023; 44 ref_32 Tverdyi (ref_24) 2023; 116 ref_39 ref_38 Kristiansson (ref_8) 1982; 47 ref_47 ref_46 ref_45 ref_44 ref_43 Petraki (ref_4) 2015; 6 ref_41 ref_40 Vasilyev (ref_37) 2013; 124 ref_3 ref_2 Parovik (ref_14) 2010; 2 ref_49 ref_48 ref_9 ref_5 ref_6
References_xml	– ident: ref_9 – ident: ref_49 – ident: ref_5 – ident: ref_27 doi: 10.1137/1.9781611971200 – volume: 39 start-page: 163 year: 2020 ident: ref_36 article-title: Parallel finite-difference algorithms for three-dimensional space-fractional diffusion equation with phi–Caputo derivatives publication-title: Comput. Appl. Math. doi: 10.1007/s40314-020-01191-x – ident: ref_26 doi: 10.1137/1.9781611972344 – volume: 116 start-page: 83 year: 2023 ident: ref_24 article-title: Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of Petropavlovsk-Kamchatsky geodynamic polygon publication-title: NEWS Kabard.-Balkar. Sci. Cent. RAS doi: 10.35330/1991-6639-2023-6-116-83-94 – ident: ref_16 – ident: ref_39 – volume: 476 start-page: 20190498 year: 2020 ident: ref_19 article-title: Applications of variable-order fractional operators: A review publication-title: Proc. R. Soc. A doi: 10.1098/rspa.2019.0498 – ident: ref_3 doi: 10.20944/preprints202406.1939.v1 – ident: ref_23 – volume: Volume 630 start-page: 105 year: 1978 ident: ref_31 article-title: The Levenberg-Marquardt algorithm: Implementation and theory publication-title: Numerical Analysis. Lecture Notes in Mathematics doi: 10.1007/BFb0067700 – volume: 52 start-page: 3043 year: 2017 ident: ref_20 article-title: On the notion of fractional derivative and applications to the hysteresis phenomena publication-title: Meccanica doi: 10.1007/s11012-017-0652-y – volume: Volume 500 start-page: 159 year: 2025 ident: ref_30 article-title: Refinement of Variable Order Fractional Derivative of Gerasimov-Caputo Type by Multidimensional Levenberg-Marquardt Optimization Method publication-title: Computing Technologies and Applied Mathematics doi: 10.1007/978-3-031-90546-9_11 – volume: 2 start-page: 180 year: 2010 ident: ref_14 article-title: Radon transfer processes in fractional structure medium publication-title: Math. Model. Comput. Simul. doi: 10.1134/S2070048210020055 – ident: ref_18 doi: 10.1007/978-3-642-18101-6 – volume: 124 start-page: 185 year: 2013 ident: ref_37 article-title: Determination of mechanisms and parameters which affect radon entry into a room publication-title: J. Environ. Radioact. doi: 10.1016/j.jenvrad.2013.04.014 – ident: ref_48 – ident: ref_41 – volume: 48 start-page: 1 year: 2016 ident: ref_34 article-title: On Mathematical modeling of Fractional-Differential Dynamics of Flushing Process for Saline Soils with Parallel Algorithms Usage publication-title: J. Autom. Inf. Sci. doi: 10.1615/JAutomatInfScien.v48.i10.10 – ident: ref_17 – ident: ref_45 – volume: 47 start-page: 1444 year: 1982 ident: ref_8 article-title: Evidence for nondiffusive transport of 86Rn in the ground and a new physical model for the transport publication-title: Geophysics doi: 10.1190/1.1441293 – volume: 44 start-page: 86 year: 2023 ident: ref_12 article-title: Research of Stress-Strain State of Geo-Environment by Emanation Methods on the Example of alpha(t)-Model of Radon Transport publication-title: Bull. KRASEC Phys. Math. Sci. – ident: ref_28 – volume: 72 start-page: 759 year: 1997 ident: ref_1 article-title: Anomaly in atmospheric radon concentration: A possible precursor of the 1995 Kobe Japan, earthquake publication-title: Health Phys. doi: 10.1097/00004032-199705000-00012 – volume: 21 start-page: 201 year: 1974 ident: ref_42 article-title: The parallel evaluation of general arithmetic expressions publication-title: J. Assoc. Comput. Mach. doi: 10.1145/321812.321815 – ident: ref_47 – volume: 271 start-page: 107310 year: 2024 ident: ref_7 article-title: Earthquake precursors: A review of key factors influencing radon concentration publication-title: J. Environ. Radioact. doi: 10.1016/j.jenvrad.2023.107310 – ident: ref_40 – volume: 6 start-page: 1000282 year: 2015 ident: ref_4 article-title: Radon-222: A Potential Short-Term Earthquake Precursor publication-title: Earth Sci. Clim. Change – ident: ref_44 – volume: 20 start-page: 790 year: 2017 ident: ref_21 article-title: Life And Science of Alexey Gerasimov, One of the Pioneers of Fractional Calculus in Soviet Union publication-title: FCAA doi: 10.1515/fca-2017-0040 – ident: ref_33 doi: 10.3390/fractalfract6010023 – ident: ref_6 – ident: ref_38 doi: 10.3390/math6020016 – ident: ref_11 doi: 10.3390/math11040850 – ident: ref_46 – ident: ref_2 doi: 10.3390/w10091276 – ident: ref_22 doi: 10.1007/b97553 – ident: ref_15 – ident: ref_13 doi: 10.1007/978-3-642-33911-0 – ident: ref_25 doi: 10.3390/geosciences15010030 – ident: ref_10 doi: 10.1007/978-3-031-18150-4 – ident: ref_43 – ident: ref_32 doi: 10.3390/math11153358 – volume: 47 start-page: 35 year: 2024 ident: ref_29 article-title: The optimization problem for determining the functional dependence of the variable order of the fractional derivative of the Gerasimov-Caputo type publication-title: Bull. KRASEC Phys. Math. Sci. – volume: 38 start-page: 105 year: 2019 ident: ref_35 article-title: A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative publication-title: Comput. Appl. Math. doi: 10.1007/s40314-019-0878-5
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SubjectTerms	algorithm efficiency Algorithms Analysis asymptotic complexity estimates Cauchy problems Complexity Derivatives Differential equations Earthquake prediction Earthquakes Effectiveness Efficiency Estimates finite difference schemes Fractals Fractional calculus fractional derivatives of variable order Geological processes Geology Geophysics Germany Inverse problems Iterative methods Mathematical analysis Modelling New York nonlinear parallel computing Radon Russia Seismology United States
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Title	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
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