International Research Laboratory «Multi-scale Mathematical Modelling and Computer Calculations»

Scientific results:

1. Our researchers have developed multi-scale methods for solving problems described by partial differential equations and  perforated regions, conducted an analysis of error in produced solutions.
2. The Laboratory has developed and researched algorithms for solving non-stationary multi-scale problems for systems of partial differential equations that are based on the use of combined schemes of splitting localized multi-scale reduced-order models.
3. We have developed multi-scale methods that allow to solve problems containing various scales both in terms of space and time.
4. Our researchers have extended the existing software packages, integrating the developed multi-scale algorithms into software packages.
5. We have created software for the numerical modeling of relevant problems of the Arctic

Implemented results of research:

On the basis of the results of our research, we have created software code. The developed computation methods and scientific code were used for the numerical modeling of applied problems (for instance, in collaboration with «YAKUTPNIIS» LLC we have conducted computations of the thermal field of soil for the real conditions in the cryolithozone). 

Education and career development:

• 8 Candidate of Sciences dissertations have been defended.
• Postgraduates and young research fellows have completed internships at Texas A&M University (USA), the Chinese University of Hong Kong (China PR), Seoul National University (South Korea), Hunan University, Xiangtan University (China PR).
• Two new courses have been created for the master’s degree program: «Averaging methods and multi-scale methods» (Yalchin Efendiev), «Neural networks for solving problems of mathematical physics» (Alexandr Grigoriyev) and two courses for postgraduate school, «Multi-scale finite-element method» (Yalchin Efendiev), «Theory of the finite-element method» (Raytcho Lazarov).

8 International and two Russian conferences have been organized:

1. «Multi-scale methods and high-performance computations» from July 30 to August 4, 2017 at the North-Eastern Federal University (Yakutsk, Russia).
2. «Multi-scale methods and high-performance computations for multi-physics problems» from August 8 to August 10, 2018  at  North-Eastern Federal University (Yakutsk, Russia).
3. «Multi-scale methods and high-performance scientific computations» from August 15 to August 17,  2018 in collaboration with the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (Moscow, Russia).
4. «Supercomputer technologies in mathematical modeling» from June 19 to June 21, 2019 in collaboration with the Steklov Institute of Mathematics of the Russian Academy of Sciences (Moscow, Russia).    
5. «Multi-scale and high-performance computations for multi-physical problems» from June 24 to June 25, 2019 at North-Eastern Federal University (Yakutsk, Russia).
6. «Multi-scale methods and high-performance scientific computations» from October 7 to October 11, 2019 in collaboration with the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Far Eastern Federal University (Vladivostok, Russia).
7. All-Russian conference «Applications of digital technologies in the industry, business, and healthcare of the Republic of Sakha (Yakutia)» from December 23 to December 25, 2019 at North-Eastern Federal University (Yakutsk, Russia).
8. 4^th International Conference «Multi-scale methods and high-performance scientific computations» from September 8 to September 13, 2020 (Sochi, Russia).
9. «Multi-scale and high-performance computations for multi-physical problems» December 7, 2020, staged online (Yakutsk, Russia).
10. All-Russian conference «Applications of mathematical modeling, digital technologies in the industry of the Republic of Sakha (Yakutia)», December 15, 2020 staged online (Yakutsk, Russia).
11. Mini-symposium «High-performance computation algorithms and multi-scale methods» as part of the All-Russian Science and Practice Conference with International  Participation «Current problems in heat physics, power generation and hydrogas dynamics in the conditions of the Arctic» devoted to the 85^th anniversary of the birth of the honored worker of science of Russia and the Yakut Autonomous Soviet Socialist Republic, Doctor of Technical Sciences, professor Eduard A. Bondarev, July 14, 2021. (Yakutsk, Russia).
12. International Conference «Mathematical modeling, inverse problems and big data» in collaboration with the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences and the Southern Federal University, form July 19 to July 24, 2021 (Yakutsk, Russia). 
13. Mini-symposium «Multi-scale and high-performance computations for multi-physics problems» within the international conference «Marchuk academic readings 2021», organized by the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, October 04, 2021 (Yakutsk, Russia).
14. 5^th International Conference  «Supercomputer technologies in mathematical modeling» in collaboration with the Steklov Institute of Mathematics of the Russian Academy of Sciences and the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (SCTeMM’2022), from June 27 to June 30, 2022. (Moscow, Russia).
15. 5^th All-Russian Scientific Conference «Multi-scale methods and high-performance scientific computations» in collaboration with the youth Laboratory «Computation technologies of the modeling of multi-physics and multi-scale processes in the cryolithozone» from September 5 to September 7, 2022 (Yakutsk, Russia).

We have conducted an international school and seminar for young researchers in multi-scale methods and high-performance scientific computations from August 3 to August 4, 2017 at the North-Eastern Federal University (Yakutsk, Russia).

7 academic seminars in our area of study with the invitation of leading researchers of the country and the world. 

Collaborations:

• Texas A&M University (USA), Seoul National University (South Korea), Fraunhofer Institute for Industrial Mathematics (Germany), Chinese University of Hong Kong (China PR), Xiangtan University (China PR), Heze University (China PR): joint research, academic internships.
• Steklov Institute of Mathematics of the Russian Academy of Sciences (Russia), Nuclear Safety Institute of the Russia Academy of Sciences (Russia), Skolkovo Innovation Center (Russia), Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (Russia), Obraztsov Institute of High Energy Physics of the Russian Academy of Sciences (Russia), Bauman Moscow State Technical University (Russia): joint  conferences and seminars, submitting applications for joint grants.
• University of Da Nang (Vietnam): a joint grant.