Pub Date : 2026-02-07DOI: 10.1016/j.camwa.2026.01.038
Karel Van Bockstal , Khonatbek Khompysh
In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is recovered from the integral measurement over the domain Ω. Based on Rothe’s method, the existence and uniqueness of a weak solution, under suitable assumptions on the data, is established. A numerical time-discrete scheme for the unique weak solution and the unknown source coefficient is designed, and the convergence of the approximations is proven. Numerical experiments are presented to support the theoretical results. Noisy data is handled through polynomial regularisation.
{"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":"10.1016/j.camwa.2026.01.038","url":null,"abstract":"<div><div>In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is recovered from the integral measurement over the domain Ω. Based on Rothe’s method, the existence and uniqueness of a weak solution, under suitable assumptions on the data, is established. A numerical time-discrete scheme for the unique weak solution and the unknown source coefficient is designed, and the convergence of the approximations is proven. Numerical experiments are presented to support the theoretical results. Noisy data is handled through polynomial regularisation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 97-112"},"PeriodicalIF":2.5,"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
An approach for formulating polygonal and polyhedral elements is presented based on the scaled boundary coordinate system, which serves as a core component of the scaled boundary finite element method (SBFEM). Within the scaled boundary coordinate system, an arbitrary bivariate polynomials can be accurately represented as a linear combination of some power functions. Therefore, interpolation basis functions with high-order polynomial completeness over polygonal elements can be constructed using only boundary nodal displacements. To demonstrate the effectiveness of the proposed method, two polygonal elements with the second- and third-order completeness are presented as illustrative examples. Further, a faceted polyhedral element depending only on boundary nodal displacements is also constructed, exhibiting second-order completeness. Different from the classic SBFEM, the shape functions of the 2D and 3D elements are explicitly expressed, and the completeness are independent of the body forces (or without additional bubble functions). Numerical results demonstrate the proposed polygonal elements and faceted polyhedral element have corresponding completeness and convergence.
{"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":"10.1016/j.camwa.2026.01.035","url":null,"abstract":"<div><div>An approach for formulating polygonal and polyhedral elements is presented based on the scaled boundary coordinate system, which serves as a core component of the scaled boundary finite element method (SBFEM). Within the scaled boundary coordinate system, an arbitrary bivariate polynomials can be accurately represented as a linear combination of some power functions. Therefore, interpolation basis functions with high-order polynomial completeness over polygonal elements can be constructed using only boundary nodal displacements. To demonstrate the effectiveness of the proposed method, two polygonal elements with the second- and third-order completeness are presented as illustrative examples. Further, a faceted polyhedral element depending only on boundary nodal displacements is also constructed, exhibiting second-order completeness. Different from the classic SBFEM, the shape functions of the 2D and 3D elements are explicitly expressed, and the completeness are independent of the body forces (or without additional bubble functions). Numerical results demonstrate the proposed polygonal elements and faceted polyhedral element have corresponding completeness and convergence.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 80-96"},"PeriodicalIF":2.5,"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
This study examines unsteady thermal convection of an Al2O3-water nanofluid in a differentially heated, wavy-walled inclined enclosure under a partially applied magnetic field. Utilizing a two-level time integration scheme combined with the dual reciprocity boundary element method (DRBEM) in space, the research investigates the impact of key parameters, including a wide range of Rayleigh and Hartmann numbers, magnetic field width, cavity inclination angle, number of undulations of wavy walls, and nanofluid solid volume fraction, on the flow dynamics and heat transfer. DRBEM approach, which focuses only on the boundary discretization, enables efficient numerical analysis while reducing computational load. Results presented through streamlines, isotherms, and average Nusselt number, reveal that increasing Hartmann number suppresses the convective motion, leading to a reduction of average Nusselt number, while increasing the Rayleigh number or nanoparticle concentration intensifies the heat transfer rate in enclosures with both flat and wavy-walls. The highest thermal performance is obtained when the enclosure with flat walls is tilted by a right angle under the presence of partially applied magnetic field for various combinations of the governing parameters. This research provides a comprehensive understanding of how multi-physical parameters and a partially applied magnetic field influence thermal convection, particularly within complex geometries, thereby contributing to advancements in the design and analysis of thermal systems.
{"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":"10.1016/j.camwa.2026.01.025","url":null,"abstract":"<div><div>This study examines unsteady thermal convection of an Al<sub>2</sub>O<sub>3</sub>-water nanofluid in a differentially heated, wavy-walled inclined enclosure under a partially applied magnetic field. Utilizing a two-level time integration scheme combined with the dual reciprocity boundary element method (DRBEM) in space, the research investigates the impact of key parameters, including a wide range of Rayleigh and Hartmann numbers, magnetic field width, cavity inclination angle, number of undulations of wavy walls, and nanofluid solid volume fraction, on the flow dynamics and heat transfer. DRBEM approach, which focuses only on the boundary discretization, enables efficient numerical analysis while reducing computational load. Results presented through streamlines, isotherms, and average Nusselt number, reveal that increasing Hartmann number suppresses the convective motion, leading to a reduction of average Nusselt number, while increasing the Rayleigh number or nanoparticle concentration intensifies the heat transfer rate in enclosures with both flat and wavy-walls. The highest thermal performance is obtained when the enclosure with flat walls is tilted by a right angle under the presence of partially applied magnetic field for various combinations of the governing parameters. This research provides a comprehensive understanding of how multi-physical parameters and a partially applied magnetic field influence thermal convection, particularly within complex geometries, thereby contributing to advancements in the design and analysis of thermal systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 184-203"},"PeriodicalIF":2.5,"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.2026.01.026
Daehee Cho , Hyeonmin Yun , Jae Yong Lee , Mikyoung Lim
We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability.
