Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 65, № 8 (2025)
General numerical methods
SPECTRAL METHODS AND QUADRATURES
Аннотация
Classical interpolation quadratures and, in particular, Gaussian quadratures are considered in the context of spectral methods, i.e., methods for solving boundary value problems for linear ODE by expanding them into series over orthogonal (and not only) polynomials. Fourier transforms are shown to play a key role here and allow calculating the required quadratures quite easily. Explicit formulas are given for some quadratures, and their efficiency is compared for high-accuracy computation of integrals. A simple Maple procedure for the Clenshaw–Curtis quadrature is given, and its application to computing the integral yielding the function of the sum of divisors of a natural number is considered.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1303–1317
1303–1317
Optimal control
Controllability of a Linear Stationary System Given the Bounded Control Norm
Аннотация
A problem of transferring the trajectory of a linear stationary system from the initial state to the equilibrium state on the given time interval for the incomplete rank of the controllability matrix and the bounded norm of control actions is considered. Using a "natural" basis, the system controllability criterion is established. A way to apply the criterion to construct optimal processes is shown. Related computational aspects and the stability problem for the equilibrium state are discussed.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1318–1327
1318–1327
Partial Differential Equations
On Time-Global Solvability of One Cauchy Problem for a Nonlinear Equation of Composite Type of the Heat-Electric Model
Аннотация
A Cauchy problem for a high-order model nonlinear evolutionary equation is considered. Sufficient conditions of existence and uniqueness of the weak time-global solution to the Cauchy problem are obtained. An estimate of decreasing of the solution with respect to coordinates and time is obtained.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1328-1350
1328-1350
1351-1372
Mathematical physics
RANS Simulation of Supersonic Flow of a Cylinder Fixed Between Parallel Plates
Аннотация
The results of RANS computations of a supersonic flow of a cylinder fixed between parallel plates are given. The Mach number of the incoming flow is M = 1.85. Methodological data on the effect of the grid resolution and turbulence model on the predicted structure of viscous-non-viscous interaction are obtained. Parametric calculations were performed for several values of the relative distance between plates. Three-dimensional effects arising from the interaction of boundary layers with the leading edge of the cylinder are studied. The flow structure is shown to change qualitatively when the distance between the plates decreases — an additional “hanging” compression shock is formed, the length and height of the separated-flow region increases, and the area of high heat flows expands.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1373–1386
1373–1386
On Preserving Spherical Symmetry on a Spherical Grid in the Cartesian Coordinate System When Calculating Gas-Dynamic Currents by Euler Finite-Volume Schemes
Аннотация
The sufficient conditions for finite-volume Euler schemes for calculating gas-dynamic currents in the Cartesian coordinate system using the Gaussian method for the divergence and gradient operators and the midpoint method for approximating integrals over cell faces to preserve spherical symmetry on a spherical grid are determined. Two approaches to ensuring the geometric condition on the ratio of the areas of the corner faces to the volume of the cell are proposed, viz. correction of areas and special selection of partitioning with respect to the polar angle. As an example of preserving the symmetry when the sufficient conditions are met, the calculation of the spherical problem of discontinuity breakdown by the Euler scheme of the Godunov type is considered.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1387–1396
1387–1396
Simultaneous Identification of the Thermal Conductivity and Volumetric Heat Capacity of a Substance in the Three-Dimensional Case
Аннотация
The study of nonlinear problems related to the process of heat transfer in matter is of great practical importance. One of the problems arising in the study of the characteristics of new materials is the problem of simultaneous identification of the temperature-dependent thermal conductivity and volumetric heat capacity of a substance based on the results of experimental observations of the dynamics of the temperature field in an object. Previously, this problem was considered only in the one-dimensional case. Since experimental data are collected from three-dimensional objects, it is important that these studies be carried out for the three-dimensional case as well. In this paper, this problem is considered in the three-dimensional case. The consideration is carried out on the basis of the first boundary value problem for the three-dimensional non-stationary heat equation. The inverse problem of coefficient identification is reduced to a variational problem. The root-mean-square deviation of the calculated temperature field in the sample from its experimental value is chosen as the cost functional. Formulas for calculating the gradient of the cost functional are obtained. The results of the numerical solution of the formulated inverse problem are presented and discussed.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1397-1407
1397-1407
Solution to contact problem between an elastic body and a rigid base covered with a layer of deformable material
Аннотация
