Journal of Computational and Applied Mathematics最新文献_第5页

A fast sequentially-decoupled matrix-decomposed algorithm for variable-order time-fractional optimal control and error estimate 变阶时间分数阶最优控制与误差估计的快速顺序解耦矩阵分解算法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.cam.2025.116667

Jinhong Jia , Hong Wang , Zhaojie Zhou , Xiangcheng Zheng

{"title":"A fast sequentially-decoupled matrix-decomposed algorithm for variable-order time-fractional optimal control and error estimate","authors":"Jinhong Jia , Hong Wang , Zhaojie Zhou , Xiangcheng Zheng","doi":"10.1016/j.cam.2025.116667","DOIUrl":"10.1016/j.cam.2025.116667","url":null,"abstract":"<div><div>We introduce a fast sequentially decoupled matrix-decomposed approach tailored for optimal control problems constrained by a Caputo time-fractional diffusion equation featuring hidden memory and space-dependent order. Our method unveils a quasi translation-invariant structure adept at managing spatio-temporal dependencies. This structure not only slashes the computational burden of coefficients from <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>M</mi><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>M</mi><mi>N</mi><mo>ln</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>M</mi></math></span> and <span><math><mi>N</mi></math></span> denote the spatial degrees of freedom and temporal steps in discretization, respectively, but also untangles the coupling between the space-dependent order and the inner product of the finite element method. Furthermore, we derive a swift matrix-decomposed algorithm designed to tackle the first-order optimality system, yielding a marked improvement in computational cost from <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>M</mi><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>M</mi><mi>N</mi><msup><mrow><mo>ln</mo></mrow><mrow><mn>3</mn></mrow></msup><mi>N</mi><mo>)</mo></mrow></mrow></math></span> in each iteration. We substantiate our approach through rigorous numerical analysis and present numerical experiments to validate the theoretical underpinnings.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116667"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 discontinuous Galerkin method for a coupled Brinkman–Biot problem 耦合Brinkman-Biot问题的不连续Galerkin方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.cam.2025.116659

Jialiang Bian , Rui Li , Zhangxin Chen

{"title":"A discontinuous Galerkin method for a coupled Brinkman–Biot problem","authors":"Jialiang Bian , Rui Li , Zhangxin Chen","doi":"10.1016/j.cam.2025.116659","DOIUrl":"10.1016/j.cam.2025.116659","url":null,"abstract":"<div><div>In this paper, the Brinkman–Biot model is used to simulate the coupling problem of the Brinkman flow and deformable poroelastic media flow, which need to interact through the interface. By introducing the total pressure to rewrite the poroelastic equations, the possible locking phenomenon of the Biot system is overcome. By taking into account complex permeability coefficient, the strong stiffness caused by the Biot system is solved. A discontinuous Galerkin finite element method is used to solve the problem of complex poroelastic media caused by coupling. Firstly, the space is discretised by the discontinuous Galerkin finite element method, and the time is discretised by the backward Euler method. Then the semi-discretisation scheme and the full discretisation scheme are given. Secondly, in the framework of the Galerkin approximation, the existence and uniqueness of solutions and error estimates of semi-discrete and fully discrete schemes are analysed by means of differential algebraic equation theory and weak compactness demonstration. Finally, through numerical experiments, the theoretical convergence rate of the numerical solution of the model and whether the interface conditions coincide are verified. The channel filtration and the actual hydraulic fracturing fluid flow situation are simulated, and the effectiveness and accuracy of the method are verified.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116659"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Error estimate of high order Runge–Kutta local discontinuous Galerkin method for nonlinear convection-dominated Sobolev equation 非线性对流主导Sobolev方程的高阶龙格-库塔局部不连续Galerkin方法误差估计

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-31 DOI: 10.1016/j.cam.2025.116657

Caiyue Du , Di Zhao , Qiang Zhang

引用次数: 0

Stability and uniqueness of coupled nonlinear finite element solution for anisotropic diffusion equation with nonlinear capacity term 具有非线性容量项的各向异性扩散方程耦合非线性有限元解的稳定性和唯一性

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-31 DOI: 10.1016/j.cam.2025.116664

