### Numerical methods for solving multidimensional problems of mathematical physics and mechanics

COUNTRY OF ORIGIN

BelarusIDENTIFIER

BO5449PUBLISHED

2022-08-19LAST UPDATE

2024-04-12DEADLINE

Linked profile in other language

Responsible

Viktor Lepin

+375 17 379 1784

math@im.bas-net.by

+375 17 379 1784

math@im.bas-net.by

Summary

The Institute of Mathematics offers consumers the development and research of numerical methods for solving multidimensional problems of mathematical physics and mechanics described by partial differential equations under an outsourcing agreement or subcontracting and is looking for partners interested in a distribution services agreement.

Description

Development and research of numerical methods for solving multidimensional problems of mathematical physics and mechanics, described by equations in partial derivatives.

Numerical modeling of actual problems of natural science, engineering, technology and national economy.

Development of parallel applications for solving computational problems on supercomputers with distributed memory.

In particular, the most important results are:

- Dynamic software simulator for training operators of the vacuum gas oil hydroconversion unit (VGKVG), which is based on mathematical models of the movement of liquid and steam flows, rectification and models of control elements (valves, gate valves, pumps);

- Algorithms and programs for mathematical modeling of fluid flows in hydraulic networks;

- Mathematical modeling of multicomponent rectification processes for tray columns;

- Simulation of technological processes of post-implantation fast heat treatment of silicon structures under conditions of multidimensionality and multilayerness of semiconductor structures;

- Mathematical modeling of phase transformations during laser processing of materials;

- Numerical modeling of geofiltration and geomigration flows that occur during the operation of several wells in two aquifers separated by a low-permeability intermediate layer, study of the pollution spot as a result of emerging filtration flows;

- Development of mathematical models of the processes of formation of gas-thermal coatings and processes associated with the subsequent heat treatment of applied materials;

- Numerical modeling of thermal and deformation processes in multilayer coatings with different thermophysical properties, used to analyze the structure of heat-shielding coatings for ceramic materials based on zirconium dioxide, operated in a wide range of loads, temperatures and environmental compositions;

- Development of numerical algorithms for solving systems of differential equations for calculating thermal processes in a spacecraft, taking into account the operation of the system for ensuring thermal regimes;

- Development of a numerical method for solving a system of equations that describes the space-time evolution of the charge arising in the dielectric of a metal-dielectric-semiconductor (MIS) structure when exposed to ionizing radiation;

- Development of a method for the numerical solution of a system of nonlinear non-stationary multidimensional equations describing the evolution of point defects and the diffusion of implanted impurities in silicon during rapid thermal annealing under conditions of multilayer semiconductor structures;

- Development of a numerical method and a parallel algorithm for solving quasi-linear two-dimensional parabolic equations with boundary conditions of the third kind for modeling the transfer of donor impurities under conditions of low-energy implantation and short thermal annealing;

- Numerical modeling of crystallization processes without explicit identification of the crystallization front under conditions of diffuse phase transitions occurring in silumin casting from AK12 alloy in a jet mold in a research installation for hardening casting;

- Tiling methods for different mapping strategies of parallel algorithms (LPGS, LSGP) on computing systems with distributed memory;

- Methods for constructing approximations of a set of tiles in the case of applying tiling to polyhedral computational areas of a fairly general form;

- Algorithms and parallel programs for the numerical solution of two-dimensional parabolic equations with boundary conditions of the first kind on supercomputers with distributed memory;

- Numerical method and parallel algorithm for solving quasi-linear two-dimensional parabolic equations with boundary conditions of the third kind by a locally one-dimensional method;

- Parallel procedures for performing matrix-vector multiplication operations for solving systems of linear equations with sparse matrices.

Numerical modeling of actual problems of natural science, engineering, technology and national economy.

Development of parallel applications for solving computational problems on supercomputers with distributed memory.

In particular, the most important results are:

- Dynamic software simulator for training operators of the vacuum gas oil hydroconversion unit (VGKVG), which is based on mathematical models of the movement of liquid and steam flows, rectification and models of control elements (valves, gate valves, pumps);

- Algorithms and programs for mathematical modeling of fluid flows in hydraulic networks;

- Mathematical modeling of multicomponent rectification processes for tray columns;

- Simulation of technological processes of post-implantation fast heat treatment of silicon structures under conditions of multidimensionality and multilayerness of semiconductor structures;

- Mathematical modeling of phase transformations during laser processing of materials;

- Numerical modeling of geofiltration and geomigration flows that occur during the operation of several wells in two aquifers separated by a low-permeability intermediate layer, study of the pollution spot as a result of emerging filtration flows;

- Development of mathematical models of the processes of formation of gas-thermal coatings and processes associated with the subsequent heat treatment of applied materials;

- Numerical modeling of thermal and deformation processes in multilayer coatings with different thermophysical properties, used to analyze the structure of heat-shielding coatings for ceramic materials based on zirconium dioxide, operated in a wide range of loads, temperatures and environmental compositions;

- Development of numerical algorithms for solving systems of differential equations for calculating thermal processes in a spacecraft, taking into account the operation of the system for ensuring thermal regimes;

- Development of a numerical method for solving a system of equations that describes the space-time evolution of the charge arising in the dielectric of a metal-dielectric-semiconductor (MIS) structure when exposed to ionizing radiation;

- Development of a method for the numerical solution of a system of nonlinear non-stationary multidimensional equations describing the evolution of point defects and the diffusion of implanted impurities in silicon during rapid thermal annealing under conditions of multilayer semiconductor structures;

- Development of a numerical method and a parallel algorithm for solving quasi-linear two-dimensional parabolic equations with boundary conditions of the third kind for modeling the transfer of donor impurities under conditions of low-energy implantation and short thermal annealing;