A contact problem for an elastic body with a base covered with a deformable layer is studied. The layer is rigid-elastic, i.e., it begins to deform when the yield strength is reached and exerts the normal pressure on the body, which depends on the penetration of the body into the layer. For the rigid base, the Signorini condition is used. The existence of a solution to the problem is proved using weak Schauder’s fixed-point theorem. The results of numerical simulation using the finite element method are presented.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1408–1422
1408–1422
Non-viscous instability of a boundary layer over the compliant surface at supersonic speeds of the incoming flow
Аннотация
Within the framework of the asymptotic theory of free interaction, the instability of the boundary layer over the compliant plate at supersonic speeds of the incoming flow with respect to non-viscous disturbances is studied. Unstable non-viscous disturbances are shown to exist only when the inertance of the plate is taken into account, and the damping of the plate plays a significant stabilizing role. Increasing the elasticity, bending stiffness, and longitudinal tension of the plate also stabilizes the flow.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1423–1435
1423–1435
Laws of Symmetry of Dynamic Processes in Media with Films
Аннотация
A sufficiently wide class of boundary value problems simulating dynamic processes of heat and mass transfer is considered in media with strongly or poorly permeable films. Formulas expressing the solutions to these problems with films via the solutions to the same problems without films are derived. Based on the general formulas, the following laws are obtained—if a strongly permeable film is introduced into the processes without films, the potentials at any two points symmetrical with respect to the film will change by the same value. Similarly, if a poorly permeable film is introduced into the processes without films, the potentials at the points symmetrical with respect to the film will change by the value of the same modulus and opposite sign. Expressions for potential increments caused by the presence of films are found. For the Poisson equation, similar laws are obtained with films in the form of a circle.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1436–1442
1436–1442
Computer science
On the Complexity of Realizating Logical Supervised Classification Procedures
Аннотация
The issues of the complexity of the correct training of supervised classification procedures that based on the use of logical data analysis methods are investigated. The metric (quantitative) properties of informative fragments of feature descriptions of precedents are studied in the case when the number of features is significantly greater than the number of precedents. The asymptotics of a typical number of fragments frequently found in descriptions of precedents that distinguish objects from different classes and are called regular representative elementary classifiers are given. The typical length of the desired fragment is specified. The technical foundations of the estimates presented are based on a methodology for obtaining similar estimates for the intractable discrete problem of enumerating irredanded coverings of an integer matrix, formulated in this paper as the problem of searching for minimal infrequent elementary classifiers. New results on the complexity of the implementation of logical classifiers allow us to theoretically substantiate the effectiveness of the training procedure based on the search for the regular representative elementary classifiers and confirm the prospects of the approach in terms of time costs.
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1443–1450
1443–1450
ACOUSTIC WAVEFORM INVERSION WITH IMAGE-TO-IMAGE SCHRODINGER BRIDGES
Аннотация
Recent developments in application of deep learning models to acoustic Full Waveform Inversion (FWI) are marked by the use of diffusion models as prior distributions for Bayesian-like inference procedures. The advantage of these methods is the ability to generate high-resolution samples, which are otherwise unattainable with classical inversion methods or other deep learning-based solutions. However, the iterative and stochastic nature of sampling from diffusion models along with heuristic nature of output control remain limiting factors for their applicability For instance, an optimal way to include the approximate velocity model into diffusion-based inversion scheme remains unclear, even though it is considered an essential part of FWI pipeline. We address the issue by employing a Schrodinger Bridge that interpolates ¨ between the distributions of ground truth and smoothed velocity models. Thus, the inference process that starts from an approximate velocity model is guaranteed to arrive at a sample from the distribution of reference velocity models in a finite time. To facilitate the learning of nonlinear drifts that transfer samples between distributions and to enable controlled inference given the seismic data, we extend the concept of Image-to-Image Schrodinger Bridge (I ¨ 2SB) to conditional sampling, resulting in a conditional Image-to-Image Schrodinger Bridge (cI ¨ 2SB) framework for acoustic inversion. To validate our method, we assess its effectiveness in reconstructing the reference velocity model from its smoothed approximation, coupled with the observed seismic signal of fixed shape. Our experiments demonstrate that the proposed solution outperforms our reimplementation of conditional diffusion model suggested in earlier works, while requiring only a few neural function evaluations (NFEs) to achieve sample fidelity superior to that attained with supervised learning-based approach. The supplementary code implementing the algorithms described in this paper can be found in the repository https://github.com/stankevich-mipt/seismic_inversion_via_
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki. 2025;65(8):1451–1466
1451–1466