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Mixed Nitsche extended finite element method for solving three-dimensional H(curl)-elliptic interface problems 求解三维H（旋度）-椭圆界面问题的混合Nitsche扩展有限元法
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-11 DOI: 10.1016/j.camwa.2025.08.031
Nan Wang , Hanyu Chu , Jinru Chen , Ying Cai
{"title":"Mixed Nitsche extended finite element method for solving three-dimensional H(curl)-elliptic interface problems","authors":"Nan Wang ,&nbsp;Hanyu Chu ,&nbsp;Jinru Chen ,&nbsp;Ying Cai","doi":"10.1016/j.camwa.2025.08.031","DOIUrl":"10.1016/j.camwa.2025.08.031","url":null,"abstract":"<div><div>In this paper, we introduce a Lagrange multiplier to relax the divergence-free constraint and propose a mixed Nitsche extended finite element method for solving three-dimensional H(curl)-elliptic interface problems. To ensure stability, we incorporate ghost penalty terms. By exploiting the commuting relationship of the de Rham complex, we derive an inf-sup stability result for the discrete bilinear form, which is uniform with respect to the mesh size, discontinuous parameters, and the interface position. Based on this, we establish the well-posedness of our method and demonstrate optimal error bounds in the discrete energy norm and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. Finally, numerical experiments are presented to illustrate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 22-44"},"PeriodicalIF":2.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050173","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
AdaPW: An adaptive point-weighting method for training physics-informed neural networks AdaPW：用于训练物理信息神经网络的自适应点加权方法
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-08 DOI: 10.1016/j.camwa.2025.08.026
Wensheng Li , Hao Wang , Hanting Guan , Ruifeng Zhou , Chao Zhang , Dacheng Tao
{"title":"AdaPW: An adaptive point-weighting method for training physics-informed neural networks","authors":"Wensheng Li ,&nbsp;Hao Wang ,&nbsp;Hanting Guan ,&nbsp;Ruifeng Zhou ,&nbsp;Chao Zhang ,&nbsp;Dacheng Tao","doi":"10.1016/j.camwa.2025.08.026","DOIUrl":"10.1016/j.camwa.2025.08.026","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations (PDEs) through deep neural networks. One main challenge in the training of PINNs is how to quickly and effectively learn the collocation points causing big errors. In this paper, we propose an adaptive point-weighting (AdaPW) method to update the distribution of collocation-point weights not only based on their PDE residual errors but also considering the training status of the current network. In this manner, AdaPW is able to balance the attention on all collocation points so as to effectively improve the training performance. Different from the existing relevant point-weighting methods, the AdaPW method does not contain any trainable parameter, and thus has a high applicability. The theoretical analysis and numerical experiments validate the effectiveness and the superiority of the AdaPW method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"198 ","pages":"Pages 255-273"},"PeriodicalIF":2.5,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010360","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
Convergence analysis of a fast ADI compact finite difference method for two-dimensional semi-linear time-fractional reaction-diffusion equations with weak initial singularity 具有弱初始奇异性的二维半线性时间分数阶反应扩散方程的快速ADI紧致有限差分法的收敛性分析
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-05 DOI: 10.1016/j.camwa.2025.08.028
Priyanka, Sunil Kumar
{"title":"Convergence analysis of a fast ADI compact finite difference method for two-dimensional semi-linear time-fractional reaction-diffusion equations with weak initial singularity","authors":"Priyanka,&nbsp;Sunil Kumar","doi":"10.1016/j.camwa.2025.08.028","DOIUrl":"10.1016/j.camwa.2025.08.028","url":null,"abstract":"<div><div>In this work, considering the solution's weak initial singularity, a rigorous error analysis of a finite difference method for simulating a two-dimensional semi-linear time-fractional reaction-diffusion equation (TFRDE) is presented. The recently introduced ADI method by Kumari and Roul (2024) <span><span>[31]</span></span> for solving a class of linear TFRDEs encounters with problematic mesh parameter adjustments and ignorance of the derivative bounds, potentially rendering the latest methodology deficient and erroneous. The present study aims to design a computationally efficient