发布求助
文献互助 智能选刊 最新文献

Computational Mathematics and Mathematical Physics最新文献

筛选
英文 中文
Asymptotics of the Solution of a Bisingular Optimal Distributed Control Problem in a Convex Domain with a Small Parameter Multiplying a Highest Derivative 具有乘以最高衍生物的小参数的凸域中比星形最优分布式控制问题解的渐近性
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700210
A. R. Danilin
{"title":"Asymptotics of the Solution of a Bisingular Optimal Distributed Control Problem in a Convex Domain with a Small Parameter Multiplying a Highest Derivative","authors":"A. R. Danilin","doi":"10.1134/s0965542524700210","DOIUrl":"https://doi.org/10.1134/s0965542524700210","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider an optimal distributed control problem in a strictly convex planar domain with a smooth boundary and a small parameter multiplying a highest derivative of an elliptic operator. A zero Dirichlet condition is set on the boundary of the domain, and control is additively involved in the inhomogeneity. The set of admissible controls is the unit ball in the corresponding space of square integrable functions. The solutions of the obtained boundary value problems are considered in the generalized sense as elements of a Hilbert space. The optimality criterion is the sum of the squared norm of the deviation of the state from a given state and the squared norm of the control with some coefficient. Due to this structure of the optimality criterion, the role of the first or second term of the criterion can be strengthen, if necessary. It is more important to achieve a given state in the first case and to minimize the resource cost in the second case. The asymptotics of the problem generated by the sum of a second-order differential operator with a small coefficient at a highest derivative and a zero-order differential operator is studied in detail.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501881","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
Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion 地震全波形反演的迭代 PDE 约束优化
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700192
M. S. Malovichko, A. Orazbayev, N. I. Khokhlov, I. B. Petrov
{"title":"Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion","authors":"M. S. Malovichko, A. Orazbayev, N. I. Khokhlov, I. B. Petrov","doi":"10.1134/s0965542524700192","DOIUrl":"https://doi.org/10.1134/s0965542524700192","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each Newton step is formulated as a PDE-constrained optimization problem, which is cast in the form of the Karush–Kuhn–Tucker (KKT) system of linear algebraic equitations. The KKT system is solved inexactly with a preconditioned Krylov solver. We introduced two preconditioners: the one based on the block-triangular factorization and its variant with an inexact block solver. The method was benchmarked against the standard truncated Newton FWI scheme on a part of the Marmousi velocity model. The algorithm demonstrated a considerable runtime reduction compared to the standard FWI. Moreover, the presented approach has a great potential for further acceleration. The central result of this paper is that it establishes the feasibility of Newton-type optimization of the KKT system in application to the seismic FWI.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532732","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
Existence of an Optimal Control for a Semilinear Evolution Equation with Unbounded Operator 带无界算子的半线性演化方程的最优控制的存在性
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700362
A. V. Chernov
{"title":"Existence of an Optimal Control for a Semilinear Evolution Equation with Unbounded Operator","authors":"A. V. Chernov","doi":"10.1134/s0965542524700362","DOIUrl":"https://doi.org/10.1134/s0965542524700362","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An optimal control problem is investigated for an abstract semilinear differential equation of the first order in time in a Hilbert space with an unbounded operator and control involved linearly in the right-hand side. The cost functional is assumed to be additively separated with respect to state and control, with a rather general dependence on the state. For this problem, the existence of an optimal control is proved and the properties of the set of optimal controls are established. The author’s previous results on the total preservation of unique global solvability (totally global solvability) and on solution estimation for such equations are developed in the context of the nonlinearity of the equation under study. The indicated estimate is found important for the present study. A nonlinear heat equation and a nonlinear wave equation are considered as examples.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523479","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
A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions 基于香农小波的密闭原子和离子托马斯-费米模型近似方案
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700350
Sharda Kumari, Pratik Majhi, M. M. Panja
{"title":"A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions","authors":"Sharda Kumari, Pratik Majhi, M. M. Panja","doi":"10.1134/s0965542524700350","DOIUrl":"https://doi.org/10.1134/s0965542524700350","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent <span>(n)</span> in the desired order of accuracy (<span>(O{{(10}^{{ - n}}}))</span>) with the resolution <span>(J)</span>, the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501880","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 Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation 论带稳定修正的中央差分方案在三维传输方程中的稳定性
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700271
V. P. Zhukov
{"title":"On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation","authors":"V. P. Zhukov","doi":"10.1134/s0965542524700271","DOIUrl":"https://doi.org/10.1134/s0965542524700271","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523614","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
Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution 稳态片状光滑反应-扩散方程中的多层内层与退化解根的多重性差异
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700179
Qian Yang, Mingkang Ni
