Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie)
type: channel
description: “Numerical Methods and Programming” is a peer-reviewed scientific research journal, which was founded and is published by the Research Computing Center of Lomonosov Moscow State University (RCC MSU). The journal publishes the results of new scientific, practical and theoretical studies obtained in the field of computational mathematics, mathematical modeling, software for computing machines, complexes and networks, as well as their applications. The editorial board of the journal accepts for consideration author's materials of high quality, prepared in the form of an original article or review. The novelty and scientific significance of the work are verified by reviewers and editors. The journal is published with a periodicity of 4 issues per year. Publication of articles is free of charge. The published papers are publicly available to all Internet users. The journal “Numerical Methods and Programming” is registered as a scientific electronic periodical by the Federal Service for Supervision of Communications, Information Thechnology, and Mass Media (certificate of registration No. 77-4356, ISSN 1726-3522). The journal is included in the RSCI bibliographic database (Russian Science Citation Index), in “The White List” of the Russian Center of Scientific Information, in the core of the Russian Science Citation Index and in All-Russian Mathematical Portal MathNet.Ru. The journal belongs to category K1 of the Higher Attestation Commission List (Russian Federation) of leading peer-reviewed scientific journals and publications recommended for the publication of the main results of dissertations for the degree of doctor of science and PhD. Bibliographic information on published papers is placed in the scientific citation database of the RSCI. Articles published in the journal are assigned doi (since 2015). Full texts of all articles of the journal are placed in pdf-format in the Scientific Electronic Library of the Russian Federation (elibrary.ru) for free access. [more]
publisher: Научно-Исследовательский Вычислительный Центр Московского Государственного Университета имени М. В. Ломоносова
language: en
publication name: Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie)
issn: 1726-3522
items: Optimal investment in S&P 500 using SDDP and the implied-calibrated ARMA–GARCH model
items: Estimation of three-phase relative permeabilities from the results of two-phase pore-scale numerical simulation
items: Finding optimal vertex on polytope of feasible solutions to linear programming problem
items: Adaptation of octree meshes for modeling supersonic airfoils and calculating tip vortex
items: Software for solving gas dynamics problems using completely conservative difference schemes with adaptive artificial viscosity
items: High-performance implementation of exponential functions for RISC-V processors
items: Three-dimensional time-dependent multiphase model of local melting processes for stationary and moving continuous bodies
items: Modifications of the ant colony matrix method for parametric optimization using CUDA-based GPUs
items: Review of methods for describing the structure of algorithms
items: Numerical solution of determining the initial condition problem in Cauchy problem for hyperbolic equation with small parameter
items: New approaches for automatic analysis of HPC application performance using the TASC software suite
items: Two decades of algorithmic Feynman integral reduction
items: Computational efficiency and adaptation of radiation transfer module within Large-eddy simulation model
items: Scalability study of parallel algorithm for numerical modeling of plasma confinement in open magnetic traps using simulation modeling methods
items: A method for constructing fully interpretable linear regressions with statistically significant estimates according to the Student’s criterion and insignificant intercorrelation coefficients
items: Numerical algorithm to estimate formation factor of digital rocks
items: Acceleration of numerical simulation of seismic data for monitoring the burial of CO₂ using a neural network
items: Applying Composable Parallelism in Programs Using Parallel
items: Numerical method for modeling multiscale dynamics of gas-dispersed media with two relaxation parameters based on Smoothed Particle Hydrodynamics
items: Algorithm for applying the structural adaptation criterion to solve problems using adaptive mesh refinement
items: Improved method of recognizing marine and coastal system objects based on combination of local binary pattern method and neural network technologies
items: Modified axisymmetric contact smoothed particle hydrodynamics method with the possibility of modeling surface tension
items: Control of the Gasoline Catalytic Reforming Process Based on a Kinetic Model Using an Artificial Neural Network
items: A software system for automated assessment of stereoscopic distortions in VR180 videos
items: Structure-oriented smoothing for wave propagation modelling by beam method with frequency dependence
items: A structural two-level neural network approach to joint inversion of gravitational and magnetic fields
items: Constructor of soil carbon dynamic models
items: Application of the nudging technique to produce initial states for the INM RAS climate model seasonal hindcasts
items: Systematic numerical search of steady-state solutions for the system of coupled Nonlinear Schrodinger Equations with additional double-well potential
items: Scheme of solution of the heat and mass transfer problem in the hydration model of cement composite

Optimal investment in S&P 500 using SDDP and the implied-calibrated ARMA–GARCH model
type: item
description: We study a dynamic portfolio optimization problem in which probabilistic forecasts of the S&P 500 index are derived from option market prices. To overcome the limitations of classical approaches to reconstructing implied density from option prices which fail to generate conditional multi-period return distributions, we propose a method that involves calibrating the discrete-time ARMA–GARCH model from the observed call option prices in a risk-neutral measure with subsequent transition to a physical measure using a representative-agent framework. The calibrated model provides conditional multi-period distributions of asset returns, which are used to construct scenario lattices in multi-stage stochastic optimization. The resulting portfolio optimization problem is formulated as a multi-stage stochastic programming problem. At each stage, a weighted combination of the expected negative objective value for the next stage and the Conditional Value-at-Risk (CVaR) is minimized. The optimization is performed by means of the Stochastic Dual Dynamic Programming (SDDP) method. Historical simulations over the period 2019–2023 demonstrate that the proposed option-calibrated ARMA–GARCH–SDDP method consistently outperforms benchmark approaches based on static implied densities, equal-probability scenarios, and buy-and-hold investment. The results underscore the economic value of using option-implied information in portfolio management.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: Portfolio Optimization
  topic: keywords
subject: conditional Value-at-Risk (CVaR)
  topic: keywords
subject: stochastic dual dynamic programming (SDDP)
  topic: keywords
subject: ARMA--GARCH models
  topic: keywords
subject: option-implied forecasting
  topic: keywords
subject: scenario generation
  topic: keywords
subject: 01.01.PN.MATHEMATICS (OECD)
  topic: subjects
creator: Petr A. Arbuzov
creator: Dmitry Yu. Golembiovsky
rights: Copyright (c) 2026 П.А. Арбузов, Д.Ю. Голембиовский https://creativecommons.org/licenses/by/4.0
date: 2026-03-17
publication date: 2026-03-17
starting page: 90
ending page: 100
doi: 10.26089/NumMet.v27r107

