Computers & Mathematics with Applications最新文献

Unconditional superconvergent error estimates of second-order linearized nonconforming quadrilateral FEMs for nonlinear nuclear reactor model 非线性核反应堆模型二阶线性化非协调四边形有限元的无条件超收敛误差估计

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.031

Jinyu Li, Chuanjun Chen, Dongyang Shi

{"title":"Unconditional superconvergent error estimates of second-order linearized nonconforming quadrilateral FEMs for nonlinear nuclear reactor model","authors":"Jinyu Li, Chuanjun Chen, Dongyang Shi","doi":"10.1016/j.camwa.2025.09.031","DOIUrl":"10.1016/j.camwa.2025.09.031","url":null,"abstract":"<div><div>The focus of this paper is to establish the linearized Crank-Nicolson (C-N) and two-step Backward Differentiation Formula (BDF2) fully discrete schemes for the nonlinear nuclear reactor model, and investigate their superclose and superconvergent behaviors without the restrictions on the relationship between mesh size <em>h</em> and time step <em>τ</em> on quadrilateral meshes of nonconforming modified quasi-Wilson element. First, we will show that the consistency error of this element can reach <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> for homogeneous Neumann boundary condition which is the same as the quasi-Wilson element on rectangular meshes for the Dirichlet boundary condition. Then, based on the combination technique of interpolation and projection, mathematical induction and interpolation post-processing approach, the superclose and superconvergent results <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> in the broken <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm are derived. Finally, a numerical illustration is executed to validate the theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 260-275"},"PeriodicalIF":2.5,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222455","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 fast fourth-order scheme and its extrapolations for two-dimensional space fractional diffusion equations 二维空间分数扩散方程的快速四阶格式及其外推

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.027

Shenpei Wang , Tao Wang , Shuyu Yue , Hairong Lian

引用次数: 0

Fundamental solution neural networks for solving inverse Cauchy problems for the Laplace and biharmonic equations 求解拉普拉斯方程和双调和方程反柯西问题的基本解神经网络

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.032

Xin Li , Fajie Wang , Renhao Wang , Shengdong Zhao , Daigeng Yang

{"title":"Fundamental solution neural networks for solving inverse Cauchy problems for the Laplace and biharmonic equations","authors":"Xin Li , Fajie Wang , Renhao Wang , Shengdong Zhao , Daigeng Yang","doi":"10.1016/j.camwa.2025.09.032","DOIUrl":"10.1016/j.camwa.2025.09.032","url":null,"abstract":"<div><div>This paper proposes a novel fundamental solution neural networks method (FSNNs) to solve inverse Cauchy problems, which combines the method of fundamental solutions (MFS) with the physics-informed neural networks (PINNs). To optimize the distribution of source points, the method starts by partitioning the interval into equal segments, determined by the number of the source points. The coordinate system is situated at the center of the computational domain. The resulting angles as network inputs for the FSNNs and the intermediate variable as outputs, which is subsequently substituted into a length function to obtain the final length. The coordinates of the source points are then determined, and the MFS is employed to approximate the numerical solutions. The loss function is formulated based on the boundary conditions on the accessible boundary, and the training is employed to optimize the network parameters in the FSNNs and source point intensities in the MFS. The introduction of the PINNs overcomes the challenge of source point selection in the MFS and effectively addresses the ill-posedness of inverse problems. In summary, the proposed scheme is a machine learning-based semi-analytical meshless method which is simple, accurate and easily implemented, making it highly suitable for the numerical solution of inverse problems. Four numerical experiments, including the Laplace and biharmonic equations, validate the effectiveness and accuracy of the proposed FSNNs.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"201 ","pages":"Pages 1-17"},"PeriodicalIF":2.5,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223319","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 second-order time-accurate, linear fully decoupled unconditional energy stabilization finite element method for tumor growth model 肿瘤生长模型的二阶时间精确、线性完全解耦无条件能量稳定有限元方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.028

Mingle Sun , Bo Wang , Guang-an Zou , Yuxing Zhang

引用次数: 0

High order energy invariant fast algorithm for space two dimensional Klein-Gordon-Zakharov equations 空间二维Klein-Gordon-Zakharov方程的高阶能量不变快速算法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.026

Jie Chen , Jianqiang Sun

引用次数: 0

Discontinuous Galerkin time-stepping method for semilinear parabolic problems with mild growth condition 半线性抛物型温和增长问题的不连续Galerkin时间步进法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-10-03 DOI: 10.1016/j.camwa.2025.09.035

Raksha Devi, Dwijendra Narain Pandey

引用次数: 0

Analysis of the spectral harmonically enriched multiscale coarse space (SHEM) in 2D 二维谱富谐多尺度粗空间（SHEM）分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-30 DOI: 10.1016/j.camwa.2025.09.024

Martin J. Gander , Atle Loneland , Talal Rahman

{"title":"Analysis of the spectral harmonically enriched multiscale coarse space (SHEM) in 2D","authors":"Martin J. Gander , Atle Loneland , Talal Rahman","doi":"10.1016/j.camwa.2025.09.024","DOIUrl":"10.1016/j.camwa.2025.09.024","url":null,"abstract":"<div><div>The Spectral Harmonically Enriched Multiscale (SHEM) coarse space for domain decomposition methods was introduced as a cheaper alternative to GenEO (Generalized Eigenvalue Problems in the Overlap) with similar performance for high contrast problems. In SHEM, one enriches the coarse space with specific, cheaply computable coarse space components to get faster convergence for domain decomposition methods. For high contrast problems, this enrichment leads to robustness against variations and discontinuities in the problem parameters both inside subdomains and across and along subdomain boundaries. We present and analyze here SHEM in 2D based on simple, sparse lower dimensional eigenvalue problems on the interfaces between subdomains, and also a variant that performs equally well in practice, and does not require the solve of eigenvalue problems at all. Our enrichment process naturally reaches the Optimal Harmonically Enriched Multiscale coarse space (OHEM) represented by the full discrete harmonic space. We give a complete convergence analysis of SHEM in 2D, and also test both SHEM variants and OHEM numerically in 2D.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 243-259"},"PeriodicalIF":2.5,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222454","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

Morphological dynamics analysis on 3D surface using the Gray-Scott model 基于Gray-Scott模型的三维表面形态动力学分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-30 DOI: 10.1016/j.camwa.2025.09.023

Jian Wang , Yu Wang , Shanshan Ge , Ziwei Han , Maodong Pan

引用次数: 0

Stable sparse operator inference for nonlinear structural dynamics 非线性结构动力学的稳定稀疏算子推理

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-26 DOI: 10.1016/j.camwa.2025.09.017

Pascal den Boef , Diana Manvelyan-Stroot , Joseph Maubach , Wil Schilders , Nathan van de Wouw

{"title":"Stable sparse operator inference for nonlinear structural dynamics","authors":"Pascal den Boef , Diana Manvelyan-Stroot , Joseph Maubach , Wil Schilders , Nathan van de Wouw","doi":"10.1016/j.camwa.2025.09.017","DOIUrl":"10.1016/j.camwa.2025.09.017","url":null,"abstract":"<div><div>Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 228-242"},"PeriodicalIF":2.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160174","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

An easy to implement numerical framework for a cancer invasion mathematical model with two distinct cancer sub-populations 一个易于实现的具有两个不同癌症亚群的癌症侵袭数学模型的数值框架

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-25 DOI: 10.1016/j.camwa.2025.09.011

Yadhavan Karuppusamy , Lingeshwaran Shangerganesh , Sally Mohammed Farghaly Abdelaliem , A.S. Hendy

引用次数: 0