Journal of Computational and Applied Mathematics最新文献

{"title":"A library in CoCoA for implementing railway interlocking systems","authors":"Antonio Hernando ,&nbsp;José Luis Galán–García ,&nbsp;Yolanda Padilla–Domínguez ,&nbsp;María Ángeles Galán–García ,&nbsp;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}

{"title":"Testing and estimation of the index of stability of univariate and bivariate symmetric α-stable distributions via modified Greenwood statistic","authors":"Katarzyna Skowronek ,&nbsp;Marek Arendarczyk ,&nbsp;Anna K. Panorska ,&nbsp;Tomasz J. Kozubowski ,&nbsp;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 ,&nbsp;Ping Lin ,&nbsp;Lixiu Wang ,&nbsp;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 ,&nbsp;Xiujun Cheng ,&nbsp;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}

{"title":"Error estimates of semi-implicit numerical scheme for a diffuse interface model of two-phase magnetohydrodynamic flows","authors":"Dongmei Duan ,&nbsp;Fuzheng Gao ,&nbsp;Jinjin Yang ,&nbsp;Xiaoming He","doi":"10.1016/j.cam.2025.116580","DOIUrl":"10.1016/j.cam.2025.116580","url":null,"abstract":"<div><div>In this paper, we carry out a rigorous error analysis of the fully discrete semi-implicit numerical scheme proposed in Yang et al. (2019) for the diffuse interface model of two-phase magnetohydrodynamics (MHD) flows with different viscosities and electric conductivities in two and three-dimensional cases. The nonlinear and strong coupled properties and the variable coefficients of the model itself bring the major analytical difficulties in the error estimates. Based on three projection operators, including Stokes projection, Maxwell projection and Ritz projection, we select appropriate test functions, apply the Lipschitz continuous properties of the variable coefficients, and develop the strategies of utilizing intermediate terms to address the major difficulties caused by the model itself. Finally, we establish both the spatial and temporal convergence rates.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116580"},"PeriodicalIF":2.1,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511525","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":"Algebraic characterization of planar cubic and quintic Pythagorean-Hodograph B-spline curves","authors":"Lucia Romani ,&nbsp;Alberto Viscardi","doi":"10.1016/j.cam.2025.116592","DOIUrl":"10.1016/j.cam.2025.116592","url":null,"abstract":"<div><div>We provide a revised representation of planar cubic and quintic Pythagorean-Hodograph B-spline curves (PH B-splines for short) that offers the following advantages: (i) the clamped and closed cases are mostly treated together; (ii) the closed case is represented by using the minimum possible number of knots thus avoiding useless control points as well as control edges of zero length when the curve is regular. The proposed simplified representation turns out to be extremely useful to provide a unified <em>complex</em> algebraic characterization of clamped and closed planar PH B-splines of degree three and five. This is aimed at distinguishing regular planar cubic and quintic PH B-splines from <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> cubic and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> quintic B-spline curves in general. As for planar cubic PH B-splines consisting of <span><math><mi>m</mi></math></span> pieces, we obtain <span><math><mi>m</mi></math></span> complex conditions that, differently from what was known so far, can be used to characterize both the clamped and the closed case. As for planar quintic PH B-splines, the complex conditions are <span><math><mrow><mn>2</mn><mi>m</mi></mrow></math></span> and, unlike what is shown for cubic PH B-splines, they also depend on the knot intervals. This is to be considered a completely new result since no <em>complex</em> algebraic characterization working for any arbitrarily chosen knot partition had ever been provided for either clamped or closed planar quintic PH B-splines. The proposed algebraic characterization is finally exploited to fully identify the preimage of a regular planar quintic PH B-spline resolving all the sign ambiguities that affected the existing results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116592"},"PeriodicalIF":2.1,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479769","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":"Multivariate degradation modeling and reliability evaluation using gamma processes with hierarchical random effects","authors":"Kai Song","doi":"10.1016/j.cam.2025.116591","DOIUrl":"10.1016/j.cam.2025.116591","url":null,"abstract":"<div><div>Degradation data analysis provides an effective way to perform reliability evaluation for highly reliable products. In engineering practice, multiple performance characteristics are usually monitored simultaneously to reflect products’ health status comprehensively, resulting in the multivariate degradation data. Analyzing such data for reliability modeling and evaluation is of great interest but challenging. In this paper, by means of hierarchical random effects, a novel multivariate gamma degradation model is proposed. The developed model takes the temporal randomness of degradation processes, the non-linearity of degradation, the unit-to-unit heterogeneity and the dependence among marginal degradation processes into consideration simultaneously. Then, the reliability function is derived analytically. Subsequently, unknown model parameters are estimated by integrating the expectation maximization algorithm and the variational inference technique, where the latter is employed to derive tractable conditional distributions of latent variables. Meanwhile, a procedure that provides plausible guesses of parameters is developed to initialize this estimation method. Further, approximate confidence intervals are constructed for uncertainty quantification. Finally, the proposed model and methods are illustrated and verified by simulation and case studies.