Estimation of three-phase relative permeabilities from the results of two-phase pore-scale numerical simulation
type: item
description: The article presents a parallel algorithm for numerical simulation of two-phase flows in digital rock images. The algorithm is based on the phase-field method and the finite-difference approach, which includes solving the Poisson equation using conjugate gradients with a spectral preconditioner. The domain decomposition method and CUDA and MPI technologies are used to parallelize the algorithm. The algorithm is applied to calculate the relative phase permeabilities using the steady-state method for oil and water, oil and CO2 in a supercritical form. Based on the calculated two-phase permeabilities, ternary relative permeability diagrams are constructed for a three-phase system using the Stone I, Stone II, and Baker models. The justification of the choice of liquid parameters for two-phase modeling is carried out.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: digital rock physics
  topic: keywords
subject: domain decomposition
  topic: keywords
subject: pore-scale simulation
  topic: keywords
subject: two-phase flows
  topic: keywords
subject: three-phase relative permeability
  topic: keywords
subject: 01.01.PO
  topic: subjects
creator: Dmitry I. Prokhorov
creator: Veronica D. Chepelenkova
creator: Vadim V. Lisitsa
rights: Copyright (c) 2026 Д.И. Прохоров, В.Д. Чепеленкова, В.В. Лисица https://creativecommons.org/licenses/by/4.0
date: 2026-03-19
publication date: 2026-03-19
starting page: 101
ending page: 117
doi: 10.26089/NumMet.v27r108

Finding optimal vertex on polytope of feasible solutions to linear programming problem
type: item
description: A new scalable AlEM algorithm for linear programming on cluster computing systems is presented. Unlike the classical simplex method, the AlEM algorithm, at each step, examines all edges coming from the current vertex of the polytope of feasible solutions, which guarantees the construction of a suboptimal path and completely prevents circling in degenerate problems. A formalized description of the algorithm and its parallel implementation using the MPI library is given.The scalability of the parallel version of the algorithm on real and synthetic linear programming problems has been experimentally investigated. The results of computational experiments confirm the high parallel efficiency of the AlEM algorithm, which remains at least 46% when using up to 200 processor nodes. It is shown that the AlEM algorithm is a possible alternative to existing linear programming methods for high-performance computing.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: linear programming
  topic: keywords
subject: projection method
  topic: keywords
subject: parallel implementation
  topic: keywords
subject: MPI
  topic: keywords
subject: cluster computing system
  topic: keywords
subject: scalability analysis
  topic: keywords
subject: AlEM algorithm
  topic: keywords
subject: 01.01.00 Mathematics
  topic: subjects
creator: Alexander E. Zhulev
creator: Leonid B. Sokolinsky
rights: Copyright (c) 2026 А. Э. Жулев, Леонид Борисович Соколинский https://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 1
ending page: 18
doi: 10.26089/NumMet.v27r101

Adaptation of octree meshes for modeling supersonic airfoils and calculating tip vortex
type: item
description: Solutions to problems of supersonic flow around the X-43 experimental aircraft and wingtip vortex modeling are presented using a unique adaptive mesh design based on the octree principle and an irregular base mesh. Unlike traditional adaptive Cartesian meshes, the base mesh cells can be shaped not only as cubes and parallelopipeds, but also as arbitrary oblique hexagons and can be connected in any way. This allows the geometry and known features of the solution to be taken into account in the base mesh, while adaptation is used only for unknown features. While maintaining the same accuracy, the mesh size is significantly smaller than with the traditional approach. The mesh manipulation tools are implemented as a library of functions using MPI, independent of the aerodynamics portion of the program.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: adaptive grids
  topic: keywords
subject: octree
  topic: keywords
subject: Cartesian grids
  topic: keywords
subject: eddy flows
  topic: keywords
subject: 01.01.UR
  topic: subjects
creator: Aleksandr E. Lutsky
creator: Aleksandr V. Severin
rights: Copyright (c) 2026 А.Е. Луцкий, А.В. Северин https://creativecommons.org/licenses/by/4.0
date: 2026-02-27
publication date: 2026-02-27
starting page: 80
ending page: 89
doi: 10.26089/NumMet.v27r106

Software for solving gas dynamics problems using completely conservative difference schemes with adaptive artificial viscosity
type: item
description: An approach to the numerical solution of the equations of gas dynamics with usage of completely conservative difference schemes with adaptive artificial viscosity is considered. Computational algorithms were developed and software implementing the proposed method within a client-server architecture was created. The client part is written in JavaScript (React), the server part is realized in Go, and the computing core is implemented in C++. Such an organization provides convenient web access, scalability, and high performance in solving hyperbolic tasks. To verify the accuracy and stability of the implemented method, numerical experiments were carried out on classical test problems of gas dynamics — on the Sod and Einfeldt problems. The obtained results confirmed the correct reproduction of shock waves, contact discontinuities and the absence of instabilities. The developed software can serve as a basic platform for further extension to spatially multidimensional formulations and the inclusion of additional physical effects.
subject: Parallel software tools and technologies
  topic: section
subject: gas dynamics
  topic: keywords
subject: completely conservative difference scheme
  topic: keywords
subject: adaptive artificial viscosity
  topic: keywords
subject: software
  topic: keywords
subject: client–server architecture
  topic: keywords
subject: 01.01.PN MATHEMATICS, APPLIED
  topic: subjects
creator: Haochen Zhang
rights: Copyright (c) 2026 Х. Чжан https://creativecommons.org/licenses/by/4.0
date: 2026-02-27
publication date: 2026-02-27
starting page: 67
ending page: 79
doi: 10.26089/NumMet.v27r105

High-performance implementation of exponential functions for RISC-V processors
type: item
description: The development of a high-performance vector library for standard mathematical functions represents a significant objective for the advancement of HPC on platforms based on the RISC-V architecture. This paper presents a detailed implementation of the exp, exp2, and expm1 functions for double-precision, single-precision, and half-precision floating-point types. Special attention is paid to aspects of computational accuracy and performance. A detailed comparison with other existing vector math libraries for the RISC-V architecture is provided.
subject: Parallel software tools and technologies
  topic: section
subject: mathematical functions
  topic: keywords
subject: exponent function
  topic: keywords
subject: exp
  topic: keywords
subject: exp2
  topic: keywords
subject: expm1
  topic: keywords
subject: vector calculations
  topic: keywords
subject: high-performance calculations
  topic: keywords
subject: RISC-V architecture
  topic: keywords
subject: 01.02.EW COMPUTER SCIENS, SOFTWARE ENGINEERING
  topic: subjects
creator: Elena A. Panova
creator: Valentin D. Volokitin
creator: Evgeny A. Kozinov
creator: Iosif B. Meyerov
rights: Copyright (c) 2026 Е. А. Панова, В. Д. Волокитин, Е.А. Козинов, И.Б. Мееров https://creativecommons.org/licenses/by/4.0
date: 2026-01-29
publication date: 2026-01-29
starting page: 27
ending page: 45
doi: 10.26089/NumMet.v27r103

