Computers & Mathematics with Applications最新文献

Two-point stress approximation: A simple and robust finite volume method for linearized (poro-)elasticity and Stokes flow 两点应力近似：线性化（孔隙）弹性和斯托克斯流的一种简单而稳健的有限体积方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-12 DOI: 10.1016/j.camwa.2025.07.035

Jan Martin Nordbotten , Eirik Keilegavlen

引用次数: 0

Data-driven SFB solutions and parameters discovery for nonlinear Schrödinger equation via time domain decomposition physics-informed neural networks 基于时域分解物理信息的神经网络的非线性Schrödinger方程的数据驱动SFB解决方案和参数发现

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-12 DOI: 10.1016/j.camwa.2025.09.007

Jiaxin Chen , Biao Li , Manwai Yuen

{"title":"Data-driven SFB solutions and parameters discovery for nonlinear Schrödinger equation via time domain decomposition physics-informed neural networks","authors":"Jiaxin Chen , Biao Li , Manwai Yuen","doi":"10.1016/j.camwa.2025.09.007","DOIUrl":"10.1016/j.camwa.2025.09.007","url":null,"abstract":"<div><div>In this paper, we integrate domain decomposition techniques into the classical physics-informed neural networks (PINNs) by introducing interface training points, and propose a time domain decomposition PINNs (TDD-PINNs) framework. This model is applied to investigate the dynamic behaviour of solitons on finite background (SFB) solutions and parameter discovery in the nonlinear Schrödinger equation (NLSE). The TDD-PINNs is employed to study various SFB solutions, including the Akhmediev breather, Peregrine soliton, Kuznetsov-Ma soliton, as well as second- and third-order rogue waves. Experimental results demonstrate that, compared to classical PINNs, the proposed TDD-PINNs significantly reduce training time and improve prediction accuracy by one to two orders of magnitude. For inverse problems, the TDD-PINNs algorithm can accurately identify unknown parameters in the NLSE, both under noisy and noise-free conditions, addressing the complete failure of classical PINNs in parameter identification for NLSE and demonstrating strong robustness.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 45-63"},"PeriodicalIF":2.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050174","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

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

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

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

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

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

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

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 , Kaysar Rahman , 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

High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals 有限尺寸二维光子晶体模拟的高阶离散ACMS方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-28 DOI: 10.1016/j.camwa.2025.08.013

Elena Giammatteo , Alexander Heinlein , Philip L. Lederer , Matthias Schlottbom

{"title":"High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals","authors":"Elena Giammatteo , Alexander Heinlein , Philip L. Lederer , Matthias Schlottbom","doi":"10.1016/j.camwa.2025.08.013","DOIUrl":"10.1016/j.camwa.2025.08.013","url":null,"abstract":"<div><div>The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic crystals. The ACMS method is a Galerkin method that relies on a non-overlapping domain decomposition and special basis functions defined based on the domain decomposition. While, in previous works, the ACMS method was realized using first-order finite elements, we use an underlying <em>hp</em>–finite element method. We study the accuracy of the ACMS method for different wavenumbers, domain decompositions, and discretization parameters. Moreover, the computational complexity of the method is investigated theoretically and compared with computing times for an implementation based on the open source software package NGSolve. The numerical results indicate that, for relevant wavenumber regimes, the size of the resulting linear systems for the ACMS method remains moderate, such that sparse direct solvers are a reasonable choice. Moreover, the ACMS method exhibits only a weak dependence on the selected domain decomposition, allowing for greater flexibility in its choice. Additionally, the numerical results show that the error of the ACMS method achieves the predicted convergence rate for increasing wavenumbers. Finally, to display the versatility of the implementation, the results of simulations of large but finite-size photonic crystals with defects are presented.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 376-394"},"PeriodicalIF":2.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908675","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