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

Multigrid method with greedy partial block Jacobi smoother for solving two-dimensional space-fractional diffusion equations 求解二维空间分数扩散方程的贪心部分块雅可比光滑多重网格法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-21 DOI: 10.1016/j.camwa.2025.05.012

Kang-Ya Lu , Xiao-Yun Zhang

引用次数: 0

Higher-order three-scale asymptotic model and efficient two-stage numerical algorithm for transient nonlinear thermal conduction problems of composite structures 复合材料结构瞬态非线性热传导问题的高阶三尺度渐近模型及高效两阶段数值算法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-19 DOI: 10.1016/j.camwa.2025.05.009

Hao Dong , Yanqi Wang , Changqing Ye , Yihan Nie , Puyang Gao

{"title":"Higher-order three-scale asymptotic model and efficient two-stage numerical algorithm for transient nonlinear thermal conduction problems of composite structures","authors":"Hao Dong , Yanqi Wang , Changqing Ye , Yihan Nie , Puyang Gao","doi":"10.1016/j.camwa.2025.05.009","DOIUrl":"10.1016/j.camwa.2025.05.009","url":null,"abstract":"<div><div>The accurate thermal analysis of composite structures remains a challenging issue due to complicated multiscale configurations and nonlinear temperature-dependent behaviors. This work offers a novel higher-order three-scale asymptotic (HOTSA) model and corresponding numerical algorithm for accurately and efficiently simulating transient nonlinear thermal conduction problems of heterogeneous structures with three-scale spatial hierarchy. Firstly, by recursively macro-meso and meso-micro two-scale asymptotic analysis, the macro-meso-micro correlative HOTSA model is established with higher-order cell functions and higher-order correction terms. Then, a rigorous error estimation of the HOTSA model is presented under some assumptions in the point-wise and integral sense. Furthermore, a two-stage numerical algorithm with offline micro-meso computation and online macro-multiscale computation is developed to implement efficient and high-accuracy thermal simulation for heterogeneous structures with three-level spatial scales. Finally, numerical experiments are conducted to assess the efficiency and accuracy of the proposed HOTSA model and two-stage algorithm. This study establishes a reliable higher-order three-scale computational framework, that has a great potential for accurately capturing the microscopic oscillatory information of composite structures along with a drastic reduction in the computation resource.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 72-103"},"PeriodicalIF":2.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090657","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

Unconditionally energy-stable discontinuous Galerkin method for the dynamics model of protein folding 蛋白质折叠动力学模型的无条件能量稳定不连续Galerkin方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-19 DOI: 10.1016/j.camwa.2025.05.002

Dan Zhang , YuXing Zhang , Bo Wang

引用次数: 0

Optimal convergence analysis of an energy dissipation property virtual element method for the nonlinear Benjamin-Bona-Mahony-Burgers equation 非线性Benjamin-Bona-Mahony-Burgers方程耗能特性虚元法的最优收敛性分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-19 DOI: 10.1016/j.camwa.2025.05.003

Yanping Chen , Wanxiang Liu , Fangfang Qin , Qin Liang

引用次数: 0

An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker–Planck equations 求解Fokker-Planck方程的半隐式不连续Galerkin格式中基于优化的正保持极限器

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-19 DOI: 10.1016/j.camwa.2025.05.008

Chen Liu , Jingwei Hu , William T. Taitano , Xiangxiong Zhang

引用次数: 0

Modal analysis of biological structures based on the smoothed finite element methods 基于光滑有限元法的生物结构模态分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-17 DOI: 10.1016/j.camwa.2025.05.006

