Последние новости
Полезные ссылки
Сообщение о землетрясении
Если Вы ощутили землетрясение, пожалуйста, сообщите о нёмAnalysis of the efficiency and complexity of parallel numerical solution algorithms in a model of radon volumetric activity with a fractional derivative of variable order
- Federal State Budget Research Institution Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences
In modern science, close attention is paid to fundamental directions that have practical
applications. the deformed state of the medium. For the Kamchatka region, in particular, this
is a research of the processes of migration of subsurface radon gas using the most modern
mathematical modeling methods in order to interpret anomalies preceding earthquakes. The
authors in [1] propose mathematical hereditary α and α(t)-models of RVA (volumetric radon
activity), taking into account the nonlocality of the radon transport process over time. The main
hypothesis of the hereditary models of OAR is that the order of the fractional derivative is
associated with a change in the permeability of the geological environment due to a change in
the stress-strain state of the medium.
In [2], the inverse problem is formulated and solved for the hereditary α-RVA model in order
to restore the values of the model parameters, on the basis of which estimates of changes in
the radon flux density are given with a change in the stress-strain state of the medium. The
estimates obtained are reliable and more accurate than those based on the ODE model. The
practical significance of the evaluation results is that it can help in more accurate selection of
radon monitoring points.
When solving inverse problems, it becomes necessary to cyclically recalculate the direct
problem for different values of model parameters and compare the results with experimental data.
At the same time, a direct problem can have a sufficiently high computational complexity both
when increasing the size of the input data N and when choosing a solution method. Therefore,
it is important that the solution of each individual direct problem is completed in the shortest
time, but at the same time it is necessary to take into account the possible memory costs of
the algorithm used. All this leads us to the development of various parallel algorithms for the
numerical solution of RVA model equations. This study examines parallel implementations of
numerical solution methods: EFDS (non-local explicit finite difference scheme) [3] and IFDS-
MNM (non-local implicit finite difference scheme solved by a modified Newton method) [3] in
order to evaluate the computational complexity and efficiency of these algorithms. In particular,
EFDS-omp and IFDS-MNM-omp based on the OpenMP API, as well as EFDS-hybrid and IFDS-
MNM-hybrid hybrid CPU-GPU algorithms based on the OpenMP and CUDA APIs.
Tverdyi D. A. , Parovik R. I. Analysis of the efficiency and complexity of parallel numerical solution algorithms in a model of radon volumetric activity with a fractional derivative of variable order // Collection of materials from the International Scientific-Practical Conference on Current problems of Algebra and analysis, Termez State University, 20–21 октября 2025 года. – Termez: Termez State University, 2025. – P. 290-293
