Computers & Mathematics with Applications最新文献

{"title":"Optimal transport in non-convex geometries and its application in shrinkage porosity prediction","authors":"Madyen Nouri ,&nbsp;Mohammad-Javad Kazemzadeh-Parsi ,&nbsp;Amine Ammar ,&nbsp;Francisco Chinesta ,&nbsp;Julien Artozoul ,&nbsp;Aude Caillaud","doi":"10.1016/j.camwa.2025.06.012","DOIUrl":"10.1016/j.camwa.2025.06.012","url":null,"abstract":"<div><div>Rooted in the Monge and Kantorovich problems, optimal transport seeks to minimize transportation costs, as quantified by Wasserstein distances, facilitating the transformation of one distribution into another distribution. However, its application faces challenges in addressing non-convex geometries, especially in interpolating mid-way distributions along transportation paths. In such scenarios, particles may breach the original shape boundaries, creating infeasible solutions. The article addresses this by proposing three innovative solutions: geometry mapping, trajectory planning and graph planning. These solutions aim to overcome the inherent limitations of optimal transport in non-convex spaces by offering mathematical formulations and implementation strategies. Importantly, the article goes beyond theoretical considerations by applying these solutions to predict shrinkage porosity in aluminum casting. This application demonstrates the broader relevance and effectiveness of the proposed solutions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 222-240"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144469977","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}

{"title":"A PDE system based on background estimation for document binarization with non-uniform background","authors":"Yu Wang,&nbsp;Chuanjiang He","doi":"10.1016/j.camwa.2025.06.009","DOIUrl":"10.1016/j.camwa.2025.06.009","url":null,"abstract":"<div><div>Document binarization, despite extensive research, still remains a challenging task for images with non-uniform background (NUB). Background estimation (BE) is an effective preprocessing technique to cope with this challenge. Previous BE-based binarization estimates a background component from the input and uses that estimate to preprocess the input to yield the compensated image, followed by a commonly sophisticated processing step for binarization. In this paper, inspired by BE, we introduce a binarization model in the framework of partial differential equation (PDE) for NUB document images. Specifically, we first model the NUB degradation as an uneven scaling map that adjusts the contrast of a normal document to produce the NUB document image. In other words, a NUB document image can be represented as the pixel-wise product of the uneven scaling map and the normal image (i.e., compensated image). The problem of compensating for the background is therefore rendered into the restoration problem of recovering the normal document image from the input NUB document image. Based on the NUB model, we propose a PDE system for binarization of document images with NUB degradation, which consists of an evolution PDE (w.r.t the scaling component) with the input NUB image as the initial condition, and a nonlinear diffusion equation (w.r.t the compensated component) with a pure white image as the initial condition. This PDE system estimates the scaling component and the compensated image dynamically and alternately during evolution. In the final compensated image, the text and background pixels are divided into two primary modes with a separation of 0.5, thereby enabling us to achieve binarization of the input NUB document image just by a binary projection separated by 0.5. Finally, the PDE system is evaluated on twenty-nine NUB document images from publicly available DIBCO datasets, in comparison to seven related PDE binarization models. Experimental results show that the proposed PDE system outperforms the seven models for comparison in terms of binarization of NUB document images.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 158-176"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470410","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}

{"title":"Simulation of plate bending vibration problems by the meshless backward substitution method","authors":"Yitong Xu ,&nbsp;Ji Lin ,&nbsp;Jun Lu ,&nbsp;Sergiy Reutskiy","doi":"10.1016/j.camwa.2025.06.019","DOIUrl":"10.1016/j.camwa.2025.06.019","url":null,"abstract":"<div><div>In this paper, the meshless backward substitution method is proposed for the first time to solve the fourth-order plate bending vibration problems. The numerical solution consists of approximation from the boundary conditions and the revised basis functions which satisfying the homogeneous conditions with weighted parameters which are obtained from the governing equations by the collocation method. Then the key issues are the organization of initial approximation and the revised basis function derived from the traditional basis functions. To demonstrate the accuracy and validity of the proposed method, several numerical examples are conducted and compared with existing methods in literature. The obtained results from numerical experiments confirm the potential of the proposed method in terms of both accuracy and efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 202-213"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470412","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}

