Journal of Computational Science最新文献

{"title":"Computational science: Guiding the way towards a sustainable society","authors":"Sergey V. Kovalchuk, Clélia de Mulatier, Valeria V. Krzhizhanovskaya, Leonardo Franco, Maciej Paszyński, Jack Dongarra, Peter M.A. Sloot","doi":"10.1016/j.jocs.2025.102663","DOIUrl":"10.1016/j.jocs.2025.102663","url":null,"abstract":"","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102663"},"PeriodicalIF":3.1,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unique analytical scheme for Fokker-Planck equation by the Matching polynomials of complete graph","authors":"Nirmala AN.,&nbsp;Kumbinarasaiah S.","doi":"10.1016/j.jocs.2025.102657","DOIUrl":"10.1016/j.jocs.2025.102657","url":null,"abstract":"<div><div>The article explores the feasibility of the graph-theoretic polynomial strategy to address the Fokker-Planck equation (FPE) employing a unique Matching Polynomial Collocation Method. Adriaan Fokker and Max Planck invented the FPE in the early twentieth century to characterize Brownian motion, and it has since grown into a cornerstone of stochastic process analysis, featuring significance in physics, biology, and economics. MPCM constructs an innovative functional matrix of integration leveraging the functional basis of matching polynomials of complete graphs, successfully translating the FPE into a system of algebraic equations with equipped collocation points. Newton's Raphson method follows to solve the consequent nonlinear algebraic equations. The proposed approach efficiently fixes technical challenges intrinsic to the FPE, including discretization errors, nonlinear encounters, substantial dimensionality, boundary conditions, stiffness, and computing costs. Illustrative samples spanning linear and nonlinear FPEs reflect MPCM's precision, computational efficacy, and versatility, with findings being consistent with well-established numerical and analytical strategies. The investigation highlights MPCM's potential as a resilient, versatile tool, paving the way for prospective studies into higher-dimensional issues and potential uses in various empirical fields, including quantum physics, demographic dynamics, and economic modeling.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102657"},"PeriodicalIF":3.1,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Bernstein–Bézier finite element method with perfectly matched layer for refraction and diffraction of waves in coastal regions","authors":"Saloua El Marri ,&nbsp;Abdellah El Kacimi ,&nbsp;Nabil El Moçayd ,&nbsp;Mohammed Seaid","doi":"10.1016/j.jocs.2025.102641","DOIUrl":"10.1016/j.jocs.2025.102641","url":null,"abstract":"<div><div>The aim of this paper is to effectively solve wave problems, governed by the linear elliptic mild-slope equation, on unstructured triangular meshes based on the Bernstein–Bézier finite element method. The present model takes into account non-uniform bathymetry and enables to accurately describe wave agitation problems and it copes with the pollution effect. A domain truncation method relying on the Perfectly Matched Layer (PML) concept is performed to address the issues related to open region domains. The proposed PML model uses a non-standard weak form of the truncated mild-slope equation to handle the incident wave field weakly and takes into account external bathymetry effects. A low-complexity procedure, exploiting the tensorial property of Bernstein polynomials in conjunction with the sum factorization method, is applied to set up the local high-order finite element matrices. Additionally, static condensation is applied element-wise to reduce the memory requirements. To avoid further sources of errors due to the interpolation of geometry, an accurate description of curved elements is adopted based on a blending map method. An analysis of <span><math><mi>h</mi></math></span>-convergence using radial PML is conducted by investigating a wave scattering problem by a circular island, where the bathymetry is initially assumed to be constant, and then including a parabolic shoal. The conditioning of the system matrix is also analyzed. The results clearly demonstrate that Bernstein–Bézier finite element method with radial PML considerably reduces memory requirements while maintaining targeted accuracy. A comparison study in the case of constant bathymetry shows that both radial and Cartesian PMLs yield similar performance in terms of accuracy. To further assess the efficiency of our model, a benchmark dealing with wave scattering by an elliptical shoal is investigated to demonstrate the performance of Cartesian PML with exterior bathymetry effects. Our numerical results are therefore compared with available experimental data as well as those found in the literature.