L1 ADI scheme for semi-linear TFRDEs and provide a comprehensive error analysis. To address intrinsically non-local characteristics of the solution, we employ sum-of-exponential approximation to the singular kernel of time-fractional derivative on a graded mesh with unequal time-steps that yield denser mesh near the initial point. As a result, we effectively mitigate the high storage and computational requirements and return the convergence point to its optimal state. The two spatial variables are treated with a fourth order compact finite difference operator. Moreover, an alternating direction implicit method is utilized to compute the solution of the derived two-dimensional system by splitting it into two separate one-dimensional problems. With the aid of local truncation error estimate and discrete fractional Grönwall inequality, the stability and convergence analysis of the scheme are carried out rigorously through the discrete energy approach. The numerical results corroborate the convergence analysis and highlight the computational efficacy of the numerical scheme. Numerical examples demonstrate the CPU performance of the fast compact ADI method, and presented comparisons distinctly showcases the effectiveness of the graded mesh enhancing convergence order to achieve optimal results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 1-21"},"PeriodicalIF":2.5,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997863","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
Natural convection resulting from exponentially varying wall heating in a square enclosure 方形围护结构中由指数变化的壁面加热引起的自然对流
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-04 DOI: 10.1016/j.camwa.2025.08.024
Nagehan Alsoy-Akgün
{"title":"Natural convection resulting from exponentially varying wall heating in a square enclosure","authors":"Nagehan Alsoy-Akgün","doi":"10.1016/j.camwa.2025.08.024","DOIUrl":"10.1016/j.camwa.2025.08.024","url":null,"abstract":"<div><div>The numerical investigation in this study explores the effects of non-uniform wall heating in a square cavity and its influence on natural convection behavior. A non-uniform heat source is applied to the left vertical wall of the cavity, whereas the right vertical wall is uniformly cooled. The remaining horizontal walls are thermally isolated. The main focus is on the heat transfer and fluid mixing caused by the convection occurring within the cavity. The governing equations are tackled with the help of the Dual Reciprocity Boundary Element Method (DRBEM). In the DRBEM procedure, the fundamental solution of the Laplace equation is used for solving the stream function equation, while for the vorticity transport and temperature equations-initially converted into the modified Helmholtz form-the fundamental solution of the modified Helmholtz equation (MHD) is applied. In order to transform the equations into this form, a relaxation parameter is applied to the corresponding term within the Laplace terms, and a forward difference scheme is employed for the time derivatives. In addition to the benefit of solving smaller-sized systems resulting from the boundary discretization in DRBEM, there is no requirement for an additional time integration scheme for the vorticity transport and energy equations, thus removing any potential stability issues. Calculations were performed for Rayleigh numbers of 10<sup>3</sup>, 10<sup>4</sup>, 10<sup>5</sup> and 10<sup>6</sup> and beta parameters <span><math><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span>. Obtained results show that the average Nusselt number was found to increase with increasing Ra and <em>β</em> parameter, indicating enhanced convective heat transfer. Thus, it has been concluded that the heater position is quite effective in heat transfer.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 235-258"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988105","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
Time-dependent inverse source problems for a pseudoparabolic equation with memory 具有记忆的伪抛物方程的时变逆源问题
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-04 DOI: 10.1016/j.camwa.2025.08.029
Kh. Khompysh , M.J. Huntul , M. Mukhambetkaliyev
