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

• Development of multiscale methods for problems described by partial differential equations, defined in inhomogeneous and perforated regions, an analysis of errors of the solutions obtained;

• Development and investigation of the algorithms for non-stationary multiscale problems for systems of partial differential equations, based on use of combined splitting schemes for localized multiscale low-order models.

• Multiscale methods development for problems of different time and space scales.

• Expansion of existing software packages and integration of the developed multiscale algorithms into the developed software packages.

• Software codes for numerical modeling of relevant tasks in the Arctic.

Implemented results of research:

Based on the research results, a program code was designed. The developed computational methods and the scientific code were applied for numerical modeling of applied problems (for example, in collaboration with YAKUTPNIIS Ltd. we have calculated a soil thermal field for real conditions of construction in the permafrost zone).

Education and career development:

Degrees earned: 6 Candidate of Science degrees (Physics and Mathematics)

Research internship: Graduate students and young scientists had research internships at Texas A&M University (USA), Chinese University in Hong Kong (China), Seoul National University (Republic of Korea), Hunan University, Xiangtan University (China).

Academic courses developed:

2 academic courses for MSc program:

• “Methods of averaging and multiscale methods” (Y. Efendiev)

• “Neural networks for problems in Mathematical Physics” (А. Grigoriev)

2 academic graduate courses:

• “Multiscale method of finite elements” (Y. Efendiev)

• “Theory of finite element method” (R. Lazarov)

Conferences organized:

8 international and 2 national conferences:

1. «Multiscale models and high-performance scientific computations», July 30- August 04, 2017 at Ammosov North - Eastern Federal University (Yakutsk, Russia).
2. «Multiscale models and high-performance scientific computations for problems of multiphysics», August 08 – 10, 2018 at Ammosov North - Eastern Federal University (Yakutsk, Russia).
3. «Multiscale methods and high-performance scientific computations», August 15 – 17, 2018 at the Institute of Computational Mathematics of the Russian Academy of Sciences (Moscow, Russia).
4. «Supercomputer technologies in Mathematical modeling», June 19- 21, 2019 in collaboration with V. A. Steklov Mathematical Institute (Moscow, Russia).
5. «Multiscale and high-performance computations for multiphysical problems», June 24 -25, 2019 at Ammosov North- Eastern Federal University (Yakutsk, Russia).
6. «Multiscale models and high-performance scientific computations», October 07-11, 2019 in collaboration with G. I. Marchuk Institute of Computational Mathematics of the Russian Academy of Sciences and the Far Eastern Federal University, Vladivostok, Russia.
7. All-Russian conference «Application of digital technologies in industry, business and healthcare in Sakha Republic (Yakutia)», December 23 -25, 2019 at Ammosov North- Eastern Federal University (Yakutsk, Russia).
8. IV International conference «Multiscale methods and high-performance scientific computations», September 08-13, 2020 (Sochi, Russia).
9. «Multiscale and high-performance computations for multiphysical problems», December 07, 2020 (online), Yakutsk, Russia.
10. All-Russian conference «Mathematical modeling and digital technologies for industry in Sakha Republic (Yakutia)», December 15, 2020, (online), Yakutsk, Russia.

International summer workshop for young scientists on multiscale methods and high-performance research computations, August 03-04, 2017, NEFU, Yakutsk, Russia.

6 research seminars on multiscale modeling and reduced multiscale models with invited Russian and international leading scientists.

Collaborations:

Texas A&M University (USA), Seoul National University (Republic of Korea), Fraunhofer Institute for Industrial Mathematics (Germany), Chinese University of Hong Kong (China), Xiangtan University (China), Heze University (China): joint research, academic internships of young researchers and postgraduate students.

V.A. Steklov Mathematical Institute of the Russian Academy of Sciences, Nuclear safety institute of the Russian Academy of Sciences, Skolkovo Innovation center, Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, I. F. Obraztsov Institute of Applied Mechanics of the Russian Academy of Sciences, Bauman Moscow State Technical University: joint conferences and seminars, joint projects for grant applications.

Joint grant project with University of Da Nang (Vietnam): joint grant project.