Computers & Mathematics with Applications最新文献_第2页

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

Kernel-based collocation methods with TBC for the elastic wave scattering by obstacles 障碍物弹性波散射的TBC核配点法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-28 DOI: 10.1016/j.camwa.2025.08.021

Wenwen Xu , Siqing Li , Junhong Yue , Qi Ye

{"title":"Kernel-based collocation methods with TBC for the elastic wave scattering by obstacles","authors":"Wenwen Xu , Siqing Li , Junhong Yue , Qi Ye","doi":"10.1016/j.camwa.2025.08.021","DOIUrl":"10.1016/j.camwa.2025.08.021","url":null,"abstract":"<div><div>Elastic wave scattering plays a crucial role in medical imaging, seismic exploration, and non-destructive testing. In this paper, the kernel-based collocation methods are constructed for elastic wave scattering problems by multiple obstacles. Using Helmholtz decomposition, the original Navier equations for elastic waves in unbounded domain are reformulated into a Helmholtz equation system with two potential functions, coupled on the obstacle boundaries. To handle the unbounded domain, the transparent boundary conditions (TBC) are built based on the Dirichlet-to-Neumann (DtN) operator. The proposed method employs a kernel-based collocation method that combines radial basis functions (RBFs) with a weighted least-squares (WLS) method. The WLS formulations are proposed by setting more collocation points than trial centers and adding weights with respect to fill distance of collocation sets at obstacle and TBC boundary collocation terms. Using Whittle-Matérn-Sobolev kernels with kernel smoothness <em>m</em>, numerical experiments demonstrate that the proposed method can obtain solutions with the expected <span><math><mi>m</mi><mo>−</mo><mn>2</mn></math></span> convergence rate for elastic scattering involving both single and multiple irregular obstacles. Furthermore, compared with the Kansa method and other mesh-dependent methods, the proposed method offers higher accuracy and more stable solutions for relatively large angular frequencies.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 200-216"},"PeriodicalIF":2.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907396","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

Numerical solutions of multidimensional nonlinear hyperbolic partial integro-differential equations using a redefined cubic B-spline-based differential quadrature method 多维非线性双曲型偏积分微分方程的重定义三次b样条微分求积分法数值解

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-28 DOI: 10.1016/j.camwa.2025.08.018

Raziyeh Mirzahashemi, Mohammad Heydari

{"title":"Numerical solutions of multidimensional nonlinear hyperbolic partial integro-differential equations using a redefined cubic B-spline-based differential quadrature method","authors":"Raziyeh Mirzahashemi, Mohammad Heydari","doi":"10.1016/j.camwa.2025.08.018","DOIUrl":"10.1016/j.camwa.2025.08.018","url":null,"abstract":"<div><div>The primary objective of this work is to present an efficient numerical method for solving multidimensional nonlinear hyperbolic partial integro-differential equations (HPIDEs). To implement this method, the following steps are sequentially followed. First, by integrating both sides of the HPIDE, we transform it into a new form of a partial integro-differential equation with a time derivative of first order. This new formulation allows the proposed method to ultimately reduce the problem of finding an approximate solution to a system of linear algebraic equations without employing linearization techniques. Next, for the discretization of the newly obtained form in temporal direction, a combination of the Crank–Nicolson finite difference technique and numerical integration methods, including the trapezoidal and rectangle integration rules, is utilized. This process results in a finite difference scheme with second-order convergence, and its stability and convergence are thoroughly examined using energy method. The Richardson extrapolation technique is also utilized to improve the convergence order in the temporal dimension. Furthermore, a differential quadrature method (DQM) based on a redefined structure of cubic B-splines is employed for the spatial discretization of the problem. Finally, some numerical examples in various dimensions are provided to evaluate the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"198 ","pages":"Pages 214-238"},"PeriodicalIF":2.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908391","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

Fast method and theoretical study of magnetohydrodynamic flow and heat transfer for fractional Maxwell fluids 分数阶麦克斯韦流体磁流体动力学流动与传热的快速方法与理论研究

