Journal of Computational and Applied Mathematics最新文献

{"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}

{"title":"A new class of extended Laplace distributions with applications to modeling contaminated Laplace data","authors":"David K. Saah,&nbsp;Tomasz J. Kozubowski","doi":"10.1016/j.cam.2025.116588","DOIUrl":"10.1016/j.cam.2025.116588","url":null,"abstract":"<div><div>We introduce a new class of Extended Laplace (EL) distributions designed to characterize Laplace data influenced by independent uniform errors. We establish the fundamental theoretical properties of the model and develop both moment-based and maximum likelihood estimation (MLE) approaches for its parameters. Specifically, we present an effective iterative estimation scheme within the MLE framework to address optimization challenges arising from the complex structure of the domain. Our simulation results demonstrate the robustness of the estimation algorithms and the effectiveness of the EL model in handling imprecise Laplace data. Additionally, a real data example from the financial sector illustrates the broad modeling potential of this new distribution.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116588"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479767","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 delta Mittag-Leffler functions and its application in monotonic analysis","authors":"Pshtiwan Othman Mohammed","doi":"10.1016/j.cam.2025.116565","DOIUrl":"10.1016/j.cam.2025.116565","url":null,"abstract":"<div><div>In this paper, we first introduce a discrete Mittag-Leffler function of delta type. Using the Laplace transformation, some properties of the new special function are obtained. Second, we use this function to define new discrete fractional operators, namely AB fractional differences and sums, based on the Riemann–Liouville operators. We also applied the Laplace transformation on the new special functions and the related discrete operators. Finally, we propose and implement the mean value technique of discrete fractional calculus and demonstrate the advantages in terms of AB fractional differences.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116565"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465468","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 fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction–diffusion systems","authors":"E.O. Asante-Asamani ,&nbsp;A. Kleefeld ,&nbsp;B.A. Wade","doi":"10.1016/j.cam.2025.116568","DOIUrl":"10.1016/j.cam.2025.116568","url":null,"abstract":"<div><div>A fourth-order exponential time differencing (ETD) Runge–Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction–diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Padé (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20X speed-up in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116568"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474730","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 efficient Crank–Nicolson scheme with preservation of the maximum bound principle for the high-dimensional Allen–Cahn equation","authors":"Yabin Hou ,&nbsp;Jingwei Li ,&nbsp;Yuanyang Qiao ,&nbsp;Xinlong Feng","doi":"10.1016/j.cam.2025.116586","DOIUrl":"10.1016/j.cam.2025.116586","url":null,"abstract":"<div><div>In this study, we present a linear second-order single time-stepping finite difference scheme for solving the Allen–Cahn equation. The temporal integration is realized by combining the predictor-correction fashion of the Crank–Nicolson scheme with a linear stabilization technique, where central finite differences are employed for spatial discretization. In contrast to the BDF2 scheme, the proposed method operates without any extrapolation strategies, avoiding the need to compute the ratio of adjacent time steps during each time iteration. The discrete Maximum bound principle (MBP) is proven under the mild constraints on the time step size. The convergence analysis in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> norms is also presented as well as the energy stability. Several typical 2D and 3D numerical experiments are carried out to verify the theoretical results and demonstrate the efficiency of the proposed scheme.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116586"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474856","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}