{"title":"Well-posedness and strong convergence analysis of stochastic space-time fractional wave problems driven by fractional Brownian sheet","authors":"Yi Yang ,&nbsp;Jin Huang ,&nbsp;Hu Li","doi":"10.1016/j.camwa.2025.06.013","DOIUrl":"10.1016/j.camwa.2025.06.013","url":null,"abstract":"<div><div>This paper is interesting in studying well-posedness and strong convergence analysis for stochastic space-time fractional wave equations driven by fractional Brownian sheet. We first discuss well-posedness of the original stochastic space-time fractional wave equation in terms of standard Picard's iteration argument and give regularity and Hölder continuity analysis of its mild solution. Afterwards, we introduce a Wong-Zakai approximation to fractional Brownian sheet using spectral basis so that a regularized stochastic space-time fractional wave equation is derived, and then the corresponding regularity, Hölder continuity, and error estimate of its regularized solution are also investigated. Further, we use spectral Galerkin method and backward Euler convolution quadrature scheme to discretize the regularized equation in space and time, respectively, and then we provide rigorously strong convergence analysis for the solution of discrete scheme. Finally, numerical examples are carried out to verify our theoretical convergence results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 177-201"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470411","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}

{"title":"On the effect of force isotropy in a multiphase cascaded lattice Boltzmann scheme with entropic stabilization","authors":"Marco Desiderio Loffredo Senesi ,&nbsp;Alessandro Coclite ,&nbsp;Michele Dassisti","doi":"10.1016/j.camwa.2025.06.014","DOIUrl":"10.1016/j.camwa.2025.06.014","url":null,"abstract":"<div><div>The study of multiphase flows is a pivotal topic in natural sciences and engineering. A modeling approach to depict such phenomena combines the Lattice Boltzmann Method (LBM), a mesoscopic Navier-Stokes solver, and the Shan-Chen (SC) pseudopotential method, the latter postulating an interparticle interaction force inducing a spontaneous phase separation within a diffuse interface. To handle the inaccuracy and instability of the <em>naive</em> SC-LBM at high density ratio (DR) and dynamic viscosity ratio (VR), a twofold approach is proposed in recent literature: enhancing the collision process by a Cascaded Lattice Boltzmann Method (CLBM) constrained by a post-collision entropy minimization (KBC), and extending the formulation while tuning parameters of the interaction force to aid thermodynamic consistency, thus damping parasitic discretization effects and enabling surface tension tuning. In our work, we investigate how the interplay between the interparticle force isotropy order and key modeling parameters affects the KBC-CLBM discretization artifacts and stability. The nontrivial results achieved in terms of isotropy effectiveness hierarchy would guide future applied research in the adoption of suitable force stencils, complying with the required physical parameters (DR and VR), while limiting the computational burden. Static tests yield thermodynamically consistent results with the spurious currents magnitude lower than <span><math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math></span> lattice units at DR ≈3000 and VR ≈600 in the E8 isotropy order case. The compliance with the Laplace law has been proven, even at tuned surface tension. Droplet oscillation test results show consistency with transient analytical models, especially at E8 and even at higher DR and VR, also with surface tension modulation. Given the model's capabilities, we consider the outcome of our work as a step towards gaining a deeper understanding of natural phenomena and solving engineering problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 214-230"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470416","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}

{"title":"Some effective numerical schemes for solving Klein-Gordon-Schrödinger system in 2D based on IEQ method","authors":"Junjie Wang,&nbsp;Hongmin Li","doi":"10.1016/j.camwa.2025.06.015","DOIUrl":"10.1016/j.camwa.2025.06.015","url":null,"abstract":"<div><div>In the paper, we study some energy-preserving schemes to solve Klein-Gordon-Schrödinger system with periodic boundary condition. However, most of energy-preserving schemes of the system face how to efficiently solve a large nonlinear system at each time step, and the accuracy is often lower. Therefore, the linear implicit and high-order energy-preserving schemes of the Klein-Gordon-Schrödinger system are very valuable research work. First, we change original Klein-Gordon-Schrödinger system into an equivalent form based on the IEQ method, which transforms energy conservation law of the original system into quadratic invariants. Second, the linear implicit Crank-Nicolson scheme is presented for the modified Klein-Gordon-Schrödinger system to arrive at semi-discrete scheme, which only requires to solve decoupled linear system at each time step, and which can preserve energy conservation law of the modified system. In addition, we also show high-order energy-preserving scheme for the modified system by symplectic Runge-Kutta in time, which can preserve the discrete mass and energy conservation laws. Third, the Fourier spectral method is applied to the resulted semi-discrete systems with periodic boundary condition, and the efficient iterative algorithms of the fully-discrete systems are given. Moreover, we show some theoretical analysis such as uniqueness and convergence for fully-discrete linear implicit Crank-Nicolson scheme. Finally, the numerical experiments of some Klein-Gordon-Schrödinger systems are given to verify the correctness of theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 231-256"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470417","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}

