Computers & Mathematics with Applications最新文献_第10页

Hybrid meshless method for solving inhomogeneous polyharmonic equations 求解非齐次多谐方程的混合无网格法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.023

C.S. Chen , Andreas Karageorghis , Q.G. Liu

引用次数: 0

U-shaped factorized Fourier neural operator for solving partial differential equations 解偏微分方程的u形分解傅立叶神经算子

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.013

Hui Liu, Peizhi Zhao, Tao Song

{"title":"U-shaped factorized Fourier neural operator for solving partial differential equations","authors":"Hui Liu, Peizhi Zhao, Tao Song","doi":"10.1016/j.camwa.2025.07.013","DOIUrl":"10.1016/j.camwa.2025.07.013","url":null,"abstract":"<div><div>In this study, we proposed a U-shaped Factorized Fourier neural operator (U-FFNO) by introducing the U-shaped architecture idea and skip connection method of U-Net and improving the F-FNO operator layer using a Gaussian low-pass filter. The Factorized Fourier neural operator (F-FNO) introduces a dimensional decomposition method to learn the nonlinear mapping from parameter space to solution space to solve a series of partial differential equations (PDEs). However, due to the existence of truncation coefficients, some high-frequency information will be lost in the process of learning the nonlinear mapping, resulting in an increase in the error when learning the solution space. The proposed U-FFNO can learn this part of the information before the high-frequency information is lost, and enhances the learning ability of low-frequency information. We conduct experiments on several challenging partial differential equations in regular grids and structured grids to demonstrate the excellent accuracy of U-FFNO. U-FFNO is a learning-based method for simulating partial differential equations. As a neural operator, it also has the characteristics of discretization invariance and still performs well in super-resolution prediction tasks.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 233-245"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686862","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

Solving unbalanced optimal transport on point cloud by tangent radial basis function method 切线径向基函数法求解点云上不平衡最优输运

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.015

Jiangong Pan , Wei Wan , Chenlong Bao , Zuoqiang Shi

引用次数: 0

A novel numerical method for solving a two-dimensional variable-order time fractional advection-diffusion problem 求解二维变阶时间分数阶平流扩散问题的一种新的数值方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.025

Saurabh Kumar , Vikas Gupta , Ajay Kumar

引用次数: 0

Analysis of H1 penalized fictitious domain method for parabolic problems 抛物型问题的H1罚虚域法分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.009

Swapnil Kale , Debasish Pradhan , Sarvesh Kumar

{"title":"Analysis of H1 penalized fictitious domain method for parabolic problems","authors":"Swapnil Kale , Debasish Pradhan , Sarvesh Kumar","doi":"10.1016/j.camwa.2025.07.009","DOIUrl":"10.1016/j.camwa.2025.07.009","url":null,"abstract":"<div><div>This work focuses on establishing optimal <em>a priori</em> error estimates and stability analysis for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> penalized fictitious domain method for parabolic problems defined over curved complex domains. We embed the given complicated domain Ω into a larger rectangular domain R and extend the governing equation to a rectangular domain R by employing penalty parameter <em>ϵ</em> in the fictitious part <span><math><mi>R</mi><mo>﹨</mo><mi>Ω</mi></math></span>. Considering the inherent characteristic of the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> penalty, in the variational formulation, we impose the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> penalty only on the elliptic part and evince that the solution of the new penalized problem converges to the original solution. In order to obtain a numerical solution to the penalized problem, for spatial discretization, we utilize linear-finite elements on structured triangular mesh irrespective of the shape of the domain, and an Euler backward scheme is employed for the discretization of time space. Convergence analysis and discrete stability estimates are derived for semi and fully-discrete schemes. Moreover, numerical experiments are accomplished to validate the theoretical convergence rate and examine the computational efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 183-200"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679087","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

Spatiotemporal dynamics deduced by nonlocal delay competition in a diffusive Lotka-Volterra population model 扩散Lotka-Volterra种群模型的非局部延迟竞争时空动力学