Three-dimensional time-dependent multiphase model of local melting processes for stationary and moving continuous bodies
type: item
description: A multiphase mathematical model has been developed and verified to describe the dynamics of stationary and moving continuous bodies undergoing local melting under gravity and surface tension forces. The key element is a modified acceleration source that enables imposing target translational or rotational velocities on the object. Its action smoothly diminishes within the first-order phase transition zone and becomes spatially localized near the phase interface through the introduction of temperature-dependent and phase-based multipliers. The model is adapted to work with arbitrary volumetric heat sources. A series of computational experiments established optimal ranges for the calibration parameters, ensuring a balance between high accuracy, numerical stability, and acceptable computational cost. Verification was confirmed through agreement with analytical solutions. The model is applicable for numerical analysis of welding, cladding, induction melting, and similar processes.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: multiphase model
  topic: keywords
subject: local melting
  topic: keywords
subject: damping source term
  topic: keywords
subject: phase transition
  topic: keywords
subject: computational experiment
  topic: keywords
subject: adaptive mesh refinement
  topic: keywords
subject: finite volume method
  topic: keywords
subject: Ansys Fluent
  topic: keywords
subject: user-defined function (UDF)
  topic: keywords
subject: 01.01.PN Mathematics Applied
  topic: subjects
creator: Ratmir S. Rublya
creator: Sergei A. Nikiforov
creator: Ivan V. Shvarts
creator: Albert K. Gilmutdinov
rights: Copyright (c) 2025 Р. С. Рубля, С. А. Никифоров, И. В. Шварц, А. Х. Гильмутдинов https://creativecommons.org/licenses/by/4.0
date: 2025-12-12
publication date: 2025-12-12
starting page: 569
ending page: 587
doi: 10.26089/NumMet.v26r437

Modifications of the ant colony matrix method for parametric optimization using CUDA-based GPUs
type: item
description: This article focuses on the development and investigation of the matrix-based modifications of the Ant Colony Optimization (ACO) method for solving parametric optimization problems using CUDA-based Graphics Processing Units (GPUs). Unlike most existing studies focusing on the Traveling Salesman Problem (TSP), the proposed method is specialized for finding optimal values of independent parameters, which leads to a different graph structure and requires the development of novel parallelization schemes. Original parallelization strategies are proposed, including a three-stage decomposition of the algorithm and introduction of “parameter-level” parallelism in the problem dimensions. Various strategies for parallelization and memory management were developed and tested: from the basic MatrixACO-Basic modification to the optimized versions of MatrixACO-Optimization (featuring warp reduction and optimized hash-table handling) and MatrixACO-Transported (utilizing transposed data storage). Experiments were conducted on NVIDIA Tesla V100 16GB SXM2 GPU, the Jetson ORIN platform, and various personal computers using multi-dimensional test functions. Results demonstrate that for a problem with 128 parameters the optimized version of MatrixACO-Optimization provides an execution time of 0.13 ms per graph layer, which corresponds to a speed-up of more than 30 times compared to the optimized CPU implementation based on OpenMP, and in the case of a very large-scale problem with 65536 parameters it speeds up by almost 45 times. For a problem with 512 parameters, the GPU realization shows 76% higher energy efficiency compared to the CPU version, as well as an almost eightfold (7.9 times) reduction in Energy-Delay Product. The study confirms the necessity of developing specialized GPU implementations for parametric tasks and reveals the excellent scalability of the proposed algorithms.
subject: Parallel software tools and technologies
  topic: section
subject: ACO
  topic: keywords
subject: parametric problem
  topic: keywords
subject: optimization
  topic: keywords
subject: CUDA
  topic: keywords
subject: Tesla V100
  topic: keywords
subject: 01.02.EW COMPUTER SCIENS, SOFTWARE ENGINEERING
  topic: subjects
creator: Yurii P. Titov
rights: Copyright (c) 2026 Ю.П. Титов https://creativecommons.org/licenses/by/4.0
date: 2026-02-27
publication date: 2026-02-27
starting page: 46
ending page: 66
doi: 10.26089/NumMet.v27r104

Review of methods for describing the structure of algorithms
type: item
description: Algorithms are the basis of the entire computational process within the traditional chain “problem–method–algorithm–implementation”, and the effective use of their properties, structure, features and characteristics can provide a multiple reduction in the time of their implementation on a specific computing system. This review paper examines the methods used to describe the structure of computational algorithms. It also examines collections of algorithm descriptions available online, providing a brief description of the areas from which algorithms are described and how they are described.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: problem
  topic: keywords
subject: method
  topic: keywords
subject: algorithm
  topic: keywords
subject: implementation
  topic: keywords
subject: parallelism
  topic: keywords
subject: supercomputer
  topic: keywords
subject: AlgoWiki
  topic: keywords
subject: 01.02.EX COMPUTER SCIENS, THEORY & METHODS
  topic: subjects
creator: Alexander S. Antonov
rights: Copyright (c) 2025 А. С. Антонов https://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 548
ending page: 568
doi: 10.26089/NumMet.v26r436

Numerical solution of determining the initial condition problem in Cauchy problem for hyperbolic equation with small parameter
type: item
description: The textconsiders the inverse problem of determining theinitialcondition fora singularly perturbed hyperbolic equation with a small parameter. This involves finding an unknown odd function using additional information about the derivative of the solution at a fixed spatial point. The main result of the text is to reduce the ill-posed initial problem to a Volterra integral equation of the second kind. An iterative method has been developed for numerically solving this equation. Computational experiments were conducted to test the effectiveness of this algorithm.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: inverse problem
  topic: keywords
subject: hyperbolic equation
  topic: keywords
subject: singular perturbation
  topic: keywords
subject: quasi-inversion methods
  topic: keywords
subject: numerical methods
  topic: keywords
subject: 01.01.00 Mathematics
  topic: subjects
creator: Daniil S. Andrianov
rights: Copyright (c) 2026 Д.С. Андрианов https://creativecommons.org/licenses/by/4.0
date: 2026-01-28
publication date: 2026-01-28
starting page: 19
ending page: 26
doi: 10.26089/NumMet.v27r102

