Pub Date : 2026-02-09DOI: 10.1016/j.camwa.2026.02.001
Heyan Xu, Haichao Li, Fuzhen Pang, Tianyi Hang, Chuanshuai Yi
For the optimization of vibration analysis methods for cylindrical shells, a numerical method based on Walsh series is proposed here for analyzing the free vibration of laminated cylindrical shells under general boundary conditions. The theoretical model is established using first-order shear deformation theory, with consideration of the effects of rotational inertia. The Walsh series method is applied in the axial direction, and a Fourier series is used in the circumferential direction. The resulting system of algebraic equations contains unknown Walsh series coefficients. By solving this system, the eigenfrequencies and related parameters of the laminated cylindrical shell are calculated. The convergence and accuracy of the proposed method are evaluated by comparing the results with those from existing literature and finite element analysis.
{"title":"Free vibration analysis of laminated cylindrical shells based on the Walsh series method","authors":"Heyan Xu, Haichao Li, Fuzhen Pang, Tianyi Hang, Chuanshuai Yi","doi":"10.1016/j.camwa.2026.02.001","DOIUrl":"https://doi.org/10.1016/j.camwa.2026.02.001","url":null,"abstract":"For the optimization of vibration analysis methods for cylindrical shells, a numerical method based on Walsh series is proposed here for analyzing the free vibration of laminated cylindrical shells under general boundary conditions. The theoretical model is established using first-order shear deformation theory, with consideration of the effects of rotational inertia. The Walsh series method is applied in the axial direction, and a Fourier series is used in the circumferential direction. The resulting system of algebraic equations contains unknown Walsh series coefficients. By solving this system, the eigenfrequencies and related parameters of the laminated cylindrical shell are calculated. The convergence and accuracy of the proposed method are evaluated by comparing the results with those from existing literature and finite element analysis.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"242 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146146659","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}
Pub Date : 2026-02-07DOI: 10.1016/j.camwa.2026.01.038
Karel Van Bockstal, Khonatbek Khompysh
{"title":"A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition","authors":"Karel Van Bockstal, Khonatbek Khompysh","doi":"10.1016/j.camwa.2026.01.038","DOIUrl":"https://doi.org/10.1016/j.camwa.2026.01.038","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"92 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134759","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}
Pub Date : 2026-02-06DOI: 10.1016/j.camwa.2026.01.035
Ying Zhang, Chong-Jun Li
{"title":"Construction of the polygonal and faceted polyhedral elements with high order completeness based on the scaled boundary coordinates","authors":"Ying Zhang, Chong-Jun Li","doi":"10.1016/j.camwa.2026.01.035","DOIUrl":"https://doi.org/10.1016/j.camwa.2026.01.035","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"17 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134767","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}
Pub Date : 2026-02-04DOI: 10.1016/j.camwa.2026.01.009
Ming Huang , Si Qi Zhang , Xiao Dan Chao , Hong Kai Song , Jin Long Yuan , Suo Suo Yang
In this research, we introduce an innovative composite proximal bundle method aimed at resolving generalized variational inequalities with the integration of inexact oracles. The essence of the problem is distilled into the pursuit of the null space of the superposition of two multivalued operators, all within the realm of a real Hilbert space and underpinned by an optimality criterion. We define the non-differentiable composite convex function and the monotone operator as f and Γ, respectively, both characterized by their roles as subdifferentials of functions that are lower semicontinuous. Central to our methodology is the proximal point approach, which entails the iterative refinement of subproblems through the lens of piecewise linear convex functions, augmented by the incorporation of inexact data. To enhance the computational efficiency and precision, we introduce a novel stopping criterion, designed to evaluate the precision of the current approximation. This innovation is pivotal in streamlining the management of subproblems. Moreover, to safeguard the convergence properties of our algorithm against the potential perturbations induced by inexact data, we have integrated a denoising technique. Subsequent to these enhancements, we demonstrate the convergence of our algorithm under specific operator properties, thereby providing a robust theoretical underpinning for its application. To verify the practical efficacy of our approach, we present the outcomes of our numerical experiments, which affirm the effectiveness of our method in the context of non-smooth optimization.