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.008

Xiaosong Tang , Jiaxin Shen , Xinchang Wang , Zhaoyun Zeng , Jingwen Zhu

{"title":"Spatiotemporal dynamics deduced by nonlocal delay competition in a diffusive Lotka-Volterra population model","authors":"Xiaosong Tang , Jiaxin Shen , Xinchang Wang , Zhaoyun Zeng , Jingwen Zhu","doi":"10.1016/j.camwa.2025.07.008","DOIUrl":"10.1016/j.camwa.2025.07.008","url":null,"abstract":"<div><div>In this article, under the influence of nonlocal delay competition, we are devoted to investigating spatiotemporal dynamics of a diffusive Lotka-Volterra population model. According to the different values of some parameters, the original model may be changed into Lotka-Volterra predator-prey model, cooperative population model, or competition population model. Then, through the characteristic equation analysis, we find that nonlocal delay competition can deduce the presence of Turing-Hopf bifurcation when the original model is Lotka-Volterra cooperative population model or competition population model. However, when the original model is Lotka-Volterra predator-prey model, nonlocal delay competition cannot deduce the presence of Turing-Hopf bifurcation, but delay can deduce stability switches and the presence of Hopf bifurcation. Moreover, in the known literatures, to our knowledge, reaction-diffusion model with nonlocal delay competition has been investigated more rarely, which implies that our results in this paper are new. Finally, by presenting some numerical calculations and simulations, we obtain the rich results of stable spatially homogeneous periodic solutions, spatially steady state solutions, spatially inhomogeneous periodic solutions and stability switches deduced by delay.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 172-182"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679086","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-constrained deep kernel learning for inverse problems with noisy data 带噪声数据逆问题的物理约束深度核学习

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-21 DOI: 10.1016/j.camwa.2025.07.022

Zhenjie Tang, Li He

{"title":"Physics-constrained deep kernel learning for inverse problems with noisy data","authors":"Zhenjie Tang, Li He","doi":"10.1016/j.camwa.2025.07.022","DOIUrl":"10.1016/j.camwa.2025.07.022","url":null,"abstract":"<div><div>We propose a novel physics-constrained deep kernel learning (PCDKL) to estimate physical parameters and learn forward solutions for problems described by partial differential equations (PDEs) and noisy data. In this framework, a Gaussian Process (GP) with a deep kernel is constructed to model the forward solution. The posterior function samples from the GP serve as surrogates for the PDE solution. These GP posterior samples are constrained by two likelihoods: one to fit the noisy observations and the other to enforce conformity with the governing equation. To efficiently and effectively infer the deep kernel and physical parameters, we develop a stochastic estimation algorithm based on the evidence lower bound (ELBO), which serves as a posterior regularization objective function. The effectiveness of the proposed PCDKL is demonstrated through a systematic comparison with a Bayesian physics-informed neural network (B-PINN), a state-of-the-art method for solving inverse problems in PDEs with noisy observations. Our experiments show that PCDKL not only achieves forward solutions with informative uncertainty estimates comparable to B-PINN, but also yields accurate estimates of physical parameters. These results suggest that PCDKL has significant potential for uncertainty quantification in forward solutions and accurate physical parameter estimation, making it valuable for practical applications.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 135-150"},"PeriodicalIF":2.9,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670241","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 efficient iterative decoupling method for thermo-poroelasticity based on a four-field formulation 基于四场公式的热孔弹性有效迭代解耦方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-21 DOI: 10.1016/j.camwa.2025.07.021

Cai Mingchao , Li Jingzhi , Li Ziliang , Liu Qiang

引用次数: 0

A family of even-order edge-oriented nonconforming finite elements in 2D with efficient locally conservative flux reconstruction 具有有效局部保守通量重建的二维偶阶边缘非协调有限元族

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-21 DOI: 10.1016/j.camwa.2025.07.024

Gwanghyun Jo , Hyeokjoo Park

引用次数: 0

Vertex-centered control-volume mimetic finite difference methods 以顶点为中心的控制-模拟体积有限差分方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-21 DOI: 10.1016/j.camwa.2025.07.018

Rainer Helmig , Martin Schneider , Ivan Yotov

{"title":"Vertex-centered control-volume mimetic finite difference methods","authors":"Rainer Helmig , Martin Schneider , Ivan Yotov","doi":"10.1016/j.camwa.2025.07.018","DOIUrl":"10.1016/j.camwa.2025.07.018","url":null,"abstract":"<div><div>We develop a new class of vertex-centered control-volume mimetic finite difference methods on polytopal meshes for second order elliptic equations. The schemes are based on a mixed velocity-pressure formulation. The pressure is constant on dual mesh control-volumes constructed around the primary mesh vertices. The normal velocity is constant on the faces of the control-volumes, resulting in local mass conservation over the control-volumes. We consider both symmetric velocity integration rules constructed over the control-volumes, as well as non-symmetric quadrature rules constructed over sub-volumes obtained by the intersection of primary and dual elements. The latter choice allows for explicit gradient construction and local multipoint flux elimination within the primary elements, resulting in a positive definite vertex-centered pressure system. On simplicial, quadrilateral or hexahedral meshes, these local flux methods are closely related, and in some cases equivalent, to the classical vertex-centered control-volume finite element methods based on piecewise polynomial finite element basis functions for the pressure. The mimetic finite difference framework is utilized to analyze the well posedness and accuracy of the proposed methods. We establish first order convergence for the pressure and the velocity in the discrete mimetic norms, as well as second order pressure superconvergence in the case of symmetric quadrature rules. A series of numerical experiments illustrates the convergence properties of the methods on problems with varying degree of anisotropy, heterogeneity, and grid complexity in two and three dimensions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 104-126"},"PeriodicalIF":2.9,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672322","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