Computers & Mathematics with Applications最新文献_第4页

Novel connection of spectral scheme and one-step of s-order approaches for MHD flows enclosed a duct 封闭管道的 MHD 流动的光谱方案与 s 阶一步法之间的新联系

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-04 DOI: 10.1016/j.camwa.2025.02.016

Muhammad Hamid , Muhammad Usman , Zhenfu Tian

{"title":"Novel connection of spectral scheme and one-step of s-order approaches for MHD flows enclosed a duct","authors":"Muhammad Hamid , Muhammad Usman , Zhenfu Tian","doi":"10.1016/j.camwa.2025.02.016","DOIUrl":"10.1016/j.camwa.2025.02.016","url":null,"abstract":"<div><div>A challenging and common problem that frequently arises in the fields of physics and engineering, two-dimensional (2D) incompressible, viscous MHD duct flows have significant theoretical and practical significance due to their numerous and widespread applications in astrophysics, geology, power generation, MHD generators, electromagnetic pumps, accelerators, blood flow measurements, drug delivery, and other areas. Therefore, a robust solution to such a problem becomes a challenging task for the research community. This framework develops a novel connection to inspect the accurate and rapid convergent solutions of a coupled system of convection-diffusion equations arising in 2D unsteady MHD flows. This coupling is based on one-step <em>s</em>-stage/order methods to approximate the temporal variable with the Vieta-Fibonacci polynomials-based spectral method to estimate the spatial variables. The spatial derivative terms given in the problem under discussion are replaced by new operational matrices of integer order. The paper incorporates related theorems to provide a mathematical validation of the techniques. Additionally, we conduct a study on convergence and error bonds to verify the computational algorithm's mathematical formulation. A thorough comparison analysis illustrates the validity, correctness, and dependability of the computational approach that is now recommended. Novel investigation includes the spectral technique coupled with the fourth-order Runge-Kutta method handles the nonlinear issue very well to investigate the exact smooth solutions to physical problems. The suggested schemes are discovered to have an exponential order of convergence in the spatial direction, and the COC in the temporal direction confirms the findings of previous research.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 185-220"},"PeriodicalIF":2.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534326","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}

引用次数: 0

Optimizing Variational Physics-Informed Neural Networks Using Least Squares

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-01 DOI: 10.1016/j.camwa.2025.02.022

Carlos Uriarte , Manuela Bastidas , David Pardo , Jamie M. Taylor , Sergio Rojas

{"title":"Optimizing Variational Physics-Informed Neural Networks Using Least Squares","authors":"Carlos Uriarte , Manuela Bastidas , David Pardo , Jamie M. Taylor , Sergio Rojas","doi":"10.1016/j.camwa.2025.02.022","DOIUrl":"10.1016/j.camwa.2025.02.022","url":null,"abstract":"<div><div>Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a least squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid least-squares/gradient-descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to one hundred times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"185 ","pages":"Pages 76-93"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519112","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}

引用次数: 0

Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-01 DOI: 10.1016/j.camwa.2025.02.020

Biswajit Khara , Kumar Saurabh , Robert Dyja , Anupam Sharma , Baskar Ganapathysubramanian

引用次数: 0

An asymptotic preserving scheme for the Euler-Poisson-Boltzmann system in the quasineutral limit

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-27 DOI: 10.1016/j.camwa.2025.02.021

K.R. Arun , R. Ghorai

引用次数: 0

A new family of B-spline based explicit time integration methods for linear structural dynamic analysis

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-27 DOI: 10.1016/j.camwa.2025.02.017

Yanqun Han, Tianhao Liu, Weibin Wen, Xiaomin Liu

引用次数: 0

Physics-informed radial basis function network based on Hausdorff fractal distance for solving Hausdorff derivative elliptic problems

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-26 DOI: 10.1016/j.camwa.2025.02.012

Lin Qiu , Fajie Wang , Yingjie Liang , Qing-Hua Qin

{"title":"Physics-informed radial basis function network based on Hausdorff fractal distance for solving Hausdorff derivative elliptic problems","authors":"Lin Qiu , Fajie Wang , Yingjie Liang , Qing-Hua Qin","doi":"10.1016/j.camwa.2025.02.012","DOIUrl":"10.1016/j.camwa.2025.02.012","url":null,"abstract":"<div><div>This paper proposes a physics-informed radial basis function network (RBFN) based on Hausdorff fractal distance to resolve Hausdorff derivative elliptic problems. In the proposed scheme, we improve the performance of RBFN via setting the source points outside the computational domain, and allocating distinct shape parameter values to each RBF. Furthermore, on the basis of the modified RBFN, we take full advantage of the physical laws described by Hausdorff derivative partial differential equations and the constraints imposed by the boundary conditions, and establish a physics-informed optimization system for Hausdorff derivative elliptic problems. Utilizing MATLAB optimization toolbox function <em>lsqnonlin</em>, we solve the optimization system and then obtain the optimized network parameters including coordinates of source points, values of shape parameters and unknown RBF weights simultaneously, with which we deal with Hausdorff derivative elliptic problems successfully. Numerical experiments associated with acoustic, anisotropic heat conduction and fourth order problems are carried out to demonstrate the performance of the developed methodology.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 271-286"},"PeriodicalIF":2.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143496180","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}