{"title":"Time-dependent inverse source problems for a pseudoparabolic equation with memory","authors":"Kh. Khompysh ,&nbsp;M.J. Huntul ,&nbsp;M. Mukhambetkaliyev","doi":"10.1016/j.camwa.2025.08.029","DOIUrl":"10.1016/j.camwa.2025.08.029","url":null,"abstract":"<div><div>In this paper, we deal with two inverse source problems for a pseudoparabolic equation with memory term, which in general, have important applications in various fields of science and technology such as non-Newtonian fluids, filtration, population dynamics, plasma physic, et al. However, the presence of certain additional terms in a system usually causes specific complications in mathematical point of view, both in analytical and numerical analysis, although they characterize important physical properties of media. The studied inverse problems consist of recovering a time-dependent source parameter under two types of integral overdetermination conditions. We establish the existence, uniqueness, and stability of strong solutions under suitable conditions on the data and explore numerical solutions by creating numerical algorithms and testing examples.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"198 ","pages":"Pages 239-254"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988429","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
High-order energy-preserving schemes for the Klein-Gordon-Zakharov system Klein-Gordon-Zakharov系统的高阶节能方案
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-04 DOI: 10.1016/j.camwa.2025.08.030
Hongji Guo , Yayun Fu , Xi Xi , Gengen Zhang
{"title":"High-order energy-preserving schemes for the Klein-Gordon-Zakharov system","authors":"Hongji Guo ,&nbsp;Yayun Fu ,&nbsp;Xi Xi ,&nbsp;Gengen Zhang","doi":"10.1016/j.camwa.2025.08.030","DOIUrl":"10.1016/j.camwa.2025.08.030","url":null,"abstract":"<div><div>This work presents a family of highly accurate energy-conserving algorithms for solving the Klein-Gordon-Zakharov equation, developed through the quadratic auxiliary variable (QAV) transformation approach. The proposed methodology employs Fourier pseudospectral discretization for spatial dimensions and symplectic Runge-Kutta methods for temporal integration, ensuring exact energy conservation in the fully-discrete framework. To handle the resulting nonlinear equations, we construct an efficient fixed-point iteration algorithm. Extensive numerical experiments are performed, comparing the proposed method with existing schemes, and the results show excellent consistency with theoretical expectations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 217-234"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988104","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
Singularly perturbed convection-diffusion elliptic problems with a non-smooth forcing term 具有非光滑强迫项的奇摄动对流扩散椭圆问题
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-02 DOI: 10.1016/j.camwa.2025.08.025
José Luis Gracia , Eugene O'Riordan
{"title":"Singularly perturbed convection-diffusion elliptic problems with a non-smooth forcing term","authors":"José Luis Gracia ,&nbsp;Eugene O'Riordan","doi":"10.1016/j.camwa.2025.08.025","DOIUrl":"10.1016/j.camwa.2025.08.025","url":null,"abstract":"<div><div>Singularly perturbed elliptic problems, of convection-diffusion type, with a non-smooth forcing term are examined. The lack of smoothness arises from the forcing term either containing an interior layer or being discontinuous across an interface. In addition to the presence of several different kinds of boundary and corner layers, this forcing term introduces an interior layer in the solution. For both problem classes, a decomposition of the continuous solution is constructed, whose components identify the various types of layer functions that can exist in the solution. Parameter-explicit pointwise bounds on the partial derivatives of these components are then established. An appropriate Shishkin mesh is identified and this is combined with upwinding to form a numerical method for each problem class. Parameter-uniform error bounds in the maximum norm are deduced. Numerical results are presented to illustrate the performance of both numerical methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 458-476"},"PeriodicalIF":2.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925051","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
XFEM for the diffusion and sub-diffusion problems in a non-convex domain 非凸域上扩散和次扩散问题的XFEM
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-01 DOI: 10.1016/j.camwa.2025.08.027
Tao Wang , Yanping Chen , Xiangquan Li , Fangfang Qin