New approaches for automatic analysis of HPC application performance using the TASC software suite
type: item
description: This paper presents new automatic analysis approaches for identifying performance issues and useful properties in jobs running on a supercomputer. Methods for detecting problematic application classes, such as “hung” programs and jobs with underutilized nodes, are proposed. New assessments for automatic preliminary evaluation of GPU processors and memory usage efficiency are developed and tested as well. These approaches extend the functionality of the existing TASC software suite designed for conducting comprehensive analysis of usage quality of modern supercomputers.
subject: Parallel software tools and technologies
  topic: section
subject: supercomputer
  topic: keywords
subject: monitoring
  topic: keywords
subject: performance analysis
  topic: keywords
subject: HPC applications
  topic: keywords
subject: supercomputer usage quality
  topic: keywords
subject: application class
  topic: keywords
subject: efficiency assessment
  topic: keywords
subject: 01.02.ET COMPUTER SCIENS, INFORMATION SYSTEMS
  topic: subjects
creator: Vladimir A. Matveev
creator: Alexander V. Setyaev
creator: Vadim V. Voevodin
rights: Copyright (c) 2025 В. А. Матвеев, А. В. Сетяев, В. В. Воеводин https://creativecommons.org/licenses/by/4.0
date: 2025-11-24
publication date: 2025-11-24
starting page: 502
ending page: 514
doi: 10.26089/NumMet.v26r433

Two decades of algorithmic Feynman integral reduction
type: item
description: We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it enables to express integrals belonging to a given family as linear combinations of master integrals. In this review, we restrict ourselves to considering general algorithms which can, in principle, be applied to any family of Feynman integrals.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: Feynman integrals
  topic: keywords
subject: dimensional regularization
  topic: keywords
subject: integration by parts
  topic: keywords
subject: master integrals
  topic: keywords
subject: 01.01.UR Mathematical Physics
  topic: subjects
creator: Alexander V. Smrinov
creator: Vladimir A. Smirnov
rights: Copyright (c) 2025 А. В. Смирнов, В. А. Смирнов https://creativecommons.org/licenses/by/4.0
date: 2025-10-29
publication date: 2025-10-29
starting page: 438
ending page: 448
doi: 10.26089/NumMet.v26r429

Computational efficiency and adaptation of radiation transfer module within Large-eddy simulation model
type: item
description: This paper examines the results of integrating the Rapid Radiative Transfer Model for GCMs (RRTMG) into the Large-Eddy simulation model developed by the Lomonosov Moscow State University Research Computing Center (RCC MSU). To test the integrated radiative transfer module, we conducted conduct analysis of the influence of turbulent aerosol particle transport on the diurnal dynamics of the atmospheric boundary layer under clear-sky conditions and in experiments modeling cold air bursts in the Arctic. A study of the sensitivity of the modeling results to the synchronization frequency of the radiative module with the dynamics core of the model revealed that the modeling results are within the ensemble spread for synchronization times much shorter than the characteristic turbulent time of the flow. This finding coupled with an analysis of the scalability of the overall computational algorithm, demonstrates that the combined models can be effectively applied to numerical analysis of direct and indirect aerosols effects, as well as to modeling cloud feedbacks.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: Large-eddy simulation
  topic: keywords
subject: atmospheric boundary layer
  topic: keywords
subject: radiative transfer
  topic: keywords
subject: 01.02.EV
  topic: subjects
subject: 01.05.QQ
  topic: subjects
creator: Andrey V. Debolskiy
creator: Evgeny V. Mortikov
creator: Aleksei A. Poliukhov
rights: Copyright (c) 2025 А. В. Дебольский, Е. В. Мортиков, А. А. Полюхов https://creativecommons.org/licenses/by/4.0
date: 2025-11-27
publication date: 2025-11-27
starting page: 515
ending page: 533
doi: 10.26089/NumMet.v26r434

Scalability study of parallel algorithm for numerical modeling of plasma confinement in open magnetic traps using simulation modeling methods
type: item
description: This article presents a methodology for evaluating the scalability of parallel algorithms. Instead of conducting costly experiments on supercomputers, we propose using a specialized simulation model. The methodology involves studying and developing the communication and computation scheme of the tested algorithm, creating a simulation model based on the actor model, configuring for a specific supercomputer architecture, and investigating its scalability. The article demonstrates the application of this methodology to a numerical modeling problem for plasma confinement in open magnetic traps. The results indicate 85% scaling efficiency of the algorithm for thousands of cores.
subject: Parallel software tools and technologies
  topic: section
subject: plasma physics
  topic: keywords
subject: parallel algorithms
  topic: keywords
subject: simulation modeling
  topic: keywords
subject: 01.01.PO Mathematics, Interdisciplinary Applications
  topic: subjects
subject: 01.03.UF PHYSICS, FLUIDS & PLASMAS
  topic: subjects
creator: Igor G. Chernykh
creator: Dmitry V. Vins
creator: Vitaly A. Vshivkov
creator: Marina A. Boronina
rights: Copyright (c) 2025 И. Г. Черных, Д. В. Винс, В. А. Вшивков, М. А. Боронина https://creativecommons.org/licenses/by/4.0
date: 2025-12-22
publication date: 2025-12-22
starting page: 601
ending page: 614
doi: 10.26089/NumMet.v26r439

A method for constructing fully interpretable linear regressions with statistically significant estimates according to the Student’s criterion and insignificant intercorrelation coefficients
type: item
description: The article is devoted to the urgent problem of constructing interpretable machine learning models, namely, multiple linear regression models. To estimate their unknown parameters, ordinary least squares is used. A probabilistically-statistical definition of fully interpretable linear regression is formulated. Its construction involves selecting the optimal number of most informative regressors based on determination coefficients in order to ensure consistency between the signs of regression coefficients and the substantive meanings of variables. Additionally, estimates are ensured to be significant and intercorrelation coefficients insignificant by using Student’s t-test. To construct fully interpretable regressions, we propose a method that uses mixed 0-1 integer linear programming. Both strict and non-strict versions of this method are considered. Computational experiments were carried out, which in most cases showed the effectiveness of the proposed method compared to the generating all subsets method.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: regression analysis
  topic: keywords
subject: fully interpretable linear regression
  topic: keywords
subject: ordinary least squares
  topic: keywords
subject: subset selection
  topic: keywords
subject: multicollinearity
  topic: keywords
subject: Student’s t-test
  topic: keywords
subject: generating all subsets
  topic: keywords
subject: mixed 0-1 integer linear programming
  topic: keywords
subject: 01.02.EP Computer science, artificial intelligence
  topic: subjects
subject: 01.01.PO Mathematics, Interdisciplinary Applications
  topic: subjects
creator: Mikhail P. Bazilevskiy
rights: Copyright (c) 2025 М. П. Базилевский https://creativecommons.org/licenses/by/4.0
date: 2025-12-01
publication date: 2025-12-01
starting page: 534
ending page: 547
doi: 10.26089/NumMet.v26r435

