Computers & Mathematics with Applications最新文献

{"title":"A geometry aware arbitrary order collocation boundary element method solver for the potential flow past three dimensional lifting surfaces","authors":"Luca Cattarossi ,&nbsp;Filippo Guido Davide Sacco ,&nbsp;Nicola Giuliani ,&nbsp;Nicola Parolini ,&nbsp;Andrea Mola","doi":"10.1016/j.camwa.2026.01.021","DOIUrl":"10.1016/j.camwa.2026.01.021","url":null,"abstract":"<div><div>This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained refining the grid or increasing the polynomial degree. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 257-279"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014794","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":"Two-stage selective segmentation method based on exponential weighted geodesic distance driven model and thresholding method","authors":"Zhi-Feng Pang ,&nbsp;Xiaojie Peng ,&nbsp;Bing Li ,&nbsp;Hong Ge","doi":"10.1016/j.camwa.2025.12.029","DOIUrl":"10.1016/j.camwa.2025.12.029","url":null,"abstract":"<div><div>Selective segmentation represents a pivotal image processing technique within the domain of computer vision. Its objective is to facilitate the precise identification and extraction of a region of interest (ROI) within an image, while excluding background regions that are irrelevant to the task at hand. Nevertheless, the challenge of segmentation for images with noise, particularly those with grayscale inhomogeneity, still exists in many state-of-the-art segmentation models. In order to address this challenge, this paper proposes a novel two-step selective segmentation method based on an exponential weighted geodesic distance-driven scheme and a thresholding method inspired by the K-means method. In particular, the exponential weighted geodesic distance is first leveraged to enhance the contrast between the ROI and the background. Subsequently, the segmentation of the ROI is obtained through thresholding on the enhanced image generated in the initial stage. The experimental results demonstrate the efficacy of the proposed method in suppressing the influence of noise and grayscale inhomogeneity to a certain extent. Furthermore, the results show that the proposed method yields a higher segmentation accuracy than several existing state-of-the-art variation-based selective segmentation models and two classical deep learning segmentation models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 133-151"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940427","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 generic framework for solving three-dimensional gas dynamics equations","authors":"Min Xiao ,&nbsp;Xihua Xu","doi":"10.1016/j.camwa.2026.01.005","DOIUrl":"10.1016/j.camwa.2026.01.005","url":null,"abstract":"<div><div>The aim of this study is to develop a generic framework to construct three-dimensional nodal solvers for Lagrangian cell-centered hydrodynamics. By utilizing the specific volume as a medium, a new relationship between pressure and velocity is derived to figure out the nodal velocity. The nodal control volume adheres to Newton’s first law, resulting in the compatible equation. This generic framework ensures conservation of total mass, total momentum, and total energy, and satisfies an entropy inequality. Furthermore, it can be reduced to well-known schemes such as GLACE (Godunov-type LAgrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian HYDrodynamics), demonstrating its versatility and ability to generate various multi-point schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 152-175"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957176","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":"An hp-adaptive Galerkin least squares intrinsic finite element method for the convection-dominated problem on surfaces","authors":"Longyuan Wu ,&nbsp;Xinlong Feng","doi":"10.1016/j.camwa.2025.12.026","DOIUrl":"10.1016/j.camwa.2025.12.026","url":null,"abstract":"<div><div>We propose an <em>hp</em>-adaptive Galerkin least squares intrinsic finite element method for the stationary convection-reaction-diffusion equation on closed surfaces. The discrete variational formulation is intrinsic to the interpolated surface, incorporating the contribution of the local parametrization. This eliminates the reliance on pre-established surface parametrization and circumvents the challenge of high-order numerical integration in the space where the surface is embedded. The Galerkin least squares method, a variant of the streamline-upwind/Petrov-Galerkin method, is employed to enhance the stability of the numerical scheme. Unique solvability of the discrete variational problem is shown. To generate appropriate anisotropic mesh, an <em>hp</em>-adaptive refinement strategy is designed by combining the Galerkin least squares method with the quadratic intrinsic finite element method. The recovery function, based on centroid weights, yields more accurate estimates compared to area-weighted counterparts. Finally, numerical experiments show the effectiveness of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 113-132"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940426","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":"Least-squares