Computers & Mathematics with Applications最新文献_第7页

Numerical methods for solving the inverse problem of 1D and 2D PT-symmetric potentials in the NLSE

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-05 DOI: 10.1016/j.camwa.2025.01.026

Yedan Zhao , Yinghong Xu , Lipu Zhang

{"title":"Numerical methods for solving the inverse problem of 1D and 2D PT-symmetric potentials in the NLSE","authors":"Yedan Zhao , Yinghong Xu , Lipu Zhang","doi":"10.1016/j.camwa.2025.01.026","DOIUrl":"10.1016/j.camwa.2025.01.026","url":null,"abstract":"<div><div>This paper establishes a numerical framework for addressing the inverse problem of PT-symmetric potentials. Firstly, we discretize the solution space and innovatively construct a mapping to project the inverse problem of the PT-symmetric potential onto a finite-dimensional real vector space, thereby transforming the inverse problem of PT-symmetric potentials in the complex domain into a root-finding problem for a system of nonlinear equations in the real-number domain. Subsequently, to address the ill-posedness of the equation system, we innovatively apply regularization techniques and numerical algebraic techniques, constructing the Regularized-Newton-GMRES method for solving nonlinear equation systems, thereby obtaining the regularized solution for the PT-symmetric potential inverse problem. Finally, we conduct numerical experiments to validate the effectiveness of the established numerical solution framework. Our numerical experiments demonstrate that the proposed Regularized-Newton-GMRES method achieves higher computational accuracy, shorter computation time, improved stability, and effective solutions for such inverse problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 137-152"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102310","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

Nonconforming virtual element method for an incompressible miscible displacement problem in porous media

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-05 DOI: 10.1016/j.camwa.2025.01.021

Sarvesh Kumar , Devika Shylaja

引用次数: 0

A bond-based linear peridynamic model for viscoelastic materials and its efficient collocation method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-05 DOI: 10.1016/j.camwa.2025.01.024

Zhiwei Yang , Jie Ma , Ning Du , Hong Wang

引用次数: 0

Generative adversarial physics-informed neural networks for solving forward and inverse problem with small labeled samples

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-05 DOI: 10.1016/j.camwa.2025.01.025

Wensheng Li , Chuncheng Wang , Hanting Guan , Jian Wang , Jie Yang , Chao Zhang , Dacheng Tao

{"title":"Generative adversarial physics-informed neural networks for solving forward and inverse problem with small labeled samples","authors":"Wensheng Li , Chuncheng Wang , Hanting Guan , Jian Wang , Jie Yang , Chao Zhang , Dacheng Tao","doi":"10.1016/j.camwa.2025.01.025","DOIUrl":"10.1016/j.camwa.2025.01.025","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), but there still remain some challenges in the application of PINNs, for example, how to exhaustively utilize a small size of (usually very few) labeled samples, which are the exact solutions to the PDEs or their high-accuracy approximations, to improve the accuracy and the training efficiency. In this paper, we propose the generative adversarial physics-informed neural networks (GA-PINNs), which integrate the generative adversarial (GA) mechanism with original PINNs, to improve the performance of PINNs by exploiting a small size of labeled samples. The numerical experiments show that, compared with the original PINNs equipped with an additive loss computed on these labeled samples, GA-PINNs can more effectively utilize the small size of labeled samples when solving forward and inverse problems. As a generalization of GA-PINNs, we also combine the GA mechanism with the deep Ritz method (DRM) and the deep Galerkin method (DGM) to form GA-DRM and GA-DGM, respectively. The experimental results validate their superiority as well.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 98-120"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102661","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 new parallel algorithm with high-order finite difference scheme for solving the Helmholtz equation in two and three dimensions

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-05 DOI: 10.1016/j.camwa.2025.01.022