Numerical algorithm to estimate formation factor of digital rocks
type: item
description: The paper presents a numerical algorithm of estimating the formation factor for digital rock samples constructed using microtomographic images. The algorithm is based on the numerical solution of the three-dimensional Poisson equation with rapidly changing high-contrast coefficients. The arising system of linear algebraic equations turns out to be ill-conditioned, so to speed up the convergence it is necessary to use a preconditioner. The conjugate gradient method is applied to solve the system and the preconditioner is constructed as the inverse Laplace operator corresponding to the homogeneous model. In its turn, the spectral decomposition of two tridiagonal matrices appearing in the approximation of one-dimensional derivatives is used for inversion. The resulting series of one dimensional problems is solved by the Thomas algorithm. The used preconditioner can be effectively applied both to the original problem with rapidly changing high-contrast coefficients and to the problem, in which the solution is calculated only in the pore space. In the latter case, the method provides the same accuracy of results as the original one for inhomogeneous models, but it converges almost twice as fast. Implementation using graphics processors allows solving problems up to 109 unknowns with a single GPU.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: Poisson equation
  topic: keywords
subject: Conjugate gradient method
  topic: keywords
subject: spectral decomposition
  topic: keywords
subject: 01.01.PO Mathematics, Interdisciplinary Applications
  topic: subjects
creator: Aleksei A. Manaev
creator: Tatyana S. Khachkova
creator: Vadim V. Lisitsa
rights: Copyright (c) 2025 А. А. Манаев, Т. С. Хачкова, В. В. Лисица https://creativecommons.org/licenses/by/4.0
date: 2025-11-19
publication date: 2025-11-19
starting page: 479
ending page: 501
doi: 10.26089/NumMet.v26r432

Acceleration of numerical simulation of seismic data for monitoring the burial of CO₂ using a neural network
type: item
description: Seismic monitoring of greenhouse gases accumulations and injection in reservoir is critical for evaluating the safety and efficiency of injection and preventing leakage. Small changes in reservoir properties caused by fluid displacement lead to changes in seismic attributes. At the same time, modelling of seismic wavefield propagation is resource-consuming due to the need to solve the problem for a series of seismogeological models of the medium corresponding to different stages of fluid injection. The paper presents an algorithm for seismic modelling using a finite-difference method and a neural network to suppress numerical errors in seismograms when applied to the problem of seismic monitoring of greenhouse gas disposal. The algorithm speeds up calculations up to 4 times due to the application of the neural network to rapidly calculated seismograms using a coarse computational grid.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: seismic monitoring
  topic: keywords
subject: greenhouse gases
  topic: keywords
subject: filtration of two-phase flow
  topic: keywords
subject: neural network
  topic: keywords
subject: 01.01.PN MATHEMATICS, APPLIED
  topic: subjects
subject: 01.05.GC GEOCHEMISTRY & GEOPHYSICS
  topic: subjects
subject: 01.02.EP COMPUTER SCIENS, ARTIFICIAL INTELLIGENCE
  topic: subjects
creator: Elena A. Gondyul
creator: Vadim V. Lisitsa
creator: Dmitry M. Vishnevsky
rights: Copyright (c) 2025 Е. А. Гондюл, В. В. Лисица, Д. М. Вишневский https://creativecommons.org/licenses/by/4.0
date: 2025-11-17
publication date: 2025-11-17
starting page: 465
ending page: 478
doi: 10.26089/NumMet.v26r431

Applying Composable Parallelism in Programs Using Parallel
type: item
description: As the number of computational cores and the threads utilizing them increases, the overhead associated with thread scheduling, creation, and destruction grows, while the amount of computation performed by each individual thread decreases. Multilevel parallelism is a way to address this issue. One potential source of such parallelism is the optimization of functions within libraries called from parallel programs. However, this approach may require additional support at the level of parallel programming models. In our study, we propose an alternative implementation of the OpenMP runtime library and evaluate its efficiency using the OpenBLAS library and the High Performance Linpack (HPL) benchmark on Arm-based systems.
subject: Parallel software tools and technologies
  topic: section
subject: Multiprocessor
  topic: keywords
subject: multilevel parallelism
  topic: keywords
subject: user threads
  topic: keywords
subject: OpenMP
  topic: keywords
subject: TBB
  topic: keywords
subject: OpenBLAS
  topic: keywords
subject: HPL
  topic: keywords
subject: 01.02.EW COMPUTER SCIENS, SOFTWARE ENGINEERING
  topic: subjects
creator: Vladimir A. Bakhtin
creator: Nikita А. Kataev
creator: Alexander S. Kolganov
creator: Dmitriy А. Zakharov
creator: Alexander A. Smirnov
creator: Anton A. Malakhov
rights: Copyright (c) 2025 А. С. Колганов, Н. А. Катаев, В. А. Бахтин, Д. А. Захаров, А. А. Смирнов, А. А. Малахов https://creativecommons.org/licenses/by/4.0
date: 2025-10-30
publication date: 2025-10-30
starting page: 449
ending page: 464
doi: 10.26089/NumMet.v26r430