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102641"},"PeriodicalIF":3.1,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preconditioned CG and GMRES for interior point methods with applications in radiation therapy","authors":"Felix Liu ,&nbsp;Måns I. Andersson ,&nbsp;Albin Fredriksson ,&nbsp;Stefano Markidis","doi":"10.1016/j.jocs.2025.102652","DOIUrl":"10.1016/j.jocs.2025.102652","url":null,"abstract":"<div><div>Interior point methods (IPMs) are widely used for different types of mathematical optimization problems. Many implementations of IPMs in use today rely on direct linear solvers to solve systems of equations in each iteration. The need to solve ever larger optimization problems more efficiently and the rise of hardware accelerators for general-purpose computing has led to much interest in using iterative linear solvers instead, though inevitable ill-conditioning of the linear systems remains a challenge. We investigate the use of the Krylov solvers CG, MINRES and GMRES for IPMs applied to optimization problems from radiation therapy. We implement a prototype IPM for convex quadratic programs and consider two different preconditioning strategies depending on the characteristics of the problem. One where a doubly augmented re-formulation of the Karush–Kuhn–Tucker linear system, originally proposed by Forsgren and Gill, is used together with a Jacobi-preconditioned conjugate gradient solver, and another with constraint preconditioning applied to a symmetric indefinite formulation of the linear system. Our results indicate that the proposed formulation provides sufficient accuracy. Furthermore, profiling of our prototype code shows that it is suitable for GPU acceleration, which may further improve its performance. The constraint preconditioner is shown to work well for cases with few, dense linear constraints, with a substantial improvement in linear solver convergence compared to the doubly augmented version. Our results indicate that our method can find solutions of acceptable accuracy in reasonable time for realistic problems from radiation therapy, as well as a simple test problem from support vector machine training. This is an extended version of a conference paper presented at the International Conference for Computational Science 2024 (Málaga, Spain) (Liu et al. 2024).</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102652"},"PeriodicalIF":3.1,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graph node classification with soft-flow convolution and linear-complexity attention mechanism","authors":"Xianming Huang ,&nbsp;Yang Yan (闫旸) ,&nbsp;Qiuyan Wang ,&nbsp;Haoyu Pan ,&nbsp;Hanning Chen ,&nbsp;Xingguo Liu","doi":"10.1016/j.jocs.2025.102628","DOIUrl":"10.1016/j.jocs.2025.102628","url":null,"abstract":"<div><div>Traditional Graph Neural Networks (GNNs) typically use a message-passing mechanism to aggregate information from neighboring nodes. This message-passing mechanism is analogous to diffusing messages, often resulting in the homogenization of node features. GNNs also tend to be ineffective at capturing features from distant nodes and learning the global structure of the graph, which can reduce performance in node classification tasks. To address these issues, this paper proposes a novel model—Enhanced Soft-Flow Graph Convolutional Network (ESAGCN) based on a global attention mechanism. This model defines a learnable, parameterized phase angle that allows the edge directions between nodes to change continuously, enabling features to flow between nodes. Additionally, it incorporates the self-attention mechanism from Transformers to capture global information within the graph network, enhancing the global representation of nodes. We also employ a simple kernel trick to reduce the complexity of the model’s global attention mechanism to linear complexity. Experimental results demonstrate that the integration of global and local information in graphs is crucial for the learning process of GNNs, especially in directed graphs, significantly improving the accuracy of node classification.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102628"},"PeriodicalIF":3.1,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Galerkin algorithm leveraging Bernoulli polynomials for accurate solutions of time-fractional diffusion-wave equations","authors":"R.M. Hafez ,&nbsp;M.A. Abdelkawy ,&nbsp;A. Biswas ,&nbsp;H.M. Ahmed","doi":"10.1016/j.jocs.2025.102607","DOIUrl":"10.1016/j.jocs.2025.102607","url":null,"abstract":"<div><div>This study presents a modified Galerkin technique utilizing Bernoulli polynomials for time-fractional diffusion-wave equations (TFDWEs). The proposed approach combines fractional calculus, namely Caputo derivatives, with a semi-discrete approach to achieve a high numerical accuracy. By utilizing Bernoulli polynomials as an efficient basis to approximate the solution, the algorithm transforms the governing equations into very sparse linear systems that can be solved computationally efficiently. Detailed numerical investigations, including applications to fractional wave equations and fourth-order diffusion-wave equations, demonstrate the method’s ability to achieve reduced errors and better computational efficiency. The results underline the stability and accuracy of the proposed technique, which turns out to be particularly suitable for simulating complex physical systems characterized by memory effects and anomalous diffusion.