{"title":"Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution","authors":"Qian Yang, Mingkang Ni","doi":"10.1134/s0965542524700179","DOIUrl":"https://doi.org/10.1134/s0965542524700179","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A singularly perturbed stationary problem for a one-dimensional reaction-diffusion equation in the case when the degenerate equation has multiple roots is studied. This is a new class of problems with discontinuous reactive terms along some curve that is independent of the small parameter. The existence of a smooth solution with the transition from the triple root of one degenerate equation to the double root of the other degenerate equation in the neighborhood of some point on the discontinuous curve is studied. Based on the existence theorem of classical boundary value problems and the technique of matching asymptotic expansion, the existence of a smooth solution is proved. And the point itself and the asymptotic representation of this solution are constructed by the matching technique and modified boundary layer function method.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523621","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
Numerical-Analytical Decomposition-Autocompensation Method for Signal Recognition from Incorrect Observations 从错误观测数据中识别信号的数值-分析分解-自动补偿方法
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700180
Yu. G. Bulychev
{"title":"Numerical-Analytical Decomposition-Autocompensation Method for Signal Recognition from Incorrect Observations","authors":"Yu. G. Bulychev","doi":"10.1134/s0965542524700180","DOIUrl":"https://doi.org/10.1134/s0965542524700180","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A numerical-analytical method is developed for solving the problem of optimal recognition of a set of possible signals observed in the form of an additive mixture involving not only fluctuation measurement errors (with an unknown statistical distribution law), but also a singular disturbance (with parametric uncertainty). The method not only detects signals in the mixture, but also estimates their parameters as based on a given cost functional and accompanying constraints. Based on the idea of generalized invariant unbiased estimation of linear functionals, the method ensures decomposition of the numerical procedure and autocompensation of the singular disturbance without resorting to conventional state space extension. Parametric finite-dimensional representations of the signals and the disturbance are obtained using linear spectral decompositions in given functional bases. The measurement error is described using only its correlation matrix. The random and systematic errors are analyzed, and an illustrative example is given.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501876","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
Spectral Methods for Solution of Differential and Functional Equations 求解微分方程和函数方程的谱方法
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700222
V. P. Varin
{"title":"Spectral Methods for Solution of Differential and Functional Equations","authors":"V. P. Varin","doi":"10.1134/s0965542524700222","DOIUrl":"https://doi.org/10.1134/s0965542524700222","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An operational approach developed earlier for the spectral method that uses Legendre polynomials is generalized here for arbitrary systems of basis functions (not necessarily orthogonal) that satisfy only two conditions: the result of multiplication by <span>(x)</span> or of differentiation with respect to <span>(x)</span> is expressed in the same functions. All systems of classical orthogonal polynomials satisfy these conditions. In particular, we construct a spectral method that uses Chebyshev polynomials, which is most effective for numerical computations. This method is applied for numerical solution of the linear functional equations that appear in problems of generalized summation of series as well as in the problems of analytical continuation of discrete maps. We also demonstrate how these methods are used for solution of nonstandard and nonlinear boundary value problems for which ordinary algorithms are not applicable.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501877","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
The Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form Revisited 将一对单元矩阵同时还原为对角线形式的再探讨
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s0965542524700234
Kh. D. Ikramov
{"title":"The Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form Revisited","authors":"Kh. D. Ikramov","doi":"10.1134/s0965542524700234","DOIUrl":"https://doi.org/10.1134/s0965542524700234","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This note is an addendum to the paper on the same subject published by the author somewhat earlier. Its aim is to more precisely characterize pairs of unitoids that admit simultaneous reduction to diagonal form.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501878","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
Application of the CABARET and WENO Schemes for Solving the Nonlinear Transport Equation in the Problem of Simulating the Propagation of a Sonic Boom Wave in the Atmosphere 应用 CABARET 和 WENO 方案求解大气中声波传播模拟问题中的非线性传输方程
IF 0.7 4区 数学
Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1134/s096554252470026x
P. A. Mishchenko, T. A. Gimon, V. A. Kolotilov
{"title":"Application of the CABARET and WENO Schemes for Solving the Nonlinear Transport Equation in the Problem of Simulating the Propagation of a Sonic Boom Wave in the Atmosphere","authors":"P. A. Mishchenko, T. A. Gimon, V. A. Kolotilov","doi":"10.1134/s096554252470026x","DOIUrl":"https://doi.org/10.1134/s096554252470026x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The most convenient model describing the propagation of a sonic boom wave in the atmosphere is the augmented Burgers equation. In this work, we studied the influence of a numerical scheme on the result of solving an equation that takes into account the nonlinear nature of the propagation of sonic boom waves in the atmosphere. This equation is a key component of the augmented Burgers equation and determines the nature of the transformation of the disturbed pressure profile during its propagation. Two numerical schemes were used for solving: CABARET and WENO—quasi-monotonic end-to-end computing schemes, which make it possible to obtain a solution without significant numerical oscillations. The applicability of these schemes for solving the problem under consideration is analyzed.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523622","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信