Jun Fang, Zhijun Shen, Xia Cui

{"title":"Stability and uniqueness of coupled nonlinear finite element solution for anisotropic diffusion equation with nonlinear capacity term","authors":"Jun Fang, Zhijun Shen, Xia Cui","doi":"10.1016/j.cam.2025.116664","DOIUrl":"10.1016/j.cam.2025.116664","url":null,"abstract":"<div><div>This paper presents the stability of a two-layer coupled discretization fully implicit finite element scheme as well as the uniqueness of its solution. The scheme has been proposed for solving multi-dimensional anisotropic diffusion equations with nonlinear capacity term, and the existence and convergence of its solution have been proved in [Fang et al., J. Comput. Appl. Math. 438 (2024) 115512]. However, the basic theoretical analysis is incomplete, for example, the stability and uniqueness have not been solved yet, which are very important for the application of numerical methods in engineering. In this paper, we further develop the discrete functional analysis techniques to establish a framework with relatively comprehensive theoretical results. Wherein by introducing Ritz projection, rewriting the error equations into equivalent forms, and choosing appropriate test functions, we propose a new inductive argument to overcome the difficulties arising from the coupled nonlinear discretization of the diffusion operator and capacity term. Consequently, on the basis of the existence and convergence properties, we prove for the first time that the nonlinear finite element method is stable, thereby its solution is unique. Numerical examples show that the scheme is stable and has no numerical oscillations compared with the classical Crank–Nicolson scheme.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116664"},"PeriodicalIF":2.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Finite element method analysis of flutter: Comparing Scott–Vogelius and Taylor–Hood elements 颤振有限元分析：Scott-Vogelius单元与Taylor-Hood单元的比较

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-31 DOI: 10.1016/j.cam.2025.116662

Karel Vacek , Petr Sváček

{"title":"Finite element method analysis of flutter: Comparing Scott–Vogelius and Taylor–Hood elements","authors":"Karel Vacek , Petr Sváček","doi":"10.1016/j.cam.2025.116662","DOIUrl":"10.1016/j.cam.2025.116662","url":null,"abstract":"<div><div>This paper focuses on the numerical simulation of the fluid–structure interaction (FSI) problem of an incompressible flow and a vibrating airfoil. The fluid flow is governed by the incompressible Navier–Stokes equations. The finite element method (FEM) is employed for the discretization of the weak form of equations. The main attention is paid to comparison of performance for different choices of finite element spaces together with a proper stabilization method. Two choices of the couple of finite element spaces are considered for velocity–pressure approximations. The first one is the standard Taylor–Hood finite element, the second one is the Scott–Vogelius element consisting of continuous piecewise quadratic velocities combined with discontinuous piecewise linear pressures. The barycentric refined mesh is used for the case of the Scott–Vogelius element in order to satisfy the Babuška–Brezzi inf-sup condition. The finite element approximations further require additional stabilization of the dominating convection. Here, the performance of the stream-line upwind Petrov–Galerkin (SUPG) stabilization, the SUPG together with the grad-div stabilization, the streamline-diffusion/local-projection stabilization approach is tested. The numerical results are presented and compared with the available data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116662"},"PeriodicalIF":2.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 error estimations and superconvergence analysis of anisotropic FEMs with variable time steps for reaction–diffusion equations 反应扩散方程各向异性变时步长fem的最优误差估计及超收敛分析

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-31 DOI: 10.1016/j.cam.2025.116656

Lifang Pei , Chao Xu , Jiwei Zhang , Yanmin Zhao

{"title":"Optimal error estimations and superconvergence analysis of anisotropic FEMs with variable time steps for reaction–diffusion equations","authors":"Lifang Pei , Chao Xu , Jiwei Zhang , Yanmin Zhao","doi":"10.1016/j.cam.2025.116656","DOIUrl":"10.1016/j.cam.2025.116656","url":null,"abstract":"<div><div>By combining variable-time-step two-step backward differentiation formula (VSBDF2) with anisotropic finite element methods (FEMs), a fully discrete scheme with non-uniform meshes both in time and space is constructed for the reaction–diffusion equations. Two approaches are provided to prove the optimal error estimates in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and global superconvergence result in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm under a mild adjacent time-step ratio restriction <span><math><mrow><mn>0</mn><mo><</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo><</mo><msub><mrow><mi>r</mi></mrow><mrow><mo>max</mo></mrow></msub><mo>≈</mo><mn>4</mn><mo>.</mo><mn>8645</mn></mrow></math></span>. The first approach is based on the use of anisotropic properties of the interpolation operators, but needs a higher regularity of the solution and is only valid for some special elements. The second approach is based on the combination technique of interpolation and energy projection operators, and needs a lower regularity of the solution, which can be regarded as a unified framework of convergence analysis. Numerical experiments are provided to demonstrate our theoretical analysis.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116656"},"PeriodicalIF":2.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Efficient and dissipation-preserving Hermite spectral Galerkin methods for diffusive-viscous wave equations in unbounded domains 无界区域中扩散-粘性波动方程的有效且保持耗散的Hermite谱伽辽金方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-30 DOI: 10.1016/j.cam.2025.116652