Jingui Zhao , Guirong Liu , Jinhui Zhao , Gang Wang , Zhonghu Wang , Zirui Li

{"title":"Modal analysis of biological structures based on the smoothed finite element methods","authors":"Jingui Zhao , Guirong Liu , Jinhui Zhao , Gang Wang , Zhonghu Wang , Zirui Li","doi":"10.1016/j.camwa.2025.05.006","DOIUrl":"10.1016/j.camwa.2025.05.006","url":null,"abstract":"<div><div>The smoothed finite element model exhibits a \"softening effect,\" resulting in reduced stiffness compared to the standard finite element model. This study employs the smoothed finite element methods (S-FEMs) with automatically generated tetrahedral meshes to perform modal analysis of biological structures subjected to arbitrary dynamic forces. Various S-FEM models are developed, including Edge-based, Face-based, and Node-based cross-element smoothing domains within the tetrahedral mesh framework, referred to as ES/FS/NS-FEM-T4. Using the gradient smoothing technique, the process of obtaining the strain-displacement matrix requires only the value of the shape function, not the inverse of the shape function, and no mapping is required. Additionally, by incorporating a Taylor expansion term for the strain gradient within the node-based smoothing domain framework, we introduce a stable node-based smoothed finite element method (SNS-FEM). Furthermore, the Lanczos algorithm and the modal superposition technique are integrated into our S-FEM models to compute the transient response of bone structures within the human body. The results obtained from S-FEMs are evaluated against the standard finite element method with respect to accuracy, convergence, and computational efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 188-227"},"PeriodicalIF":2.9,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070929","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 implicit Runge-Kutta Fourier pseudospectral methods for wave equations 波动方程的高阶隐式龙格-库塔傅立叶伪谱方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-16 DOI: 10.1016/j.camwa.2025.05.007

Ian T. Morgan , Youzuo Lin , Songting Luo

{"title":"High-order implicit Runge-Kutta Fourier pseudospectral methods for wave equations","authors":"Ian T. Morgan , Youzuo Lin , Songting Luo","doi":"10.1016/j.camwa.2025.05.007","DOIUrl":"10.1016/j.camwa.2025.05.007","url":null,"abstract":"<div><div>The dispersion error, also known as the pollution effect, is one of the main difficulties in numerical solutions to the wave propagation problem at high wavenumbers. The pollution effect, especially in mesh-based methods, can potentially be controlled by using either finer meshes or higher-order discretizations. Using finer meshes often leads to large systems that are computationally expensive to solve, especially for medium to high wavenumbers. Therefore, higher-order approximations are preferred to achieve good accuracy with manageable complexity. In this work, we will present high-order methods with implicit Runge-Kutta time integration and Fourier pseudospectral spatial approximations for the wave equation in a domain of interest surrounded by a sponge layer. At each time step, applying an appropriate A-stable implicit Runge-Kutta time-stepping method results in a modified Helmholtz equation that needs to be solved, for which an efficient iterative functional evaluation method with Fourier pseudospectral approximations will be proposed. The functional evaluation method transforms the equation into a functional iteration problem associated with an exponential operator that can be solved iteratively with guaranteed efficient convergence, where the exponential operator is evaluated by high-order operator splitting techniques and Fourier pseudospectral approximations. Numerical experiments are performed to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"192 ","pages":"Pages 1-13"},"PeriodicalIF":2.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067223","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

Physics informed neural network framework for unsteady discretized reduced order system 非定常离散化降阶系统的物理信息神经网络框架

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-13 DOI: 10.1016/j.camwa.2025.05.004

Rahul Halder , Giovanni Stabile , Gianluigi Rozza

{"title":"Physics informed neural network framework for unsteady discretized reduced order system","authors":"Rahul Halder , Giovanni Stabile , Gianluigi Rozza","doi":"10.1016/j.camwa.2025.05.004","DOIUrl":"10.1016/j.camwa.2025.05.004","url":null,"abstract":"<div><div>This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent full-order and reduced-order system. In this work, first, the governing equations are discretized using a finite difference scheme (whereas any other discretization technique can be adopted), then projected on a reduced or latent space using the Proper Orthogonal Decomposition (POD)-Galerkin approach, and next, the residual arising from discretized reduced order equation is considered as an additional loss penalty term alongside the data-driven loss term using different variants of deep learning method such as Artificial neural network (ANN), Long Short-Term Memory based neural network (LSTM). The LSTM neural network has been proven to be very effective for time-dependent problems in a purely data-driven environment. The current work demonstrates the LSTM network's potential over ANN networks in PINN as well. The major difficulties in coupling PINN with external forward solvers often arise from the inability to access the discretized forms of the governing equation directly through the PINN solver and also to include those forms in the computational graph of the network. This poses a significant challenge, especially when a gradient-based optimization approach is considered in the neural network. Therefore, we propose an additional step in the PINN algorithm to overcome these difficulties. The proposed methods are applied to a pitch-plunge airfoil motion governed by rigid-body dynamics and a one-dimensional viscous Burgers' equation. The potential of using discretized governing equations instead of a continuous form lies in the flexibility of input to the PINN. The current work also demonstrates the prediction capability of various discretized-physics-informed neural networks outside the domain where the data is available or where the governing equation-based residuals are minimized.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 167-187"},"PeriodicalIF":2.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934816","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 simulation for pulmonary airway reopening in alveolar duct by lattice Boltzmann method 点阵玻尔兹曼方法对肺泡管内气道重开的数值模拟