{"title":"Conformal mapping based Physics-informed neural networks for designing neutral inclusions","authors":"Daehee Cho , Hyeonmin Yun , Jae Yong Lee , Mikyoung Lim","doi":"10.1016/j.camwa.2026.01.026","DOIUrl":"10.1016/j.camwa.2026.01.026","url":null,"abstract":"<div><div>We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 347-362"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110517","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
This paper presents a high-order operator splitting method incorporating a weighted essentially non-oscillatory (WENO) scheme for solving the Allen-Cahn equation. We employ the Strang operator splitting technique to decompose the original equation into linear and nonlinear subequations. The linear subequation is discretized using a sixth-order WENO scheme for spatial derivatives and a third-order Runge-Kutta method for the time direction, while the nonlinear subequation admits an analytical solution. This approach yields a high-order WENO-operator splitting (WENO-OS) scheme for the Allen-Cahn equation. In theory, the stability and convergence of the proposed scheme have been rigorously analyzed. Numerical experiments have verified that the proposed scheme can achieve sixth-order accuracy in space, second-order accuracy in time, verify stability condition and energy decline characteristic.
{"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":"10.1016/j.camwa.2026.01.030","url":null,"abstract":"<div><div>This paper presents a high-order operator splitting method incorporating a weighted essentially non-oscillatory (WENO) scheme for solving the Allen-Cahn equation. We employ the Strang operator splitting technique to decompose the original equation into linear and nonlinear subequations. The linear subequation is discretized using a sixth-order WENO scheme for spatial derivatives and a third-order Runge-Kutta method for the time direction, while the nonlinear subequation admits an analytical solution. This approach yields a high-order WENO-operator splitting (WENO-OS) scheme for the Allen-Cahn equation. In theory, the stability and convergence of the proposed scheme have been rigorously analyzed. Numerical experiments have verified that the proposed scheme can achieve sixth-order accuracy in space, second-order accuracy in time, verify stability condition and energy decline characteristic.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 171-183"},"PeriodicalIF":2.5,"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}
Pub Date : 2026-02-01DOI: 10.1016/j.camwa.2026.01.029
Jian Sun , Wenshuai Wang
A scalable MQRBF-FD framework is developed for full-vector elastic wave simulation in heterogeneous media with a spatially varying stiffness tensor C(x). The method resolves P- and S-wave separation and mode conversion at material interfaces using MQRBF spatial discretization on scattered nodes. Parallel subdomain decomposition with ghost-node continuity enables independent execution of all stages—adaptive node refinement, shape parameter optimization using parallel Adam-BP, localized interpolation, and CG solving. Subdomain-specific hierarchical time-stepping and error-driven ANR reduce the number of computational nodes by 35% in the Marmousi model while preserving sharp interface resolution. Compared with structured FD methods, the proposed approach achieves 39% higher accuracy and 15% lower memory usage at equivalent runtime. Validated across 2D and true 3D benchmarks, it establishes a scalable, high-fidelity parallel platform for seismic imaging and advanced material wave modeling.
{"title":"An enhanced MQRBF-FD method with parallel computing and multiscale modeling for efficient elastic wave propagation","authors":"Jian Sun , Wenshuai Wang","doi":"10.1016/j.camwa.2026.01.029","DOIUrl":"10.1016/j.camwa.2026.01.029","url":null,"abstract":"<div><div>A scalable MQRBF-FD framework is developed for full-vector elastic wave simulation in heterogeneous media with a spatially varying stiffness tensor <strong>C</strong>(<strong>x</strong>). The method resolves P- and S-wave separation and mode conversion at material interfaces using MQRBF spatial discretization on scattered nodes. Parallel subdomain decomposition with ghost-node continuity enables independent execution of all stages—adaptive node refinement, shape parameter optimization using parallel Adam-BP, localized interpolation, and CG solving. Subdomain-specific hierarchical time-stepping and error-driven ANR reduce the number of computational nodes by 35% in the Marmousi model while preserving sharp interface resolution. Compared with structured FD methods, the proposed approach achieves 39% higher accuracy and 15% lower memory usage at equivalent runtime. Validated across 2D and true 3D benchmarks, it establishes a scalable, high-fidelity parallel platform for seismic imaging and advanced material wave modeling.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 152-170"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110518","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.2026.01.028
Lixian Zhao, Yeping Li
In this paper, we present first-order and second-order fully discrete finite element schemes for the Caginalp model with periodic boundary conditions. First, we derive the corresponding regularity estimates for the exact solution under different initial conditions, which are essential for subsequent numerical analysis. Next, based on these regularity results, we systematically analyze the energy stability of both schemes and rigorously derive error estimates, providing a theoretical justification for their advantages in terms of accuracy and stability. Finally, we perform numerical simulations to validate the theoretical results.
{"title":"Error analysis of the first-order and second-order fully discrete schemes for the Caginalp model","authors":"Lixian Zhao, Yeping Li","doi":"10.1016/j.camwa.2026.01.028","DOIUrl":"10.1016/j.camwa.2026.01.028","url":null,"abstract":"<div><div>In this paper, we present first-order and second-order fully discrete finite element schemes for the Caginalp model with periodic boundary conditions. First, we derive the corresponding regularity estimates for the exact solution under different initial conditions, which are essential for subsequent numerical analysis. Next, based on these regularity results, we systematically analyze the energy stability of both schemes and rigorously derive error estimates, providing a theoretical justification for their advantages in terms of accuracy and stability. Finally, we perform numerical simulations to validate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 318-336"},"PeriodicalIF":2.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110768","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号