Tiantian Bao, Xiufang Feng

{"title":"A new parallel algorithm with high-order finite difference scheme for solving the Helmholtz equation in two and three dimensions","authors":"Tiantian Bao, Xiufang Feng","doi":"10.1016/j.camwa.2025.01.022","DOIUrl":"10.1016/j.camwa.2025.01.022","url":null,"abstract":"<div><div>This paper reports a class of new hybrid compact finite-difference schemes with high-order accuracy for solving the Helmholtz equation in two and three dimensions. The innovation of the scheme is to hybridize explicit and implicit compact schemes to deal with the solution and its first- and second-order derivatives, and to solve it by a step-by-step coupled iterative method. In response to the inefficiency of serial algorithms in solving the Helmholtz equation with large wavenumber and the issue of memory overflow on a single processor making computation infeasible because of excessively large computational scale, a parallel algorithm is proposed based on the Message Passing Interface (MPI) environment. Truncation error analysis demonstrates sixth-order accuracy for the proposed scheme, and numerical experiments confirm the theoretical sixth-order accuracy for problems with variable and large wavenumber. Also, the MPI-based parallel algorithm exhibits great parallel speedup and enables the tackling of large-scale problems that are beyond the reach of serial algorithms.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 71-97"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102663","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

Numerical solution of nonlinear convection-diffusion-reaction equation using a stabilized virtual element method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-04 DOI: 10.1016/j.camwa.2025.01.034

M. Arrutselvi , E. Natarajan , S. Natarajan

引用次数: 0

Adaptive fast L1 − 2 scheme for solving time fractional parabolic problems 自适应快速L1 − 2方案解决时间分数抛物线问题

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.003

Jiliang Cao , Wansheng Wang , Aiguo Xiao

{"title":"Adaptive fast L1 − 2 scheme for solving time fractional parabolic problems","authors":"Jiliang Cao , Wansheng Wang , Aiguo Xiao","doi":"10.1016/j.camwa.2024.12.003","DOIUrl":"10.1016/j.camwa.2024.12.003","url":null,"abstract":"<div><div>In this paper, we study a posteriori error estimates of the fast <span><math><mi>L</mi><mn>1</mn><mo>−</mo><mn>2</mn></math></span> scheme for time discretization of time fractional parabolic differential equations. To overcome the huge workload caused by the nonlocality of fractional derivative, a fast algorithm is applied to the construction of the <span><math><mi>L</mi><mn>1</mn><mo>−</mo><mn>2</mn></math></span> scheme. Employing the numerical solution obtained by the fast <span><math><mi>L</mi><mn>1</mn><mo>−</mo><mn>2</mn></math></span> scheme, a piecewise continuous function approximating the exact solution is constructed. Then, by exploring the error equations, a posteriori error estimates are obtained in different norms, which depend only on the discretization parameters and the data of the problems. Various numerical experiments for the fractional parabolic equations with smooth or nonsmooth exact solutions on different time meshes, including the frequently-used graded mesh, are carried out to verify and complement our theoretical results. Based on the obtained a posteriori error estimates, a time adaptive algorithm is proposed to reduce the computational cost substantially and provides efficient error control for the solution.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 59-76"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804472","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

Effective nonlocal finite element formulation for free vibration analysis of S-FGM doubly curved nanoshells based on linear strain–displacement relations using TSDT 基于线性应变-位移关系的S-FGM双弯曲纳米壳自由振动分析的有效非局部有限元公式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.021

Weeraphan Jiammeepreecha , Komkorn Chaidachatorn , Boonchai Phungpaingam , Karun Klaycham , Somchai Chucheepsakul