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-26 DOI: 10.1016/j.camwa.2025.08.022

Yi Liu

{"title":"Fast method and theoretical study of magnetohydrodynamic flow and heat transfer for fractional Maxwell fluids","authors":"Yi Liu","doi":"10.1016/j.camwa.2025.08.022","DOIUrl":"10.1016/j.camwa.2025.08.022","url":null,"abstract":"<div><div>This study investigates the magnetohydrodynamic flow and heat transfer in inclined pipes filled with fractional Maxwell fluids. The proposed model incorporates the momentum equation derived from the fractional constitutive relation and the fractional heat equation based on Fourier's law. Temporal and spatial discretization are implemented using the second-order fractional backward difference method and the finite element method, respectively. The stability of the fully discrete scheme is analyzed, ensuring numerical accuracy of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>)</mo></math></span>, where <em>τ</em> is time step size, <em>h</em> is space step size and <em>r</em> is the order of accuracy of the spatial discretization. To enhance computational efficiency, a fast numerical method is introduced. A numerical example validates the effectiveness of the proposed approach and supports the theoretical framework. Additionally, simulations are conducted to examine the effects of pipe inclination and thermal radiation on velocity and temperature distributions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 355-375"},"PeriodicalIF":2.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902334","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

Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions 具有Neumann边界条件的波动方程的自适应时域边界元方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-26 DOI: 10.1016/j.camwa.2025.08.020

A. Aimi , G. Di Credico , H. Gimperlein , C. Guardasoni

引用次数: 0

Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions 三维椭圆型问题虚元法的最优最大范数估计

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-26 DOI: 10.1016/j.camwa.2025.08.011

Wenming He , Ren Zhao

引用次数: 0

A time-domain finite element method for Kerr and Raman type nonlinear hyperbolic metamaterials with application for enhanced third-harmonic generation Kerr和Raman型非线性双曲型超材料的时域有限元法及其在增强三次谐波产生中的应用

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-26 DOI: 10.1016/j.camwa.2025.08.019

Fuhao Liu , Wei Yang , Jichun Li , Yunqing Huang

引用次数: 0

Adaptive design and adaptive finite element verification of bifunctional layer-wise cloak metamaterials for thermal and electrical insulation 热电绝缘双功能分层斗篷材料的自适应设计与自适应有限元验证

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-08-26 DOI: 10.1016/j.camwa.2025.08.016

Wei Wang, Tiancheng Wang, Wei Yang

{"title":"Adaptive design and adaptive finite element verification of bifunctional layer-wise cloak metamaterials for thermal and electrical insulation","authors":"Wei Wang, Tiancheng Wang, Wei Yang","doi":"10.1016/j.camwa.2025.08.016","DOIUrl":"10.1016/j.camwa.2025.08.016","url":null,"abstract":"<div><div>In this paper, a bifunctional metamaterial device with thermal and insulating functions is designed by utilizing the principles of transformational thermodynamics and transformational electrostatics in combination with the adaptive finite element method. Our main idea in designing this stealth material is to first derive the ideal stealth material parameters (typically represented as a function matrix) that vary with spatial position through the principles of transformation thermotics and transformation electrostatics. We recognize that there are significant differences in the rate of variation of these parameters in space. Based on the actual characteristics of the material parameters, we perform adaptive layered design according to the magnitude of their spatial variation rates. In regions where the parameters change drastically, finer layering is employed, while in areas with relatively gentle parameter variations, coarser layering is used. This method aims to enhance the manufacturability of stealth devices, enabling the design of dual-functional electrothermal stealth devices in a more efficient manner In order to verify the feasibility of this approach, an adaptive finite element method has been used to numerically simulate the proposed device. The numerical results validate the rationality of the adaptive layering design strategy proposed in this paper and suggest a reasonable scheme for the actual fabrication of the material.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 183-199"},"PeriodicalIF":2.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896138","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