enhanced physics-informed learning for singular and ill-posed partial differential equations","authors":"Eunjung Lee","doi":"10.1016/j.camwa.2026.01.027","DOIUrl":"10.1016/j.camwa.2026.01.027","url":null,"abstract":"<div><div>Partial differential equations that exhibit reduced regularity due to geometric singularities or possess nontrivial null space components arising from intrinsic properties of the differential operator pose serious challenges for both conventional numerical methods and standard physics-informed neural networks (PINNs). Least-squares finite element methods (LSFEM) have long provided robust tools for addressing such issues through weighted norm formulations and null-space projection techniques. In this work, we propose a hybrid PINN framework that systematically incorporates key elements of LSFEM to overcome limitations of existing PINNs. By embedding weighted least-squares functionals or projection mechanisms into the PINN architecture, the proposed method effectively handles singularities and ill-posedness within a deep learning paradigm. This approach enhances solution stability, avoids pollution from singular modes, and improves accuracy in problems where standard PINNs struggle.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 301-315"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033539","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":"Mean-square contractivity and convergence rate of stochastic theta Milstein schemes for non-autonomous SDEs with non-globally Lipschitz diffusion coefficients","authors":"Jinran Yao,&nbsp;Zhengwei Yin,&nbsp;Luozhong Gong","doi":"10.1016/j.camwa.2026.01.007","DOIUrl":"10.1016/j.camwa.2026.01.007","url":null,"abstract":"<div><div>This study is dedicated to investigating the mean-square contractivity and convergence rate of stochastic theta Milstein (STM) schemes for non-autonomous stochastic differential equations (SDEs) in the non-globally Lipschitz setting. More precisely, we begin by analyzing the mean-square contractivity of the numerical discretization for the STM schemes with <em>θ</em> ∈ [1/2, 1] under the coupled monotonicity condition along with the polynomial growth condition with respect to the state variable. Additionally, we employ an iterative strategy to deduce the strong convergence order of the STM schemes under non-globally Lipschitz conditions. It is demonstrated that the numerical approximations of the STM schemes with <em>θ</em> ∈ [1/2, 1] converges strongly with order one in the mean-square sense to the exact solution of the considered SDEs, under Assumptions 2.1 and 4.1 with respect to both the spatial and time variables. In the present study, the convergence analysis specifically addresses the case where <span><math><mrow><mi>L</mi><mo>∈</mo><mi>R</mi></mrow></math></span> in the coupled monotonicity condition, rather than <em>L</em> ≥ 0, as commonly presented in the literature. This analysis does not count upon a priori high-order moment estimates of the considered numerical schemes in establishing the convergence theorem. Finally, numerical experiments are performed to empirically substantiate the theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 228-256"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014831","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":"Analytical-to-AI pipeline: Modeling and optimization of entropy generation in pulsating non-Newtonian heat flow","authors":"Ayse Nur Altunkaya,&nbsp;Erkan Caner Ozkat,&nbsp;Mete Avci","doi":"10.1016/j.camwa.2025.12.021","DOIUrl":"10.1016/j.camwa.2025.12.021","url":null,"abstract":"<div><div>This study introduces an integrated analytical-to-AI framework for modeling and optimizing entropy generation in pulsating non-Newtonian heat and fluid flow specifically within two basic geometries: circular pipe and plane duct geometries. A semi-analytical model, based on the second law of thermodynamics, is first developed using the perturbation method to evaluate entropy generation under fully developed laminar flow and constant heat flux conditions. The model is validated against existing benchmark solutions, confirming its accuracy. Using this model, a comprehensive dataset is created by varying key dimensionless numbers: Brinkman number (<em>Br</em>), power-law index (<em>n</em>), pulsation amplitude (ε), and frequency (<em>F</em>). Four machine learning (ML) models are then trained to predict entropy generation, among which Gaussian Process Regression (GPR) shows the highest accuracy and is selected as the surrogate ML model for optimization. It is performed using the Grey Wolf Optimization (GWO) algorithm under different flow scenarios. The results indicate that shear-thinning fluids, especially with high amplitude (ε = 0.3) and moderate-to-high frequency pulsation (<em>F</em> = 60.803 for the circular pipe and <em>F</em> = 53.843 for the plane duct), yield the lowest entropy generation (<span><math><msub><mi>N</mi><msub><mi>s</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></msub></math></span> = 1.850 for the circular pipe and <span><math><msub><mi>N</mi><msub><mi>s</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></msub></math></span> = 0.911 for the plane duct), while an increase in the power-law index leads to higher <span><math><msub><mi>N</mi><msub><mi>s</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></msub></math></span>. The frequency range where entropy generation is significantly affected expands with increasing power-law index. These findings demonstrate the combined effect of fluid rheology and pulsation in reducing entropy generation. Furthermore, they emphasize that the proposed framework offers a reliable and efficient approach for analyzing and improving thermal systems using a combination of analytical modeling, machine learning, and optimization.