Numerical method for modeling multiscale dynamics of gas-dispersed media with two relaxation parameters based on Smoothed Particle Hydrodynamics
type: item
description: In some applications, it is advisable to simulate the dynamics of gas-dispersed media using the particle method. In this case, when using the particle-particle approach to calculate the interphase interaction, there is a problem of excess dissipation when solving problems with a small parameter. It is known that the particle-mesh approach solves this problem in the case of one relaxation process (momentum exchange). The work is an experimental study of the possibilities of extending this approach to the case of two relaxation processes (momentum and thermal energy exchange). The test problem is the problem of the motion of a plane sound wave, which has a reference solution for small-amplitude waves. The modes are considered in which the relaxation times are significantly longer, comparable, and significantly shorter than the wave period. It is found that the method under consideration does not introduce dissipation into the solution even with a small number of particles in a cell, but introduces excess counting dispersion in the mode when the relaxation times are comparable to the wave period. To reduce the level of dispersion, it is necessary to increase the number of particles in the cell (up to 5 in the one-dimensional case) and select the time step according to the Courant condition, in which the length scale is the distance from the particle to its nearest neighbor.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: gas-dispersed media
  topic: keywords
subject: smoothed particle hydrodynamics
  topic: keywords
subject: interphase exchange
  topic: keywords
subject: 01.01.PN MATHEMATICS, APPLIED
  topic: subjects
creator: Tatiana A. Savvateeva
rights: Copyright (c) 2025 Т.А. Савватеева https://creativecommons.org/licenses/by/4.0
date: 2025-12-19
publication date: 2025-12-19
starting page: 588
ending page: 600
doi: 10.26089/NumMet.v26r438

Algorithm for applying the structural adaptation criterion to solve problems using adaptive mesh refinement
type: item
description: Adaptive mesh refinement (AMR) is widely used in solving modern mathematical modeling problems. The specifics of the implementation of numerical methods for AMR require compliance with certain ratios between the linear sizes of adjacent elements, which are called the structural criterion. Structural criterion allows creation of buffer layer of cells between regions, which cell division level difference is greater than two. In this paper we discuss the algorithm for buffer layer generation for tree-based adaptive mesh refinement on distributed computational system. Estimates of the algorithmic complexity and efficiency of the algorithm on distributed computational system are obtained. Experiments have shown the possibility of algorithm for forming a buffer layer in areas of complex shape, but at the same time its poor scalability with an increasing number of processes.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: MPI
  topic: keywords
subject: distributed computing
  topic: keywords
subject: AMR
  topic: keywords
subject: buffer layer
  topic: keywords
subject: octree-mesh
  topic: keywords
subject: 01.01.PN Mathematics Applied
  topic: subjects
creator: Sergey K. Grigoriev
creator: Pavel A. Kuchugov
rights: Copyright (c) 2025 С. К. Григорьев, П. А. Кучугов https://creativecommons.org/licenses/by/4.0
date: 2025-10-09
publication date: 2025-10-09
starting page: 410
ending page: 421
doi: 10.26089/NumMet.v26r427

Improved method of recognizing marine and coastal system objects based on combination of local binary pattern method and neural network technologies
type: item
description: The work proposes a hybrid model LBP+PSPNet to increase the accuracy of oil spill segmentation on RGB-images of remote sensing of the Earth, especially in conditions of low contrast between pollution and marine background. The model combines local texture feature extraction (LBP) with global context analysis based on Pyramid Scene Parsing Network (PSPNet). LBP enhances the detail of the texture features of oil film, which are often masked by solar flares or small spots. PSPNet provides large-scale image analysis, which allows for the precise segmentation of both large spills and low-level pollution. Experiments showed that LBP integration increases the IoU metric by 4.6% compared to the basic PSPNet architecture. The proposed model reaches F1-measure 0.85 when tested on low contrast scenarios, demonstrating resistance to noise and atmospheric distortions. The results confirm the effectiveness of synthesis of classical methods of texture analysis and deep learning for environmental monitoring tasks.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: PSPNet
  topic: keywords
subject: LBP
  topic: keywords
subject: oil spill detection
  topic: keywords
subject: image segmentation
  topic: keywords
subject: 01.01.PO MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
  topic: subjects
creator: Alexander I. Sukhinov
creator: Denis A. Solomakha
rights: Copyright (c) 2025 А. И. Сухинов, Д. А. Соломаха https://creativecommons.org/licenses/by/4.0
date: 2025-09-21
publication date: 2025-09-21
starting page: 366
ending page: 379
doi: 10.26089/NumMet.v26r324

Modified axisymmetric contact smoothed particle hydrodynamics method with the possibility of modeling surface tension
type: item
description: The conservation accuracy of total momentum and total energy is important in modeling many physical problems, including capillary phenomena, since non-physical acceleration can lead to incorrect deformation of free surfaces. Because the standard axisymmetric CSPH method of Parshikov does not satisfy the conservation laws, a modified axisymmetric CSPH method is considered to improve the accuracy of preserving the total momentum and the total energy. An external pressure boundary condition is proposed for the CSPH method. This boundary condition is used for surface tension modeling with the new axisymmetric CSPH method. The verification of the surface tension model is performed for three test cases: modeling the establishment of Laplace pressure in a water droplet, modeling small oscillations of a water droplet (comparing the period of small oscillations with Rayleighʼs formula), and modeling the effect of surface tension on a thin film (comparing the velocity of propagation of rims created by surface tension with Taylor-Culickʼs formula). A simulation of the development of Rayleigh-Plateau instability is conducted.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: contact SPH
  topic: keywords
subject: surface tension
  topic: keywords
subject: axisymmetric SPH schemes
  topic: keywords
subject: conservative SPH schemes
  topic: keywords
subject: Riemann solver
  topic: keywords
subject: ghost particles
  topic: keywords
subject: 01.03.UF PHYSICS, FLUIDS & PLASMAS
  topic: subjects
creator: Georgii D. Rublev
rights: Copyright (c) 2025 Г. Д. Рублев https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 422
ending page: 437
doi: 10.26089/NumMet.v26r428