{"title":"The new inexact bundle-type technique to solve variational inequalities of composite structures","authors":"Ming Huang , Si Qi Zhang , Xiao Dan Chao , Hong Kai Song , Jin Long Yuan , Suo Suo Yang","doi":"10.1016/j.camwa.2026.01.009","DOIUrl":"10.1016/j.camwa.2026.01.009","url":null,"abstract":"<div><div>In this research, we introduce an innovative composite proximal bundle method aimed at resolving generalized variational inequalities with the integration of inexact oracles. The essence of the problem is distilled into the pursuit of the null space of the superposition of two multivalued operators, all within the realm of a real Hilbert space and underpinned by an optimality criterion. We define the non-differentiable composite convex function and the monotone operator as <em>f</em> and Γ, respectively, both characterized by their roles as subdifferentials of functions that are lower semicontinuous. Central to our methodology is the proximal point approach, which entails the iterative refinement of subproblems through the lens of piecewise linear convex functions, augmented by the incorporation of inexact data. To enhance the computational efficiency and precision, we introduce a novel stopping criterion, designed to evaluate the precision of the current approximation. This innovation is pivotal in streamlining the management of subproblems. Moreover, to safeguard the convergence properties of our algorithm against the potential perturbations induced by inexact data, we have integrated a denoising technique. Subsequent to these enhancements, we demonstrate the convergence of our algorithm under specific operator properties, thereby providing a robust theoretical underpinning for its application. To verify the practical efficacy of our approach, we present the outcomes of our numerical experiments, which affirm the effectiveness of our method in the context of non-smooth optimization.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 55-79"},"PeriodicalIF":2.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116550","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}
Pub Date : 2026-02-04DOI: 10.1016/j.camwa.2026.01.032
R. Shivananda Rao, M. Ramakrishna
In this paper, we adapt a troubled-cell indicator proposed by Fu and Shu [1] for discontinuous Galerkin (DG) methods to finite volume methods (FVM) employing third-order MUSCL reconstruction. We show that limiting only in troubled-cells is advantageous in terms of convergence but at the expense of the overall solution quality. We investigate the optimal number of troubled-cells required in the vicinity of an oblique shock to obtain a solution with minimal oscillations and enhanced convergence using a novel monotonicity parameter. An oblique shock is characterized primarily by the upstream Mach number, the shock angle β, and the deflection angle θ. We study these factors and their combinations by employing two dimensional compressible Euler equations and find that the degree of the shock misalignment with the grid determines the optimal number of troubled-cells. We show that, on each side of the shock, the optimal set consists of three troubled-cells for aligned shocks, and the troubled-cells identified by tracing the shock and four lines parallel to it, separated by the grid spacing, for nonaligned shocks. We show that, for a threshold constant , the adapted troubled-cell indicator identifies a set of cells that is close to and contains the optimal set of cells, and consequently, produces a solution close to that obtained by limiting everywhere, but with improved convergence. We demonstrate the effectiveness of the adapted troubled-cell indicator for unsteady problems using the double Mach reflection test case.