{"title":"Effective nonlocal finite element formulation for free vibration analysis of S-FGM doubly curved nanoshells based on linear strain–displacement relations using TSDT","authors":"Weeraphan Jiammeepreecha , Komkorn Chaidachatorn , Boonchai Phungpaingam , Karun Klaycham , Somchai Chucheepsakul","doi":"10.1016/j.camwa.2024.11.021","DOIUrl":"10.1016/j.camwa.2024.11.021","url":null,"abstract":"<div><div>This paper presents an effective nonlocal finite element method (FEM) for investigating the free vibration behavior of sigmoid functionally graded material (S-FGM) nanoshells using nonlocal elasticity theory. The effective nonlocal parameters via third-order shear deformation theory (TSDT) are varied along the thickness of the nanoshells following the sigmoid function. In this study, two different sigmoid functions FGM (S1-FGM and S2-FGM) are considered for the ceramic volume fraction. For S1-FGM, the top and bottom surfaces are ceramic and metal, respectively, whereas the middle surface has the average properties of its constituent materials. In order to increase the stiffness of S1-FGM, ceramic and metal are used at the bottom and midplane surfaces, respectively, to form S2-FGM, which is used to investigate and compare with S1-FGM. The governing equation of the S-FGM nanoshells is formulated based on Hamilton's principle. The numerical results are obtained by finite element method (FEM) with a nine-node quadrilateral (Q9) Lagrangian element and are in close agreement with the published results. The numerical investigation indicates that the frequency parameter decreases with increasing nonlocal parameters. The frequency parameters of S1-FGM nanoshells decrease slowly when the sigmoid material index increases, whereas the frequency parameters of the S2-FGM shells increase quickly (0 ≤ <em>n</em> ≤ 1). then slowly as the sigmoid material index increases. Finally, the effects of the geometrical parameters of the S-FGM nanoshells accounting for the effective nonlocal parameters on the non-dimensional frequency parameter are investigated.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 77-102"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841383","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

Numerical study of the non-conservative NET-RAT traffic flow model by path-conservative central-upwind schemes 非保守NET-RAT交通流模型的路径保守中心逆风方案数值研究

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.014

Saeed Mohammadian , Zuduo Zheng , Shaoshuai Chu , Alexander Kurganov

{"title":"Numerical study of the non-conservative NET-RAT traffic flow model by path-conservative central-upwind schemes","authors":"Saeed Mohammadian , Zuduo Zheng , Shaoshuai Chu , Alexander Kurganov","doi":"10.1016/j.camwa.2024.12.014","DOIUrl":"10.1016/j.camwa.2024.12.014","url":null,"abstract":"<div><div>Behavioral non-equilibrium hyperbolic traffic models, derived from approximated car-following models with human factors, can lose their conservative form, rendering traditional flux-based numerical methods ineffective. This challenge also applies to the recently proposed behavioral continuum (non-equilibrium traffic model based on risk allostasis theory, that is, NET-RAT) model. This paper is focused on solving the Riemann problem and several other initial-value problems for the novel NET-RAT model in the non-conservative form by path-conservative central-upwind (PCCU) schemes. We design extensive numerical tests considering the unique behavioral properties of the NET-RAT model. The PCCU schemes are then applied to these tests and the obtained results demonstrate that major wave types are effectively and accurately captured. At the same time, the fifth-order scheme, which is constructed using an alternative weighted essentially non-oscillatory (A-WENO) approach, yields substantially sharper resolution than its second-order counterpart. The presented numerical study can facilitate the practical implementation of the NET-RAT model for real-world traffic.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 212-228"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911898","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

A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model 求解热带太平洋模式的再现核粒子法（RKPM）算法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.011

Mostafa Abbaszadeh , Maryam Parvizi , Amirreza Khodadadian , Thomas Wick , Mehdi Dehghan

{"title":"A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model","authors":"Mostafa Abbaszadeh , Maryam Parvizi , Amirreza Khodadadian , Thomas Wick , Mehdi Dehghan","doi":"10.1016/j.camwa.2024.12.011","DOIUrl":"10.1016/j.camwa.2024.12.011","url":null,"abstract":"<div><div>Meshless methods have become increasingly popular for solving a wide range of problems in both solid and fluid mechanics. In this study, we focus on a meshless numerical approach to solve the tropical Pacific Ocean model, which captures the horizontal velocity and layer thickness of ocean waves, using an advanced meshless Galerkin technique known as the reproducing kernel particle method (RKPM). To address the temporal component in this scheme, we apply a Crank-Nicolson finite difference method, resulting in a semi-discrete formulation. For spatial discretization, we use a kernel-based meshless Galerkin method that integrates the strengths of finite element methods with reproducing kernel particle approximations. We conduct a comprehensive stability analysis and provide an a priori estimate for the semi-discrete solution. Furthermore, we derive error estimates for both the semi-discrete and fully discrete solutions. Finally, we validate the theoretical findings and evaluate the method's efficiency through real-world test cases.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 197-211"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911904","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