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102607"},"PeriodicalIF":3.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A computational approach to developing two-derivative ODE-solving formulations: γβI-(2+3)P method","authors":"Mehdi Babaei","doi":"10.1016/j.jocs.2025.102653","DOIUrl":"10.1016/j.jocs.2025.102653","url":null,"abstract":"<div><div>This paper presents the first set of two-derivative γβ formulations for time-integration of initial value (IV) ordinary differential equations (ODEs) in applied science. It belongs to the extended families of general linear methods (GLMs) and Runge-Kutta (RK) methods covering both linear and nonlinear ODEs. The present formulation is an advanced version of the basic form <span><math><mrow><mi>α</mi><mi>I</mi><mo>−</mo><mo>(</mo><mi>q</mi><mo>+</mo><mi>r</mi><mo>)</mo><mi>P</mi></mrow></math></span>, previously published by the author [1]. The key idea behind these formulations is the body decomposition of the RK methods and GLMs into two distinctive parts including interpolation and integration. This interesting idea has many advantages. First, it increases the flexibility of the formulation process. Second, each of these parts is supported by strong theorems in numerical analysis and can be developed independently through its own theories. In addition to these advantages, a knowledge-based approach, strengthened with swarm intelligence, is employed to formulate the integrator. Accordingly, a significant level of expertise is utilized in formulating the integrators. It leads to a series of interconnectivity relations between the weights of the integrators. These are known as weighting rules (WRs), which come in different types. The interpolators are obtained from approximation theory in which a polynomial is fitted to a given set of data. Consequently, a number of high-precision interpolators are developed to collaborate with the extended integrator. They approximate solution values at intermediate stages of the integration step, while the integrator bridges between the start and end points of the step. Working with interpolators has the advantages of generating solution values at all stages. It enables us to report the solution at more points rather than merely the mesh points. All the WRs, integrator, interpolators, and the ODE are systematically arranged in a specific order to construct the new algorithms of <span><math><mrow><mi>γ</mi><mi>β</mi><mi>I</mi><mo>−</mo><mo>(</mo><mi>q</mi><mo>+</mo><mi>r</mi><mo>)</mo><mi>P</mi></mrow></math></span>. Butcher tableaus are also provided for the new methods. Finally, they are carefully verified on several IVPs, including long-term and high-frequency problems. The obtained results demonstrate the practicality and efficiency of the formulations, and confirm that the collaboration of WRs, integrators, and interpolators performs exceptionally well.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"91 ","pages":"Article 102653"},"PeriodicalIF":3.7,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Realistic wildfire growth simulations applying a differentiable parametric representation of the fire front based on Composite Bézier curves","authors":"Irene González,&nbsp;Carlos Carrillo,&nbsp;Ana Cortés,&nbsp;Tomàs Margalef","doi":"10.1016/j.jocs.2025.102640","DOIUrl":"10.1016/j.jocs.2025.102640","url":null,"abstract":"<div><div>Modelling the evolution of a forest fire in Wildland Urban Interface (<em>WUI</em>) areas is still a major challenge in the field of forest fire simulation. Most existing forest fire spread simulators are based on polygonal representations of the fire perimeter, which often fail to capture the complexities of fire behaviour in these areas. Elliptical Wave Propagation (<em>EWP</em>) based simulators rely on this type of forest fire perimeter representation, that is, they represent the fire perimeter as a series of points connected by straight lines where the evolution of the fire front is performed by evaluating the spread of each perimeter point using as the spread direction the direction of the normal vector at each of them. To this end, <em>EWP</em>-based simulators have been built on top of the Richard model, which uses a differentiable parametric representation of the fire front. However, due to the polygonal representation used by <em>EWP</em>-based simulators, these cannot exploit the mathematical potential of using a parametric representation of the fire perimeter, which could compromise the accuracy of the simulations.