{"title":"A comprehensive numerical investigation of the application of troubled-cells to finite volume methods using a novel monotonicity parameter","authors":"R. Shivananda Rao, M. Ramakrishna","doi":"10.1016/j.camwa.2026.01.032","DOIUrl":"10.1016/j.camwa.2026.01.032","url":null,"abstract":"<div><div>In this paper, we adapt a troubled-cell indicator proposed by Fu and Shu [1] for discontinuous Galerkin (DG) methods to finite volume methods (FVM) employing third-order MUSCL reconstruction. We show that limiting only in troubled-cells is advantageous in terms of convergence but at the expense of the overall solution quality. We investigate the optimal number of troubled-cells required in the vicinity of an oblique shock to obtain a solution with minimal oscillations and enhanced convergence using a novel monotonicity parameter. An oblique shock is characterized primarily by the upstream Mach number, the shock angle <em>β</em>, and the deflection angle <em>θ</em>. We study these factors and their combinations by employing two dimensional compressible Euler equations and find that the degree of the shock misalignment with the grid determines the optimal number of troubled-cells. We show that, on each side of the shock, the optimal set consists of three troubled-cells for aligned shocks, and the troubled-cells identified by tracing the shock and four lines parallel to it, separated by the grid spacing, for nonaligned shocks. We show that, for a threshold constant <span><math><mrow><mi>K</mi><mo>=</mo><mn>0.05</mn></mrow></math></span>, the adapted troubled-cell indicator identifies a set of cells that is close to and contains the optimal set of cells, and consequently, produces a solution close to that obtained by limiting everywhere, but with improved convergence. We demonstrate the effectiveness of the adapted troubled-cell indicator for unsteady problems using the double Mach reflection test case.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 1-32"},"PeriodicalIF":2.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116551","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}
Pub Date : 2026-02-04DOI: 10.1016/j.camwa.2026.01.036
Sooncheol Hwang , Patrick J. Lynett , Sangyoung Son
In this paper, we develop a two-dimensional, second-order central-upwind scheme based on the finite volume method for the shallow water equations in the presence of wet/dry fronts. The proposed scheme is positivity-preserving and well-balanced, and remains robust for shallow water flows over complex bathymetry and wet-dry interfaces. We extend existing one-dimensional positivity-preserving and well-balanced schemes to two-dimensional spaces, addressing the challenges posed by partially flooded cells with varying bottom gradients in each direction. A novel draining time step for two-dimensional spaces is introduced to ensure the non-negativity of computed water depths across the entire computational domain. The performance of the proposed scheme is validated through several numerical experiments using both analytical solutions and experimental data, demonstrating its accuracy in capturing wet/dry fronts. The results for the lake-at-rest steady-state case confirm that numerical oscillations near the wet/dry fronts are successfully minimized, maintaining the initial state. Moreover, other examples show reduced numerical oscillations during wave run-up and rundown processes, further confirming the performance of the proposed scheme.
{"title":"A second-order well-balanced reconstruction for the shallow flows with wet/dry fronts","authors":"Sooncheol Hwang , Patrick J. Lynett , Sangyoung Son","doi":"10.1016/j.camwa.2026.01.036","DOIUrl":"10.1016/j.camwa.2026.01.036","url":null,"abstract":"<div><div>In this paper, we develop a two-dimensional, second-order central-upwind scheme based on the finite volume method for the shallow water equations in the presence of wet/dry fronts. The proposed scheme is positivity-preserving and well-balanced, and remains robust for shallow water flows over complex bathymetry and wet-dry interfaces. We extend existing one-dimensional positivity-preserving and well-balanced schemes to two-dimensional spaces, addressing the challenges posed by partially flooded cells with varying bottom gradients in each direction. A novel draining time step for two-dimensional spaces is introduced to ensure the non-negativity of computed water depths across the entire computational domain. The performance of the proposed scheme is validated through several numerical experiments using both analytical solutions and experimental data, demonstrating its accuracy in capturing wet/dry fronts. The results for the lake-at-rest steady-state case confirm that numerical oscillations near the wet/dry fronts are successfully minimized, maintaining the initial state. Moreover, other examples show reduced numerical oscillations during wave run-up and rundown processes, further confirming the performance of the proposed scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 33-54"},"PeriodicalIF":2.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116549","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}
Pub Date : 2026-02-02DOI: 10.1016/j.camwa.2026.01.025
F.S. Oğlakkaya, C. Bozkaya
{"title":"Impact of partial magnetic field on natural convection in nanofluid-filled inclined cavities","authors":"F.S. Oğlakkaya, C. Bozkaya","doi":"10.1016/j.camwa.2026.01.025","DOIUrl":"https://doi.org/10.1016/j.camwa.2026.01.025","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"276 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110516","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}
Pub Date : 2026-02-01DOI: 10.1016/j.camwa.2026.01.030
Chun-Hua Zhang, Long Kuang, Wen-Ping Yuan, Xiang Wang
{"title":"Stability and convergence of high-order WENO-OS scheme for the Allen-Cahn equation","authors":"Chun-Hua Zhang, Long Kuang, Wen-Ping Yuan, Xiang Wang","doi":"10.1016/j.camwa.2026.01.030","DOIUrl":"https://doi.org/10.1016/j.camwa.2026.01.030","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"8 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110519","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}
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