{"title":"Efficient discretization of fractional SPDEs via Galerkin and exponential Euler methods","authors":"Minoo Kamrani","doi":"10.1016/j.camwa.2025.06.010","DOIUrl":"10.1016/j.camwa.2025.06.010","url":null,"abstract":"<div><div>This paper presents an efficient numerical method for solving stochastic partial differential equations (SPDEs) involving infinite-dimensional fractional Brownian motion. Fractional Brownian motion, characterized by a Hurst parameter <span><math><mi>H</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, is a Gaussian process widely used to model various real-world phenomena. It is a fundamental model for representing persistent behaviors in physical systems, making it highly effective for simulating correlated noise in quantum mechanics, material science, and astrophysics. Our method combines the Galerkin approach for spatial discretization with the exponential Euler scheme for time discretization to approximate solutions for fractional SPDEs. Specifically, we consider <em>Q</em>-fractional Brownian motion with two distinct types of operator <em>Q</em>. This study aims to establish theoretical results regarding the convergence and error estimates of the proposed method, followed by validation through numerical experiments. The structure of the paper is designed to provide a comprehensive explanation of the problem, analyze spatial and temporal discretization errors, and include a numerical example in subsequent sections.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 205-221"},"PeriodicalIF":2.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144364428","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}

{"title":"Low-cost adaptive pressure-correction projection method for the 2D/3D time-dependent natural convection problems","authors":"Jilian Wu ,&nbsp;Ning Li ,&nbsp;Mengru Jiang ,&nbsp;Xinlong Feng","doi":"10.1016/j.camwa.2025.06.008","DOIUrl":"10.1016/j.camwa.2025.06.008","url":null,"abstract":"<div><div>The paper firstly develops a high-order and low-complexity time-stepping technique for solving two- and three-dimensional (2D/3D) natural convection problems, which is based on the standard pressure-correction projection (PCP) method and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method can offset the weakness of PCP method while preserving its inherent advantages and can achieve higher-order in time by making a minimally intrusive modification to the PCP program at no extra computational and cognitive complexity. More importantly, it generates a low cost error estimator for adapting the time stepsize that can enhance time efficiency and reliability. Subsequently, the unconditional stability and error analysis of the fully-discrete PCP plus TF (PCP+TF) finite element method are proved. Notably, we construct low-complexity adaptive PCP algorithm, adaptive PCP+TF algorithm and the variable step, variable order (VSVO) algorithm using the TF technique. Ultimately, we verify the above viewpoints and theoretical analysis through some 2D/3D numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 86-109"},"PeriodicalIF":2.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144364875","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}

{"title":"IS-PINN: Integrating mathematical principles to solve inhomogeneous wave equations via physics-informed neural networks","authors":"Tianhao Wu,&nbsp;Changxiang Zhao,&nbsp;Xuewen Liu","doi":"10.1016/j.camwa.2025.06.006","DOIUrl":"10.1016/j.camwa.2025.06.006","url":null,"abstract":"<div><div>In recent years, Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs) by incorporating physical laws into the learning process, thus reducing dependency on labeled data. However, existing PINN frameworks face limitations in handling inhomogeneous wave equations, which introduce external forcing terms and complex boundary conditions. This study proposes an Inhomogeneous-Solved PINN (IS-PINN) model, integrating traditional mathematical principles, namely the separation of variables, the principle of superposition, and Duhamel’s Principle, into the neural network architecture. The IS-PINN model effectively addresses the challenges of both homogeneous and inhomogeneous wave equations under Dirichlet and Neumann boundary conditions. Through extensive experiments, we demonstrate that IS-PINN achieves superior accuracy compared to traditional PINNs, especially in handling the complexities of inhomogeneous cases. This work not only advances the PINN methodology but also opens new avenues for applying neural networks in solving complex PDEs with high physical fidelity.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 177-204"},"PeriodicalIF":2.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313928","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}

{"title":"A new decoupled unconditionally stable scheme and its optimal error analysis for the Cahn-Hilliard-Navier-Stokes equations","authors":"Haijun Gao ,&nbsp;Xi Li ,&nbsp;Minfu Feng","doi":"10.1016/j.camwa.2025.06.004","DOIUrl":"10.1016/j.camwa.2025.06.004","url":null,"abstract":"<div><div>We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the Cahn-Hilliard equations, and the other part is to calculate the Navier-Stokes equations subsequently by utilizing the phase field and chemical potential values obtained from the above step. Specifically, the velocity in the Cahn–Hilliard equation is discretized explicitly at the discrete time level, which enables the computation of the Cahn–Hilliard equations to be fully decoupled from that of Navier–Stokes equations. Furthermore, the pressure-correction projection method, in conjunction with the scalar auxiliary variable approach, not only enables the discrete scheme to satisfy unconditional energy stability, but also allows the convective term in the Navier-Stokes equations to be treated explicitly. We subsequently prove that the time semi-discrete scheme is unconditionally stable and analyze the optimal error estimates for the fully discrete scheme. Finally, several numerical experiments validate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 53-85"},"PeriodicalIF":2.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306579","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}