引用次数: 0

A scalable well-balanced Taylor-Galerkin scheme for a lava flow depth-integrated model with point source vents

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-24 DOI: 10.1016/j.camwa.2025.02.014

Federico Gatti , Carlo de Falco , Marco Fois , Luca Formaggia

{"title":"A scalable well-balanced Taylor-Galerkin scheme for a lava flow depth-integrated model with point source vents","authors":"Federico Gatti , Carlo de Falco , Marco Fois , Luca Formaggia","doi":"10.1016/j.camwa.2025.02.014","DOIUrl":"10.1016/j.camwa.2025.02.014","url":null,"abstract":"<div><div>We propose a scalable well-balanced numerical method to efficiently solve a modified set of shallow water equations targeting the dynamics of lava flows. The governing equations are an extension of a depth-integrated model already available in the literature and proposed to model lava flows. Here, we consider the presence of vents that act as point sources in the mass and energy equations. Starting from a scheme developed in the framework of landslide simulation, we prove its capability to deal with lava flows. We show its excellent performances in terms of parallel scaling efficiency while maintaining good results in terms of accuracy. To verify the reliability of the proposed simulation tool, we first assess the accuracy and efficiency of the scheme on ideal scenarios. In particular, we investigate the well-balancing property, we simulate benchmarks taken from the literature in the framework of lava flow simulations, and provide relevant scaling results for the parallel implementation of the method. Successively, we challenge the scheme on a real configuration taken from the available literature.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 153-167"},"PeriodicalIF":2.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479139","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}

引用次数: 0

Rot-div mixed finite element method of two dimensional Hodge Laplacian problem

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-24 DOI: 10.1016/j.camwa.2025.02.005

Hailong Wang , Liang Wang , Guoqing Zhu , Chunguang Xiong

引用次数: 0

The use of polynomial-augmented RBF collocation method with ghost points for plane elastostatic equations of anisotropic functionally graded materials

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-24 DOI: 10.1016/j.camwa.2025.02.019

Ömer Oruç

{"title":"The use of polynomial-augmented RBF collocation method with ghost points for plane elastostatic equations of anisotropic functionally graded materials","authors":"Ömer Oruç","doi":"10.1016/j.camwa.2025.02.019","DOIUrl":"10.1016/j.camwa.2025.02.019","url":null,"abstract":"<div><div>In the current study, we propose an accurate numerical method for plane elastostatic equations of anisotropic functionally graded materials. The proposed method uses radial basis functions augmented with polynomial basis functions in a collocation framework by employing ghost point centers which cover physical domain of considered problem. Unlike in classical collocation approach where the centers and collocation points are taken identically, using ghost centers different from the collocation points greatly improves the accuracy of the proposed method. Addition of polynomial basis function to the radial basis functions stabilized the method against shape parameter of radial basis functions and also increases accuracy of solution, mostly. Some numerical examples are solved via the proposed method both on regular and irregular domains. <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and RMS error norms are calculated and for sufficient number of collocation points their values are smaller than <span><math><mn>1</mn><mi>e</mi><mo>−</mo><mn>10</mn></math></span>. The obtained error norms and their comparison with other methods available in literature confirm precision of the suggested numerical method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 116-133"},"PeriodicalIF":2.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479133","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}

引用次数: 0

Generalized soft finite element method for elliptic eigenvalue problems

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-24 DOI: 10.1016/j.camwa.2025.02.013

Jipei Chen , Victor M. Calo , Quanling Deng

{"title":"Generalized soft finite element method for elliptic eigenvalue problems","authors":"Jipei Chen , Victor M. Calo , Quanling Deng","doi":"10.1016/j.camwa.2025.02.013","DOIUrl":"10.1016/j.camwa.2025.02.013","url":null,"abstract":"<div><div>The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to improve the approximation accuracy and further reduce the discrete systems' stiffness. Firstly and most naturally, we generalize SoftFEM by adding a least-square term to the mass bilinear form. Superconvergent results of rates <span><math><msup><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>h</mi></mrow><mrow><mn>8</mn></mrow></msup></math></span> for eigenvalues are established for linear uniform elements; <span><math><msup><mrow><mi>h</mi></mrow><mrow><mn>8</mn></mrow></msup></math></span> is the highest order of convergence known in the literature. Secondly, we generalize SoftFEM by applying the blended Gaussian-type quadratures. We demonstrate further reductions in stiffness compared to traditional FEM and SoftFEM. The coercivity and analysis of the optimal error convergences follow the work of SoftFEM. Thus, this paper focuses on the numerical study of these generalizations. For linear and uniform elements, analytical eigenpairs, exact eigenvalue errors, and superconvergent error analysis are established. Various numerical examples demonstrate the potential of generalized SoftFEMs for spectral approximation, particularly in high-frequency regimes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 168-184"},"PeriodicalIF":2.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479161","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}

引用次数: 0