{"title":"Auto-stabilized weak Galerkin finite element methods on polytopal meshes without convexity constraints","authors":"Chunmei Wang","doi":"10.1016/j.cam.2025.116572","DOIUrl":"10.1016/j.cam.2025.116572","url":null,"abstract":"<div><div>This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex elements in finite element partitions, marking a significant advancement over existing stabilizer-free WG methods. It overcomes the restrictive conditions of previous approaches and is applicable in any dimension <span><math><mi>d</mi></math></span>, offering substantial advantages. The proposed method maintains a simple, symmetric, and positive definite structure. These benefits are evidenced by optimal order error estimates in both discrete <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms, highlighting the effectiveness and accuracy of our WG method for practical applications.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116572"},"PeriodicalIF":2.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519489","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}
Denise Aregba-Driollet , Patrick Lacoste , Corentin Prigent
{"title":"Non-reflecting boundary conditions for solving Maxwell’s equations in waveguides","authors":"Denise Aregba-Driollet , Patrick Lacoste , Corentin Prigent","doi":"10.1016/j.cam.2025.116598","DOIUrl":"10.1016/j.cam.2025.116598","url":null,"abstract":"<div><div>We present here a method for solving the electromagnetic wave–matter interaction, on the one hand in closed waveguides, single or multi-port, and on the other hand with infinite materials periodic in two directions. In this presentation, the guides are coaxial or rectangular, but extension to any regular guide section is straightforward. This paper presents a method for solving Maxwell’s equations in real or virtual waveguides, using a decomposition of the DtN operator, and also introduces an adapted basis of the solution space based on a variational formulation. Finally, 2D axisymmetric and 3D finite elements are used. The text presents a number of resolutions of guided plane-wave scattering problems in a material, confirming the validity of the method and its generality.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116598"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519590","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":"Effects of higher order discretization on the predictions of steady turbulent airflow in human respiratory system","authors":"A. Lancmanová, T. Bodnár","doi":"10.1016/j.cam.2025.116593","DOIUrl":"10.1016/j.cam.2025.116593","url":null,"abstract":"<div><div>This study aims to evaluate the efficiency and accuracy of two distinct numerical schemes, the first order upwind scheme and the second-order central scheme with Van Leer limiter for convective terms, in predicting steady turbulent airflow in human airways for different flow rates ( <span><math><mrow><mi>Q</mi><mo>=</mo><mn>15</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>60</mn><mspace></mspace><mrow><mo>[</mo><mstyle><mi>ℓ</mi></mstyle><mspace></mspace><msup><mrow><mstyle><mi>m</mi><mi>i</mi><mi>n</mi></mstyle></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></mrow></mrow></math></span> ). A 3D model of the human respiratory system, extending from the oral cavity to the trachea and incorporating a simplified lung model (with branches from the 4th to 7th generations merged into larger funnels), is used to simulate steady inhalation and exhalation, excluding nasal tract respiration.</div><div>Through a series of simulations and subsequent analysis of the results, this study mutually compares the performance of the two numerical schemes in terms of their assumed accuracy, convergence, and computational efficiency with reference to available experimental data.</div><div>This study has shown significant differences in numerical predictions of respiratory flows obtained by first and second order schemes, pointing out that the second order approximation not only offers a potentially more accurate results, but also lower computational cost.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116593"},"PeriodicalIF":2.1,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527178","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}
Zhechen Zhang , Sanyang Liu , Lixia Liu , Zhiping Lin
{"title":"A symmetric ADMM-type algorithm for robust tensor completion problems using a regularized SCAD-Schatten-p model with application in color image and video recovery","authors":"Zhechen Zhang , Sanyang Liu , Lixia Liu , Zhiping Lin","doi":"10.1016/j.cam.2025.116604","DOIUrl":"10.1016/j.cam.2025.116604","url":null,"abstract":"<div><div>In this work, we design an efficient method for tackling the robust tensor completion problem. Tensor nuclear norm (TNN) is a conventional approach to solve the robust tensor completion problem. However, TNN may yield suboptimal solutions because the tensor rank is non-convex. With this purpose, we introduce an innovative tensor rank approximation that combines the Schatten-p norm with the Smoothly Clipped Absolute Deviation function. Additionally, we incorporate the Total Variation technique into the model to preserve the local smoothing properties of the image. To address the resulting model, we formulate a symmetric Alternating Direction Method of Multipliers algorithm (ADMM). Under some mild conditions, we validate that the solution produced by the algorithm converges to the KKT point of the model. Comprehensive experiments indicate the excellent performance of the proposed approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116604"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512123","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":"Fractional multiplicative Newton-type inequalities for multiplicative s-convex positive functions with application","authors":"Abdelghani Lakhdari , Djaber Chemseddine Benchettah , Badreddine Meftah","doi":"10.1016/j.cam.2025.116600","DOIUrl":"10.1016/j.cam.2025.116600","url":null,"abstract":"<div><div>In this paper, we begin by demonstrating a novel fractional multiplicative integral identity applicable to multiplicative differentiable functions. Leveraging this identity, we derive fractional Newton-type inequalities for multiplicative <span><math><mi>s</mi></math></span>-convex functions. Graphical representations accompany illustrative examples to validate the accuracy of our findings. Additionally, we provide applications of our results to special means.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116600"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508326","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":"Boundary value problems modeling moisture transport in soils","authors":"Vasyl Marynets , Kateryna Marynets , Oksana Kohutych","doi":"10.1016/j.cam.2025.116597","DOIUrl":"10.1016/j.cam.2025.116597","url":null,"abstract":"<div><div>To model the moisture transport in soil and to better understand physics underneath, we study a boundary value problem for a nonlinear hyperbolic PDE. Using a constructive method for approximation of solutions of the problem, we derive sufficient conditions for existence and uniqueness of its regular solutions and show that these solutions satisfy the sign-preserving inequalities. Additionally, we prove a comparison theorem and a theorem about differential inequalities, and derive an posteriori error of the method. Theoretical results are validated on an illustrative numerical example.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116597"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Antonio Hernando , José Luis Galán–García , Yolanda Padilla–Domínguez , María Ángeles Galán–García , Gabriel Aguilera–Venegas