Control of the Gasoline Catalytic Reforming Process Based on a Kinetic Model Using an Artificial Neural Network
type: item
description: This study presents an approach to accelerated modeling of one of the key processes in the oil refining industry — catalytic reforming of gasoline — using a deep neural network. The product of catalytic reforming constitutes the majority of commercial gasoline and determines its octane number. In addition, aromatic hydrocarbons are formed during the process, the content of which can be regulated by adjusting the reaction conditions. The aim of the study was to develop a model capable of replacing resource-intensive direct calculations for evaluating the output parameters of the process, thereby enabling real-time analysis and control. Traditional methods require significant time and computational resources, making them unsuitable for rapid deployment in industrial environments. The training dataset was generated based on the results of direct simulations performed in MATLAB. A significant reduction in data generation time was achieved through the use of parallel computing. Optimal hyperparameters for the neural network were identified. Model training was carried out using the minimization of the mean squared error (MSE) and the coefficient of determination (R²). The developed model demonstrates high prediction accuracy with minimal computational time, which makes it especially suitable for implementation in automated control systems at oil refineries. The resulting neural network approximation effectively acts as a simulator capable of instantaneously estimating key parameters of the catalytic reforming process, including reformate yield, content of aromatic hydrocarbons and benzene, and the octane number of the mixture.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: catalytic reforming of gasoline
  topic: keywords
subject: oil refining
  topic: keywords
subject: machine learning
  topic: keywords
subject: neural networks
  topic: keywords
subject: Python
  topic: keywords
subject: MATLAB
  topic: keywords
subject: predictive modeling
  topic: keywords
subject: data processing
  topic: keywords
subject: deep learning
  topic: keywords
subject: process control
  topic: keywords
subject: 01.02.EP COMPUTER SCIENS, ARTIFICIAL INTELLIGENCE
  topic: subjects
subject: 01.02.EV COMPUTER SCIENS, INTERDISCIPLINARY APPLICATIOONS
  topic: subjects
creator: Kamila F. Koledina
creator: Radmir R. Minigaliev
creator: Sergey N. Koledin
rights: Copyright (c) 2025 К. Ф. Коледина, Р. Р. Минигалиев, С. Н. Коледин https://creativecommons.org/licenses/by/4.0
date: 2025-10-06
publication date: 2025-10-06
starting page: 397
ending page: 409
doi: 10.26089/NumMet.v26r426

A software system for automated assessment of stereoscopic distortions in VR180 videos
type: item
description: The paper presents a comprehensive software system for automatically evaluating stereoscopic distortions in VR180 video. The proposed approach takes into account the most common types of artifacts: color mismatches, differences in sharpness, geometric distortions (vertical shift, rotation, scaling), and channel mismatches. Specialized algorithms have been developed for each type of distortion, based on disparity maps, motion vectors and their confidence maps, as well as neural network regression or classification methods. The proposed solutions have been successfully tested on several datasets, demonstrating high accuracy in detecting various types of distortions in VR180 video. The system can be integrated into standard post-processing pipelines and provides automated generation of detailed reports, allowing stereoscopic content creators to quickly identify and eliminate stereoscopic distortions before releasing their products to a wide audience.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: stereoscopic distortions
  topic: keywords
subject: stereoscopic video
  topic: keywords
subject: VR180
  topic: keywords
subject: color mismatch
  topic: keywords
subject: sharpness mismatch
  topic: keywords
subject: geometric distortions
  topic: keywords
subject: channel mismatch
  topic: keywords
subject: deep learning
  topic: keywords
subject: 01.02.EW COMPUTER SCIENS, SOFTWARE ENGINEERING
  topic: subjects
subject: 01.02.EX COMPUTER SCIENS, THEORY & METHODS
  topic: subjects
creator: Sergey V. Lavrushkin
rights: Copyright (c) 2025 С.В. Лаврушкин https://creativecommons.org/licenses/by/4.0
date: 2025-09-20
publication date: 2025-09-20
starting page: 340
ending page: 365
doi: 10.26089/NumMet.v26r323

Structure-oriented smoothing for wave propagation modelling by beam method with frequency dependence
type: item
description: This paper considers an empirical method for obtaining a frequency-dependent velocity model using structure-oriented smoothing. Smoothing is performed depending on the source position, frequency, and time field. Three smoothing methods are implemented: smoothing along a locally flat wavefront, smoothing by anisotropic diffusion and volumetric smoothing in the Fresnel zone. Anisotropic diffusion smoothing time is compared with the frequency of the smoothing in the Fresnel zone. A comparison of smoothing methods is carried out, showing that volumetric smoothing in the Fresnel zone provides the most stable solution.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: structure–oriented smoothing
  topic: keywords
subject: frequency dependence
  topic: keywords
subject: smoothing
  topic: keywords
subject: Lomax smoothing
  topic: keywords
subject: anisotropic diffusion
  topic: keywords
subject: Fresnel zone
  topic: keywords
subject: Gauss smoothing
  topic: keywords
subject: 01.01.PN MATHEMATICS, APPLIED
  topic: subjects
creator: Aleksandr D. Stein
creator: Maksim I. Protasov
rights: Copyright (c) 2025 А. Д. Штейн, М. И. Протасов https://creativecommons.org/licenses/by/4.0
date: 2025-09-09
publication date: 2025-09-09
starting page: 304
ending page: 321
doi: 10.26089/NumMet.v26r321

A structural two-level neural network approach to joint inversion of gravitational and magnetic fields
type: item
description: The paper proposes a new two-level neural network approach to joint inversion of gravitational and magnetic fields in the problem of mineral exploration. The lower level uses two neural networks with equivalent architecture. The first network calculates the distribution of gravitational field sources in a given domain based on measurements of this field on a certain remote surface. The second one finds the distribution of magnetic field sources in the same area based on magnetic field measurements. At the upper level, a structural residual between the two obtained source distributions is calculated, which determines the “degree of difference” of their geometries. The resulting neural network is trained to minimize this structural discrepancy. As a result, this two-level system implements a computational algorithm that finds geometrically close sources of fields of different nature. Test simulations demonstrate the high quality of joint inversion of model gravitational and magnetic fields within the proposed aproach.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: inverse problem
  topic: keywords
subject: joint processing of gravitational and magnetic fields
  topic: keywords
subject: neural networks
  topic: keywords
subject: structural residual
  topic: keywords
subject: 01.01.PN
  topic: subjects
subject: 01.01.UR
  topic: subjects
creator: Yanfei Wang
creator: Dmitry V. Churbanov
creator: Raul L. Argun
creator: Alexander V. Gorbachev
creator: Alexander S. Leonov
creator: Dmitry V. Lukyanenko
rights: Copyright (c) 2025 Янфей Ван, Д. В. Чурбанов, Р. Л. Аргун, А. В. Горбачев, А. С. Леонов, Д. В. Лукьяненко https://creativecommons.org/licenses/by/4.0
date: 2025-09-15
publication date: 2025-09-15
starting page: 322
ending page: 339
doi: 10.26089/NumMet.v26r322