</div><div>To address these limitations, we propose a novel parametric representation of the fire front using <em>Composite Bézier Curves</em> (CBC). The proposed wildfire perimeter representation improves the realism of the fire shapes being smooth and rounded. The first implementation of this proposal was done keeping the original method of normal vector calculation. This approach has been called <em>Composite Bézier Curves</em> using Neighbours (<em>CBCN</em>). However, an improved methodology has also been proposed where a more accurate method for calculating the normal vector directions is used, which is aligned with the curvatures of the fire front, thereby improving the overall modelling of fire dynamics. This advanced proposal has been called <em>Composite Bézier Curves</em> using Differentials (<em>CBCD</em>). Both proposed methodologies have been integrated into FARSITE, a well-known <em>EWP</em>-based forest fire spread simulator. Traditional polygonal representation (<em>LIN</em>) and the new CBC-based approach (<em>CBCN</em> and <em>CBCD</em>) were tested in ideal scenarios and two real cases. The obtained results show that any CBC-based representation generates more realistic fire shapes and they also enhance the simulator’s ability to model fire spread in <em>WUI</em> areas, with <em>CBCD</em> being the proposal that obtains the best results.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102640"},"PeriodicalIF":3.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PINN-parafoil: A physics-informed neural network method for complex parafoil dynamics simulating","authors":"Yu Yan ,&nbsp;Yufeng Fan ,&nbsp;Lulu Ning ,&nbsp;Caixia Su ,&nbsp;Pengju Wang ,&nbsp;Yongfeng Cao","doi":"10.1016/j.jocs.2025.102639","DOIUrl":"10.1016/j.jocs.2025.102639","url":null,"abstract":"<div><div>Accurately solving complex parafoil dynamics is essential for simulating para-foil system behavior. However, traditional numerical integration methods struggle with computational efficiency due to the high complexity of these models. This paper introduces a physics-informed neural network approach (PINN-Parafoil) that efficiently estimates numerical solutions for complex parafoil dynamics. By leveraging the superior function approximation capabilities of neural networks, PINN-Parafoil delivers near closed-form solutions, overcoming the computational challenges associated with conventional integration techniques. Unlike standard neural network methods, PINN-Parafoil incorporates the governing physical laws of parafoil dynamics as prior constraints, ensuring that the model outputs align with both training data and underlying physical principles. To validate this approach, the PINN-Parafoil model was trained and tested against the traditional Runge–Kutta solver for the 9-degree-of-freedom (DOF) parafoil model. Experimental results show that PINN-Parafoil achieves 25 times greater computational efficiency compared to traditional methods, while maintaining high accuracy with negligible numerical differences from true values. The resulting motion curves exhibit consistent dynamic characteristics with reference trajectories. Additionally, ablation studies highlight the critical role of physical constraints in enhancing model accuracy and stability. PINN-Parafoil offers a fast, accurate, and reliable proxy for simulating complex parafoil dynamics. Its efficiency and effectiveness make it a promising tool for various applications, including parafoil system design, trajectory planning, and homing control. This method provides robust technical support for both research and practical implementations in these fields, setting a foundation for further exploration and refinement of physics-informed neural network methodologies.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102639"},"PeriodicalIF":3.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A computational approach for solving the Gierer-Meinhardt (G-M) model in the context of biological pattern formation","authors":"Nek Muhammad Katbar ,&nbsp;Shengjun Liu ,&nbsp;Hongjuan Liu","doi":"10.1016/j.jocs.2025.102651","DOIUrl":"10.1016/j.jocs.2025.102651","url":null,"abstract":"<div><div>A mathematical framework with a particular focus on developmental biology can be attained from the Gierer-Meinhardt model, which explains the emergence of spatial patterns within biological systems. These patterns emerge when different chemical substances interact in a complicated manner, following a structured mathematical framework (Gierer-Meinhardt model), which helps explain how these patterns develop over time. The production of animal stripes on the skin and the organization of embryonic development are biological processes that usually involve these patterns. The present study conducts a detailed mathematical analysis of the Gierer-Meinhardt model by incorporating activation function such as radial basis function. The findings of the present study indicate that the radial basis function neural network is an effective tool for analyzing such complex mathematical models. By correlating the well-established biological models with computational tools like the ANN-RBF networks, new opportunities are created for examining the intricacy of living systems, and the foundation for further research in developmental biology and other fields.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"90 ","pages":"Article 102651"},"PeriodicalIF":3.1,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}