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116591"},"PeriodicalIF":2.1,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474857","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 iterative method for Helmholtz boundary value problems arising in wave propagation","authors":"Francisco Bernal ,&nbsp;Xingyuan Chen ,&nbsp;Gonçalo dos Reis","doi":"10.1016/j.cam.2025.116581","DOIUrl":"10.1016/j.cam.2025.116581","url":null,"abstract":"<div><div>The complex Helmholtz equation <span><math><mrow><mrow><mo>(</mo><mi>Δ</mi><mo>+</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mi>f</mi></mrow></math></span> (where <span><math><mrow><mi>k</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow><mo>,</mo><mi>f</mi><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow><mo>∈</mo><mi>ℂ</mi></mrow></math></span>) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to design and, in some applications, regarded as an open problem. Two sources of difficulty are the large number of degrees of freedom and the indefiniteness of the matrices arising after discretisation. Seeking to meet them within the novel framework of probabilistic domain decomposition, we set out to rewrite the Helmholtz equation into a form amenable to the Feynman–Kac formula for elliptic boundary value problems. We consider two typical scenarios, the scattering of a plane wave and the propagation inside a cavity, and recast them as a sequence of Poisson equations. By means of stochastic arguments, we find a sufficient and simulatable condition for the convergence of the iterations. Upon discretisation a necessary condition for convergence can be derived by adding up the iterates using the harmonic series for the matrix inverse—we illustrate the procedure in the case of finite differences.</div><div>From a practical point of view, our results are ultimately of limited scope. Nonetheless, the unexpected—even paradoxical—new direction of attack on the Helmholtz equation proposed by this work offers a fresh perspective on this classical and difficult problem. Our results show that there indeed exists a predictable range <span><math><mrow><mi>k</mi><mo>&lt;</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></math></span> in which this new ansatz works, with <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span> being far below the challenging situation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116581"},"PeriodicalIF":2.1,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551033","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 parallel domain decomposition-based implicit finite volume lattice Boltzmann method for incompressible thermal convection flows on unstructured grids","authors":"Lei Xu ,&nbsp;Rongliang Chen ,&nbsp;Linyan Gu ,&nbsp;Wu Zhang","doi":"10.1016/j.cam.2025.116578","DOIUrl":"10.1016/j.cam.2025.116578","url":null,"abstract":"<div><div>The double distribution function lattice Boltzmann method is known for its ability to handle various temperature changes and maintain strong numerical stability for incompressible thermal convection flows. However, being an explicit scheme on a Cartesian grid, it necessitates small time step sizes and limits its use in simulating fluid flows with intricate geometries. In this paper, a parallel fully implicit finite volume lattice Boltzmann method for incompressible thermal convection flows on unstructured grids is introduced. The double distribution function lattice Boltzmann equations are discretized by a finite volume method in space and an implicit backward Euler scheme in time. The resulting large sparse nonlinear system of algebraic equations is solved by a highly parallel Schwarz type domain decomposition preconditioned Newton–Krylov algorithm. The effectiveness of the proposed method is validated through five benchmark problems with a wide range of Rayleigh numbers: (a) porous plate problem with a temperature gradient, (b) natural convection in a square cavity, (c) natural convection in a concentric annulus, (d) mixed heat transfer from a heated circular cylinder and (e) nature convection in a sine-walled cavity. The numerical results demonstrate the robustness of the proposed method across all test cases, achieving a linear speedup in solving a problem with almost 40 million degrees of freedom using thousands of processor cores. The corresponding parallel efficiency reaches as high as 91.96% using 4096 processor cores.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116578"},"PeriodicalIF":2.1,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479766","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":"Embedding representation of words in sign language","authors":"Marcin Mateusz Czajka ,&nbsp;Daria Kubacka ,&nbsp;Aleksandra Świetlicka","doi":"10.1016/j.cam.2025.116590","DOIUrl":"10.1016/j.cam.2025.116590","url":null,"abstract":"<div><div>Word Embedding is currently the standard in machine learning methods for natural language processing. It is a matrix that represents the interdependence between words in a given linguistic corpus. This matrix is N x dimension, where N is the number of words in a given linguistic corpus, and the dimension is most often 100 or 300. The embedding matrix mathematically represents the semantic distance between individual words. Various methods exist for generating such a matrix for natural language, such as Word2Vec or GloVe.</div><div>In this work, we want to focus on creating an embedding matrix for Polish Sign Language (PSL). Sign language has different characteristics than the spoken language; it is the so-called spatial language, encompassing not only gestures but also facial expressions and body language. As a result, it has no official written form, though signs can be represented using glosses. With a dataset of sentences annotated with glosses, we attempted the generation of an embedding matrix that could be used in further researches on translation between Polish and PSL. For this purpose, the abovementioned Word2Vec and GloVe methods, with addition of fastText, ELMo and BERT algorithms, will be employed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116590"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465472","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}