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 195-211"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902641","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 fast compact ADI method for the generalized two-dimensional fractional Oldroyd-B type fluid model","authors":"Xinyu Diao ,&nbsp;Bo Yu","doi":"10.1016/j.camwa.2025.12.009","DOIUrl":"10.1016/j.camwa.2025.12.009","url":null,"abstract":"<div><div>This paper puts forward a fast compact alternating direction implicit (ADI) method for solving the generalized two-dimensional fractional Oldroyd-B type fluid model involving multi-term fractional diffusion and diffusion-wave behavior. By employing the fast L1 methods with the variable substitution technique to approximate the time fractional derivatives involving (0,1) and (1,2), and the spatial fourth-order compact scheme to approximate the spatial derivative and the coupled time-fractional spatial derivative, a fast compact ADI method with convergence accuracy <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>τ</mi><mrow><mi>min</mi><mo>{</mo><mn>3</mn><mo>−</mo><msub><mi>θ</mi><mi>l</mi></msub><mo>,</mo><mn>2</mn><mo>−</mo><msub><mi>γ</mi><mi>s</mi></msub><mo>,</mo><mn>2</mn><mo>−</mo><mi>α</mi><mo>}</mo></mrow></msup><mo>+</mo><msubsup><mi>h</mi><mrow><mi>x</mi></mrow><mn>4</mn></msubsup><mo>+</mo><msubsup><mi>h</mi><mrow><mi>y</mi></mrow><mn>4</mn></msubsup><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span> is constructed where <em>θ_l, γ_s</em> and <em>α</em> are orders of the Caputo fractional derivatives, <em>τ, h_x</em> and <em>h_y</em> are the time and space step sizes, respectively. The convergence analysis of the proposed fast compact ADI method is rigorously elaborated by the energy method. The temporal and spatial convergence orders are tested through two numerical examples, and the comparisons of the convergence orders and CPU time with the previous results are also listed in tabular forms. The numerical experimental results demonstrate the effectiveness of the proposed fast compact ADI method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 1-18"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822953","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 high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures","authors":"Caterina B. Leimer Saglio,&nbsp;Stefano Pagani,&nbsp;Mattia Corti,&nbsp;Paola F. Antonietti","doi":"10.1016/j.camwa.2025.12.017","DOIUrl":"10.1016/j.camwa.2025.12.017","url":null,"abstract":"<div><div>Epilepsy is a neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain. This work employs the monodomain model, coupled with specific models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure, and keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes. We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an <em>a-priori</em> convergence analysis for a simplified mathematical problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 112-131"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885771","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 matching boundary conditions of two-dimensional honeycomb lattice for atomic simulations","authors":"Baiyili Liu ,&nbsp;Songsong Ji ,&nbsp;Gang Pang ,&nbsp;Shaoqiang Tang ,&nbsp;Lei Zhang","doi":"10.1016/j.camwa.2025.12.015","DOIUrl":"10.1016/j.camwa.2025.12.015","url":null,"abstract":"<div><div>In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections. First, we formulate the dynamic equations and calculate the dispersion relation for the harmonic honeycomb lattice, then symmetrically choose specific atoms near the boundary to design different forms of matching boundary conditions. The boundary coefficients are determined by matching a residual function at some selected wavenumbers. Several atomic simulations are performed to test the effectiveness of matching boundary conditions in the example of a harmonic honeycomb lattice and a nonlinear honeycomb lattice with the FPU-<em>β</em> potential. Numerical results illustrate that the low-order matching boundary conditions mainly treat long waves, while the high-order matching boundary conditions can efficiently suppress short waves and long waves simultaneously. Decaying kinetic energy curves indicate the stability of matching boundary conditions in numerical simulations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 86-111"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885773","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}