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Russian Journal of Numerical Analysis and Mathematical Modelling最新文献

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Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach 北冰洋热含量变率低频模态的可预测性:一种完美的模式方法
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0008
A. Gritsun
{"title":"Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach","authors":"A. Gritsun","doi":"10.1515/rnam-2022-0008","DOIUrl":"https://doi.org/10.1515/rnam-2022-0008","url":null,"abstract":"Abstract The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability of the Arctic Ocean circulation. The initial estimate of its predictability is made by using the method of analogues and calculating the resonances of the invariant measure. Then this estimate is verified by direct ensemble calculations with the model. The results obtained indicate that the maximum predictability time interval reaches ten years for 15-year average values of heat content and corresponds to the states with maximum positive anomalies along the leading low-frequency variability modes.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"99 - 109"},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46346036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal stochastic forcings for sensitivity analysis of linear dynamical systems 线性动力系统灵敏度分析的最优随机强迫
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0009
Y. Nechepurenko, G. Zasko
{"title":"Optimal stochastic forcings for sensitivity analysis of linear dynamical systems","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0009","DOIUrl":"https://doi.org/10.1515/rnam-2022-0009","url":null,"abstract":"Abstract The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"111 - 118"},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field 保留地磁场方向的电离层模型中扩散算子的近似
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0003
P. A. Ostanin
{"title":"On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field","authors":"P. A. Ostanin","doi":"10.1515/rnam-2022-0003","DOIUrl":"https://doi.org/10.1515/rnam-2022-0003","url":null,"abstract":"Abstract New methods for constructing an approximation of the diffusion operator for the two-dimensional equation of the ambipolar diffusion process in the F layer of the Earth's ionosphere are presented. This equation is solved in the framework of modelling the global thermosphere and ionosphere dynamics (for the altitudes from 90 to 500 km). The proposed schemes have finite-difference versions of the integral identity, which is a property of differential diffusion equation and which represents the geometric properties of the process (diffusion proceeds along the magnetic field lines of the Earth). The stability of the proposed schemes is analyzed, as well as the accuracy estimates are obtained on the base of the model analytical solution and during the calculations with physically realistic data. A comparison is made with the second-order finite-difference scheme developed earlier for solving the same problem.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"25 - 39"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48801876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method 传递矩阵与气溶胶团簇随机动力学问题的蒙特卡罗解法
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0001
A. Cheremisin
{"title":"Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method","authors":"A. Cheremisin","doi":"10.1515/rnam-2022-0001","DOIUrl":"https://doi.org/10.1515/rnam-2022-0001","url":null,"abstract":"Abstract A Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"1 - 14"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44597766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Constant upper bounds on the matrix exponential norm 矩阵指数范数的常数上界
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0002
Y. Nechepurenko, G. Zasko
{"title":"Constant upper bounds on the matrix exponential norm","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0002","DOIUrl":"https://doi.org/10.1515/rnam-2022-0002","url":null,"abstract":"Abstract This work is devoted to the constant (time-independent) upper bounds on the function ∥ exp(tA)∥2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper bound is proposed that has significant advantages. A detailed comparison of all these constant upper bounds is carried out using 2 × 2 matrices and matrices of medium size from the well-known NEP collection.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"15 - 23"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47556151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2022-frontmatter1","DOIUrl":"https://doi.org/10.1515/rnam-2022-frontmatter1","url":null,"abstract":"Article Frontmatter was published on February 1, 2022 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 37, issue 1).","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"28 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems 变分同化问题中响应函数对系统输入灵敏度的数值计算
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0004
V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong
{"title":"On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems","authors":"V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong","doi":"10.1515/rnam-2022-0004","DOIUrl":"https://doi.org/10.1515/rnam-2022-0004","url":null,"abstract":"Abstract Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs. The theoretical results related to the procedure based adjoint approach for computing a sensitivity of the response function (RF) to changes in the input source are presented in the paper. It is shown that this approach allows to compute, by one single integration of the adjoint equation over a given time interval, a sensitivity of the RF to any source located in the domain of interest. The proposed approach is applied to the 2D Saint-Venant flow equations for modelling the water pollution problem. A numerical experiment is formulated and implemented for the Thanh Nhan Lake in Hanoi for studying a sensitivity of some RF to observations. The numerical model is constructed by applying the well-known finite-volume method. Two appropriate optimization problems are introduced and solved on the basis of the BFGS algorithm. The numerical results show the efficiency of the proposed method and confirm the theoretical findings.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"41 - 61"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48246963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Sketching for a low-rank nonnegative matrix approximation: Numerical study 低秩非负矩阵近似的速写:数值研究
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-01-26 DOI: 10.1515/rnam-2023-0009
S. Matveev, S. Budzinskiy
{"title":"Sketching for a low-rank nonnegative matrix approximation: Numerical study","authors":"S. Matveev, S. Budzinskiy","doi":"10.1515/rnam-2023-0009","DOIUrl":"https://doi.org/10.1515/rnam-2023-0009","url":null,"abstract":"Abstract We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"99 - 114"},"PeriodicalIF":0.6,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42931067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
General finite-volume framework for saddle-point problems of various physics 各种物理鞍点问题的一般有限体积框架
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0029
K. Terekhov
{"title":"General finite-volume framework for saddle-point problems of various physics","authors":"K. Terekhov","doi":"10.1515/rnam-2021-0029","DOIUrl":"https://doi.org/10.1515/rnam-2021-0029","url":null,"abstract":"Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"359 - 379"},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-frontmatter6
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2021-frontmatter6","DOIUrl":"https://doi.org/10.1515/rnam-2021-frontmatter6","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43713542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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