- Numerical modeling of crystallization processes without explicit identification of the crystallization front under conditions of diffuse phase transitions occurring in silumin casting from AK12 alloy in a jet mold in a research installation for hardening casting;

- Tiling methods for different mapping strategies of parallel algorithms (LPGS, LSGP) on computing systems with distributed memory;

- Methods for constructing approximations of a set of tiles in the case of applying tiling to polyhedral computational areas of a fairly general form;

- Algorithms and parallel programs for the numerical solution of two-dimensional parabolic equations with boundary conditions of the first kind on supercomputers with distributed memory;

- Numerical method and parallel algorithm for solving quasi-linear two-dimensional parabolic equations with boundary conditions of the third kind by a locally one-dimensional method;

- Parallel procedures for performing matrix-vector multiplication operations for solving systems of linear equations with sparse matrices.

Advantages and Innovations

Highly qualified staff, innovative solutions.

Stage of development

Already on the market

Funding source

State budged

Internal

Internal

IPR status

Exclusive rights

Secret know-how

Secret know-how

Sector group

Aeronautics, Space and Dual-Use Technologies

Intelligent Energy

Environment

ICT Industry & Services

Maritime Industry and Services

Mobility

Intelligent Energy

Environment

ICT Industry & Services

Maritime Industry and Services

Mobility

#### Client information

Type

R&D institution

Year established

1959

NACE keywords

M.72.19 - Other research and experimental development on natural sciences and engineering

M.74.90 - Other professional, scientific and technical activities n.e.c.

J.62.09 - Other information technology and computer service activities

M.74.90 - Other professional, scientific and technical activities n.e.c.

J.62.09 - Other information technology and computer service activities

Turnover (in EUR)

10-20M

Already engaged in transnational cooperation

Yes

Additional comments

Activity of Institute.

- Main directions of scientific research in the field of Algebra. (in Russian)

- Directions of fundamental and applied scientific research in the field of Computational Mathematics and Mathematical Modeling.(in Russian)

- Directions of fundamental and applied scientific research in the field of Differential equations.(in Russian)

- Directions of fundamental and applied scientific research in the field of Nonlinear and Stochastic Analysis.(in Russian)

- Directions of fundamental and applied scientific research in the field of Number Theory and Discrete Mathematics.(in Russian)

The Institute maintains active creative ties with leading scientific institutions in many countries of the world (Germany, France, Belgium, Russia, Georgia, Ukraine, Greece, Italy, Poland, Austria, China, USA, Great Britain, Denmark, Switzerland, Czech Republic, Yugoslavia, Japan, Bulgaria), is the organizer of a number of international conferences, schools, symposia.

The achievements of the institute's scientists were awarded the Lenin Prize (1978), the State Prize of the USSR (1970, 1972), State Prizes of the BSSR (1974, 1978, 1982), the State Prize of the Republic of Belarus (1998, 2000, 2004), the Prize of the Council of Ministers of the USSR (1986), prizes of the Lenin Komsomol (1970, 1987) and Lenin Komsomol of Belarus (1976, 1984, 1990), prizes of the National Academy of Sciences of Belarus (1993, 1995).

- Main directions of scientific research in the field of Algebra. (in Russian)

- Directions of fundamental and applied scientific research in the field of Computational Mathematics and Mathematical Modeling.(in Russian)

- Directions of fundamental and applied scientific research in the field of Differential equations.(in Russian)

- Directions of fundamental and applied scientific research in the field of Nonlinear and Stochastic Analysis.(in Russian)

- Directions of fundamental and applied scientific research in the field of Number Theory and Discrete Mathematics.(in Russian)

The Institute maintains active creative ties with leading scientific institutions in many countries of the world (Germany, France, Belgium, Russia, Georgia, Ukraine, Greece, Italy, Poland, Austria, China, USA, Great Britain, Denmark, Switzerland, Czech Republic, Yugoslavia, Japan, Bulgaria), is the organizer of a number of international conferences, schools, symposia.

The achievements of the institute's scientists were awarded the Lenin Prize (1978), the State Prize of the USSR (1970, 1972), State Prizes of the BSSR (1974, 1978, 1982), the State Prize of the Republic of Belarus (1998, 2000, 2004), the Prize of the Council of Ministers of the USSR (1986), prizes of the Lenin Komsomol (1970, 1987) and Lenin Komsomol of Belarus (1976, 1984, 1990), prizes of the National Academy of Sciences of Belarus (1993, 1995).

Languages spoken

English

Russian

Russian

#### Information about partnership

Type of partnership considered

Distribution services agreement

Outsourcing agreement

Subcontracting

Outsourcing agreement

Subcontracting

Type and role of partner sought

Consumers interested in purchasing and using the results of applying and researching numerical methods for solving multidimensional problems of mathematical physics and mechanics described by partial differential equations under an outsourcing agreement or subcontracting.

Partners interested in purchasing services for the development and research of numerical methods for solving multidimensional problems of mathematical physics and mechanics, described by partial differential equations under a distribution services agreement.

Partners interested in purchasing services for the development and research of numerical methods for solving multidimensional problems of mathematical physics and mechanics, described by partial differential equations under a distribution services agreement.

Type and size of partner sought

> 500 MNE

> 500

251-500

SME 51-250

SME 11-50

SME <= 10

R&D Institution

University

Sole proprietor

> 500

251-500

SME 51-250

SME 11-50

SME <= 10

R&D Institution

University

Sole proprietor

#### Attachments

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Статистика ведется с 19.08.2022 15:07:56

Статистика ведется с 19.08.2022 15:07:56