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-13 DOI: 10.1016/j.camwa.2025.05.005

Qianyu Lv , Bing He , Chunyan Qin , Binghai Wen

{"title":"Numerical simulation for pulmonary airway reopening in alveolar duct by lattice Boltzmann method","authors":"Qianyu Lv , Bing He , Chunyan Qin , Binghai Wen","doi":"10.1016/j.camwa.2025.05.005","DOIUrl":"10.1016/j.camwa.2025.05.005","url":null,"abstract":"<div><div>Aerosols, which are generated by the rupture of the liquid plug in the pulmonary respiratory tract, are important carriers of the viruses of infectious respiratory diseases, such as flu, tuberculosis, COVID-19, and Measles. In this study, we investigate liquid plug rupture and aerosol generation in the low respiratory tract with the alveolar structures by the chemical-potential multiphase lattice Boltzmann method. In a single alveolus duct, the opening expedites a unilateral break of the liquid plug due to a portion of the liquid flowing into the alveolus, and a microdroplet is yielded in the rupture. Aerosol would be deflected and reintegrated into the liquid film when the force is not great enough, which generates greater shear stresses to the inner wall where the microdroplet falls. In two alveoli duct, the rupture times of the upper and lower neck of the liquid plug depend on the radius ratio of the upper and lower alveolar. After the rupture of the liquid plug, the movement trajectory of the droplet is influenced by the alveoli structure to move forward or upward deflection. Interestingly, with the increase of radius ratio of the upper and lower alveolar, the mass of the fluid inflow into the alveoli decreases, while the mass of the aerosol generated by the rupture increase. This work contributes to understanding complex flow properties in the pulmonary airways, and the model can be extended to study the transport of liquid plugs and the generation of aerosol particles in more complex respiratory tract structures.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 206-218"},"PeriodicalIF":2.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937560","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 new numerical strategy for the drift-diffusion equations based on bridging the hybrid mixed and exponential fitted methods 基于桥接混合法和指数拟合法的漂移扩散方程的一种新的数值策略

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-05-09 DOI: 10.1016/j.camwa.2025.04.028

Aline C. da Rocha

{"title":"A new numerical strategy for the drift-diffusion equations based on bridging the hybrid mixed and exponential fitted methods","authors":"Aline C. da Rocha","doi":"10.1016/j.camwa.2025.04.028","DOIUrl":"10.1016/j.camwa.2025.04.028","url":null,"abstract":"<div><div>We present a new discretization scheme to solve the stationary drift-diffusion equations based on the hybrid mixed finite element method. A convenient change of variables is adopted and the partial differential equations of the system are decoupled and linearized through Gummel's map. This gives rise to three equations that need to be solved in a staggered fashion: one of reaction-diffusion type (Poisson) and two exhibiting a diffusion-reaction character (continuity equations). The Poisson's equation is solved by the classical hybrid mixed finite element method, while the continuity equations are discretized by a new version of the hybrid mixed exponential fitted method. The novelty here lies on the bridging terms between Poisson and each continuity equation, pursued by exploring direct relations between the Lagrange multipliers, thereby avoiding the use of a projection operator. The static condensation technique is adopted to reduce the number of degrees of freedom. Moreover, the finite dimensional functional spaces characterizing the hybrid mixed methods are chosen to ensure that the discrete problems satisfy the discrete maximum principle when a mesh of rectangular elements is used. Numerical experiments simulating semiconductor devices are presented, showing that the proposed methodology is capable of producing solutions free from spurious oscillations and accurate fluxes without the need of highly refined or complex meshes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 185-205"},"PeriodicalIF":2.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143924078","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