{"title":"XFEM for the diffusion and sub-diffusion problems in a non-convex domain","authors":"Tao Wang ,&nbsp;Yanping Chen ,&nbsp;Xiangquan Li ,&nbsp;Fangfang Qin","doi":"10.1016/j.camwa.2025.08.027","DOIUrl":"10.1016/j.camwa.2025.08.027","url":null,"abstract":"<div><div>This paper proposes a space-time finite element method for solving diffusion and sub-diffusion problems in a non-convex domain. This method employs the discontinuous Galerkin (DG) method for temporal discretization and the eXtended Finite Element Method (XFEM) for spatial discretization, which offers higher accuracy than the standard linear finite element method. Sharp error estimates are derived for diffusion and sub-diffusion problems with smooth and non-smooth initial data in a unified approach. Finally, two numerical examples are provided to verify the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 415-432"},"PeriodicalIF":2.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922066","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
Development and theoretical analysis of the energy stable nonsymmetric time-domain schemes for the 2D transverse electric mode of nonlinear Maxwell's equations 二维非线性麦克斯韦方程组横向电模能量稳定非对称时域格式的建立与理论分析
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-09-01 DOI: 10.1016/j.camwa.2025.08.017
Sishang Xu, Wanshan Li
{"title":"Development and theoretical analysis of the energy stable nonsymmetric time-domain schemes for the 2D transverse electric mode of nonlinear Maxwell's equations","authors":"Sishang Xu,&nbsp;Wanshan Li","doi":"10.1016/j.camwa.2025.08.017","DOIUrl":"10.1016/j.camwa.2025.08.017","url":null,"abstract":"<div><div>In this paper, we focus on the construction and theoretical analysis of the energy-stable nonsymmetric time-domain schemes of the 2D transverse electric mode of Maxwell's equations incorporating the linear Lorentz effect, the third-order nonlinear instantaneous Kerr and delayed Raman effects. The leap-frog scheme for temporal discretization and the nonsymmetric scheme based on the unstaggered grids in space are employed to develop the NSTD schemes, which are of second-order accuracy in time and high-order accuracy in space. Specifically, for the proposed NSTD(2,3) scheme, the energy-stable property and error estimate in the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> norm are demonstrated. Numerical examples verify the energy-stable property, convergence as well as the efficiency of the developed NSTD schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 433-457"},"PeriodicalIF":2.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922067","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
Split-step quintic uniform algebraic trigonometric tension b-spline collocation method for cubic Ginzburg-Landau equations 三次金兹堡-朗道方程的分步五次一致代数三角张力b样条配点法
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-08-28 DOI: 10.1016/j.camwa.2025.08.003
Jinsong Shi , Kaysar Rahman , Jiawen Deng
{"title":"Split-step quintic uniform algebraic trigonometric tension b-spline collocation method for cubic Ginzburg-Landau equations","authors":"Jinsong Shi ,&nbsp;Kaysar Rahman ,&nbsp;Jiawen Deng","doi":"10.1016/j.camwa.2025.08.003","DOIUrl":"10.1016/j.camwa.2025.08.003","url":null,"abstract":"<div><div>This paper proposes a novel numerical framework for solving the one- and multi-dimensional cubic Ginzburg-Landau (CGL) equation by integrating the quintic Uniform Algebraic Trigonometric (UAT) tension B-spline collocation method with the Strang splitting technique. The approach decomposes the original equation into two nonlinear subproblems and one or more linear subproblems via a time-splitting strategy, achieving second-order temporal accuracy. The linear subproblems are resolved using the quintic UAT tension B-spline collocation method to ensure fourth-order spatial accuracy, while the nonlinear subproblems are solved analytically, forming an unconditionally stable scheme. The framework is extendable to other nonlinear PDEs, such as the Schrödinger equation, Kuramoto-Tsuzuki equation, and reaction-diffusion systems, enabling efficient simulations of complex systems in physics, engineering, and materials science. Numerical experiments and comparative analysis validate its accuracy, high convergence orders, and computational efficiency, establishing it as a new high-performance tool for solving such nonlinear PDEs.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 395-414"},"PeriodicalIF":2.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908683","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
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