Dan Ling , Zhiping Mao

{"title":"Efficient and dissipation-preserving Hermite spectral Galerkin methods for diffusive-viscous wave equations in unbounded domains","authors":"Dan Ling , Zhiping Mao","doi":"10.1016/j.cam.2025.116652","DOIUrl":"10.1016/j.cam.2025.116652","url":null,"abstract":"<div><div>The diffusive-viscous wave equation (DVWE) resulting from the diffusive-viscous wave theory is usually used to describe frequency-dependent seismic reflections in fluid-saturated media, leading to a wider application in seismic exploration. In a previous work (Ling and Mao, 2023), we considered the DVWE in unbounded domain to avoid artificial reflections and truncation errors, and then established its well-posedness and regularity as well as developed a Hermite spectral Galerkin approximation for the space discretization. However, for the time discretization, an explicit Runge–Kutta scheme is employed resulting an extremely restricted time step due to the stability. In the present work, to resolve this issue, we develop two second-order implicit (Crank–Nicolson and BDF2) Hermite spectral methods and show that the proposed schemes are unconditionally energy stable and further establish the convergence. Furthermore, for the two-dimensional case, we develop an efficient algorithm with <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> (where <span><math><mi>N</mi></math></span> is the degree of freedom of each direction and <span><math><mi>d</mi></math></span> is the space dimension) computational cost. In particular, we use the matrix diagonalization technique for the cases of constant coefficients while we employ the preconditioned conjugate gradient method for the cases of variable coefficients. Finally we provide several numerical examples to verify our theoretical results and to demonstrate the effectiveness and efficiency along with other good behavior of the proposed schemes.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116652"},"PeriodicalIF":2.1,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Key distributions in the preservation of aging classes under the construction of systems 系统构造下老化类保存的关键分布

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-30 DOI: 10.1016/j.cam.2025.116650

Jorge Navarro , Tomasz Rychlik , Magdalena Szymkowiak

引用次数: 0

Adaptive regularisation for PDE-constrained optimal control pde约束最优控制的自适应正则化

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.cam.2025.116651

Jenny Power , Tristan Pryer

引用次数: 0

Recovery conditions for generalized orthogonal matching pursuit based coherence 基于广义正交匹配追踪的相干恢复条件

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-03-27 DOI: 10.1016/j.cam.2025.116648

Hanbing Liu , Chongjun Li , Yijun Zhong

{"title":"Recovery conditions for generalized orthogonal matching pursuit based coherence","authors":"Hanbing Liu , Chongjun Li , Yijun Zhong","doi":"10.1016/j.cam.2025.116648","DOIUrl":"10.1016/j.cam.2025.116648","url":null,"abstract":"<div><div>In sparse approximation, a key theoretical issue is the guarantee conditions for the exact recovery of <span><math><mi>s</mi></math></span>-sparse signals. The Orthogonal Matching Pursuit (OMP) and the Generalized Orthogonal Matching Pursuit (GOMP) are two important algorithms commonly used in sparse approximation. The main difference is that the OMP algorithm selects one atom in each iteration, while the GOMP algorithm selects multiple atoms. In the current theoretical analysis, the GOMP algorithm can only guarantee the selection of at least one correct atom in each iteration. However, in practical applications, the GOMP algorithm has been shown to select multiple correct atoms in each iteration but lacks theoretical guarantee conditions. In this paper, we discuss the extended coherence-based conditions for exact support recovery of the <span><math><mi>s</mi></math></span>-sparse signals using the GOMP algorithm. We propose several sufficient conditions for the GOMP algorithm to select <span><math><mi>M</mi></math></span> (<span><math><mrow><mn>1</mn><mo>≤</mo><mi>M</mi><mo>≤</mo><mi>s</mi></mrow></math></span>) correct atoms in each iteration in noiseless and bounded-noise cases respectively. Some of the conditions involve the decay of nonzero entries in sparse signals. Numerical experiments demonstrate the effectiveness of the proposed sufficient conditions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116648"},"PeriodicalIF":2.1,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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