Constructor of soil carbon dynamic models
type: item
description: This paper introduces a carbon cycle model constructor (CCMC) — a software framework for specifying and solving systems of equations in soil carbon cycle models. The CCMC is based on the structure of a generalized system of ordinary differential equations with a multiplicative representation of mass transfer rates between pools. Most known carbon cycle models found in the literature are special cases of this system. The current implementation allows users to select a model from established formulations (INMCM soil block, SOCS, RothC), provide external environmental state variables, and define a spatial–temporal grid to simulate the evolution of soil carbon content. The CCMC enables subject-matter experts in biology, ecology, soil science, and Earth system dynamics to utilize the implemented mathematical models without requiring specialized knowledge in computational mathematics or programming.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: carbon cycle
  topic: keywords
subject: dynamical system
  topic: keywords
subject: numerical experiments
  topic: keywords
subject: 01.01.PO MATHEMATICS, INTERDISCIPLINARY
  topic: subjects
creator: George M. Faykin
creator: Victor M. Stepanenko
creator: Alexander I. Medvedev
creator: Siumbel K. Shangareeva
creator: Irina M. Ryzhova
creator: Vladimir A. Romanenkov
creator: Ilshat T. Khusniev
rights: Copyright (c) 2025 Г. М. Файкин, В. М. Степаненко, А. И. Медведев, С. К. Шангареева, И. М. Рыжова, В. А. Романенков, И. Т. Хусниев https://creativecommons.org/licenses/by/4.0
date: 2025-08-26
publication date: 2025-08-26
starting page: 281
ending page: 303
doi: 10.26089/NumMet.v26r320

Application of the nudging technique to produce initial states for the INM RAS climate model seasonal hindcasts
type: item
description: This study examines the implementation of nudging in the INM RAS global coupled climate model to improve the initial states for seasonal hindcasts. We compare results of three nudging experiments with both reanalyses data and ensemble of CMIP6 historical experiments. The results show that nudging significantly reduces model biases in atmosphere and ocean fields. The experiment with nudging excluding lower atmospheric levels yields the best performance by minimizing the impact of the relaxation procedures on the model physics in the atmosphere boundary layer. We compare the quality of the hindcasts for November–March obtained with different initialization techniques. The initialization approach using nudging outperforms other initialization methods for hindcasts of the Northern Hemisphere winter season with one-month lead time. However, for the first forecast month the full field initialization demonstrates the best results. The study highlights that nudging in the ocean model is essential to maintain hindcast skill over longer lead times and proposes nudging as a promising approach for initialization of the annual-to-decadal climate predictions.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: INM RAS climate model
  topic: keywords
subject: nudging
  topic: keywords
subject: seasonal hindcasts
  topic: keywords
subject: initialization
  topic: keywords
subject: 01.02.EV Computer Science, Interdisciplinary Applications
  topic: subjects
subject: 01.05.QQ METEOROLOGY & ATMOSPHERIC SCIENCES
  topic: subjects
creator: Maria A. Tarasevich
creator: Evgeny M. Volodin
rights: Copyright (c) 2025 М. А. Тарасевич, Е. М. Володин https://creativecommons.org/licenses/by/4.0
date: 2025-09-22
publication date: 2025-09-22
starting page: 380
ending page: 395
doi: 10.26089/NumMet.v26r325

Systematic numerical search of steady-state solutions for the system of coupled Nonlinear Schrodinger Equations with additional double-well potential
type: item
description: We study stationary solutions of a system of coupled Nonlinear Schrodinger equations with additional double-well potential. In the theory of Bose-Einstein Condensate (BEC) these equations are called the Gross-Pitaevskii equations and the system describes the dynamics of a sigar-shape BEC cloud that consists of atom of two types. Stationary solutions of the system (called also "nonlinear modes") satisfy a system of two non-autonomous ODEs. The problem is stated as follows: it is necessary (i) to find all localized (i.e., that vanish at plus and minus infinity) solutions of this ODE system that coexist for given parameter values and (ii) to justify the completeness of the search conducted. For this purpose, we employed the method of "filtering out" solutions with singularities developed by our team previously. It consists in scanning of some area in the space of initial data for the Cauchy problem for the system. While this procedure, the solutions that have singularities (i.e., that tend to infinity at a finite value of argument) are detected and excluded from consideration. The diagnostics of the singularities and the criterium for the scanning to stop are based on rigorous mathematical statements. As a result, we identify the parameter regions where nonlinear modes of different types exist ("bright-dark solitons", "dark-dark solitons" etc.)
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: The Nonlinear Schrodinger Equation
  topic: keywords
subject: the Gross-Pitaevskii equation
  topic: keywords
subject: stationary nonlinear modes
  topic: keywords
subject: double well potential
  topic: keywords
subject: Proof-of-concept computations
  topic: keywords
subject: two-component solitons
  topic: keywords
subject: 01.01.PN MATHEMATICS, APPLIED
  topic: subjects
creator: Nikita A. Kutsenko
creator: Georgy L. Alfimov
rights: Copyright (c) 2025 Н.А. Куценко, Г.Л. Алфимов https://creativecommons.org/licenses/by/4.0
date: 2025-07-18
publication date: 2025-07-18
starting page: 267
ending page: 280
doi: 10.26089/NumMet.v26r319

Scheme of solution of the heat and mass transfer problem in the hydration model of cement composite
type: item
description: The paper presents a developed model of related physical and chemical processes in reacting medium, according to which a cement composite is considered as a heterogeneous mixture of reagents and filler with specified concentrations and porosity. Water filtration due to capillary and thermocapillary forces ensures convective heat and mass transfer. The heat and mass transfer problem is presented as a two-temperature non-stationary nonlinear boundary value problem of heat conductivity of the frame and liquid phase with heat sources of chemical nature and sinks caused by water evaporation. Verification of the adequacy of the developed scheme for solving the boundary value problem of thermal conductivity is realized by solving a test one-dimensional problem with constant coefficients. The convergence of the problem solution scheme is confirmed in the process of modeling the hydration process of a cement composite at different steps in time and space.
subject: Methods and algorithms of computational mathematics and their applications
  topic: section
subject: computer modeling
  topic: keywords
subject: cement hydration
  topic: keywords
subject: composite material
  topic: keywords
subject: two-temperature heat balance equations
  topic: keywords
subject: heat transfer problem
  topic: keywords
subject: phase transformations
  topic: keywords
subject: filtration
  topic: keywords
subject: 1.02.EV “Computer sciens, interdisciplinary applications”
  topic: subjects
creator: Maria A. Dmitrieva
creator: Vladimir N. Leitsin
creator: Alina D. Kogai
rights: Copyright (c) 2025 М.А. Дмитриева, В.Н. Лейцин, А.Д. Когай https://creativecommons.org/licenses/by/4.0
date: 2025-07-18
publication date: 2025-07-18
starting page: 254
ending page: 266
doi: 10.26089/NumMet.v26r318