{"title":"A library in CoCoA for implementing railway interlocking systems","authors":"Antonio Hernando , José Luis Galán–García , Yolanda Padilla–Domínguez , María Ángeles Galán–García , Gabriel Aguilera–Venegas","doi":"10.1016/j.cam.2025.116594","DOIUrl":"10.1016/j.cam.2025.116594","url":null,"abstract":"<div><div>In this paper, we propose a user-friendly library in CoCoA to address and completely resolve the challenges posed by the highly efficient and intriguing mathematical model introduced in Hernando et al., (2023) for implementing railway interlocking systems. Although the algebraic model (Hernando et al., 2023) allows for fast performance, it requires implementers and users to have a high level of mathematical knowledge, mastering concepts such as Gröbner bases, ideals, rings, and polynomials. This expertise is necessary to manually define ideals generated by numerous complex polynomials in multiple variables, which depend on the railway station’s topology, a process that can be both tedious and error-prone. To completely resolve these challenges, we have developed a CoCoA library that streamlines the implementation of interlocking systems using our mathematical framework, effectively eliminating manual errors. Consequently, thanks to the library we have developed and presented here, even users without mathematical knowledge can easily implement and manage a railway interlocking system.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116594"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519491","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}
Katarzyna Skowronek , Marek Arendarczyk , Anna K. Panorska , Tomasz J. Kozubowski , Agnieszka Wyłomańska
{"title":"Testing and estimation of the index of stability of univariate and bivariate symmetric α-stable distributions via modified Greenwood statistic","authors":"Katarzyna Skowronek , Marek Arendarczyk , Anna K. Panorska , Tomasz J. Kozubowski , Agnieszka Wyłomańska","doi":"10.1016/j.cam.2025.116587","DOIUrl":"10.1016/j.cam.2025.116587","url":null,"abstract":"<div><div>We propose a testing and estimation methodology for univariate and bivariate symmetric <span><math><mi>α</mi></math></span>-stable distributions using a modified version of the Greenwood statistic. Originally designed for positive-valued random variables, the Greenwood statistic, and its modified version tailored for symmetric distributions, have been predominantly applied to univariate random samples. In this paper, we extend the modified Greenwood statistic to a bivariate setting and examine its probabilistic properties within the class of <span><math><mi>α</mi></math></span>-stable distributions, with a focus on the sub-Gaussian case. Additionally, we introduce a novel testing approach that considers two variations of the modified Greenwood statistic as test statistics for the bivariate case. In the univariate setting, we adapt the proposed testing methodology for estimating the stability index. The simulation studies presented demonstrate that our proposed methodology outperforms classical approaches previously used in this context and serves as an effective tool for distinguishing between Gaussian and <span><math><mi>α</mi></math></span>-stable distributions with a stability index close to 2. The theoretical and simulation results are further illustrated with practical data examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116587"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580624","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":"Graddiv-conforming spectral element method for fourth-order div problems","authors":"Yang Han , Ping Lin , Lixiu Wang , Qian Zhang","doi":"10.1016/j.cam.2025.116599","DOIUrl":"10.1016/j.cam.2025.116599","url":null,"abstract":"<div><div>This paper introduces a novel numerical method to solve fourth-order div problems using <span><math><mrow><mtext>graddiv</mtext></mrow></math></span>-conforming spectral elements on cuboidal meshes. We start by determining the continuity requirements for <span><math><mrow><mtext>graddiv</mtext></mrow></math></span>-conforming spectral elements, followed by constructing these elements using generalized Jacobi polynomials and the Piola transformation. The resulting basis functions exhibit a hierarchical structure, making them easily extendable to higher orders. We apply these <span><math><mrow><mtext>graddiv</mtext></mrow></math></span>-conforming spectral elements to solve the fourth-order div problem and present numerical examples to verify both the efficiency and effectiveness of the method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116599"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508324","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":"Error estimates and parallel evaluation of hybrid schemes for parabolic, wave, and Schrödinger equations","authors":"Wenzhuo Xiong , Xiujun Cheng , Qifeng Zhang","doi":"10.1016/j.cam.2025.116579","DOIUrl":"10.1016/j.cam.2025.116579","url":null,"abstract":"<div><div>In this paper, we study error estimates of parallel evaluation for two types of hybrid difference schemes: HIEuler scheme and HBDF2 scheme. Each scheme is composed of the explicit midpoint scheme at the intermediary time-steps combined with the implicit Euler method/the backward difference formula at the final time-step. The key ingredient lies in that error estimates are rigorously proved under the parallel setting with the help of the energy method. To reduce storage requirements and computational costs, efficient parallel solvers for the parabolic, wave and Schrödinger equations are developed, respectively. Finally, several numerical examples are carried out to verify theoretical findings.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116579"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508571","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}