Pub Date : 2025-12-25DOI: 10.1016/j.camwa.2025.12.004
Xiaohao Zhang, Shimin Guo, Liquan Mei
In this work, a novel class of linearized high-order energy-preserving schemes are developed for simulating the coupled Klein-Gordon-Schrödinger equations in three-dimensional unbounded domains. We first reformulate the original system into an equivalent one by employing the exponential scalar auxiliary variable (ESAV) approach. Then, we construct extrapolated Gauss collocation methods to discretize the reformulated system, yielding a class of semi-discrete schemes with high-order accuracy in time. The Hermite-Galerkin spectral methods are utilized for spatial approximation. The fully discrete schemes are proved to satisfy the unconditional preservation of the original energy. Meanwhile, the schemes are easy to implement as they only require solving decoupled linear systems with constant coefficients at each time step. An adaptive time-stepping strategy is proposed to further improve efficiency without sacrificing accuracy. We present ample numerical tests to demonstrate the accuracy, efficiency and conservative properties of proposed schemes. In addition, the nonlinear dynamics of vector solitons in 3D are simulated to deepen the understanding of nonlinear KGS system.
{"title":"Linear high-order energy-conserving Hermite spectral schemes for three-dimensional Klein-Gordon-Schrödinger equations","authors":"Xiaohao Zhang, Shimin Guo, Liquan Mei","doi":"10.1016/j.camwa.2025.12.004","DOIUrl":"10.1016/j.camwa.2025.12.004","url":null,"abstract":"<div><div>In this work, a novel class of linearized high-order energy-preserving schemes are developed for simulating the coupled Klein-Gordon-Schrödinger equations in three-dimensional unbounded domains. We first reformulate the original system into an equivalent one by employing the exponential scalar auxiliary variable (ESAV) approach. Then, we construct extrapolated Gauss collocation methods to discretize the reformulated system, yielding a class of semi-discrete schemes with high-order accuracy in time. The Hermite-Galerkin spectral methods are utilized for spatial approximation. The fully discrete schemes are proved to satisfy the unconditional preservation of the original energy. Meanwhile, the schemes are easy to implement as they only require solving decoupled linear systems with constant coefficients at each time step. An adaptive time-stepping strategy is proposed to further improve efficiency without sacrificing accuracy. We present ample numerical tests to demonstrate the accuracy, efficiency and conservative properties of proposed schemes. In addition, the nonlinear dynamics of vector solitons in 3D are simulated to deepen the understanding of nonlinear KGS system.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 140-161"},"PeriodicalIF":2.5,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822944","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 : 2025-12-24DOI: 10.1016/j.camwa.2025.12.009
Xinyu Diao , Bo Yu
This paper puts forward a fast compact alternating direction implicit (ADI) method for solving the generalized two-dimensional fractional Oldroyd-B type fluid model involving multi-term fractional diffusion and diffusion-wave behavior. By employing the fast L1 methods with the variable substitution technique to approximate the time fractional derivatives involving (0,1) and (1,2), and the spatial fourth-order compact scheme to approximate the spatial derivative and the coupled time-fractional spatial derivative, a fast compact ADI method with convergence accuracy is constructed where θl, γs and α are orders of the Caputo fractional derivatives, τ, hx and hy are the time and space step sizes, respectively. The convergence analysis of the proposed fast compact ADI method is rigorously elaborated by the energy method. The temporal and spatial convergence orders are tested through two numerical examples, and the comparisons of the convergence orders and CPU time with the previous results are also listed in tabular forms. The numerical experimental results demonstrate the effectiveness of the proposed fast compact ADI method.
{"title":"A fast compact ADI method for the generalized two-dimensional fractional Oldroyd-B type fluid model","authors":"Xinyu Diao , Bo Yu","doi":"10.1016/j.camwa.2025.12.009","DOIUrl":"10.1016/j.camwa.2025.12.009","url":null,"abstract":"<div><div>This paper puts forward a fast compact alternating direction implicit (ADI) method for solving the generalized two-dimensional fractional Oldroyd-B type fluid model involving multi-term fractional diffusion and diffusion-wave behavior. By employing the fast L1 methods with the variable substitution technique to approximate the time fractional derivatives involving (0,1) and (1,2), and the spatial fourth-order compact scheme to approximate the spatial derivative and the coupled time-fractional spatial derivative, a fast compact ADI method with convergence accuracy <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>τ</mi><mrow><mi>min</mi><mo>{</mo><mn>3</mn><mo>−</mo><msub><mi>θ</mi><mi>l</mi></msub><mo>,</mo><mn>2</mn><mo>−</mo><msub><mi>γ</mi><mi>s</mi></msub><mo>,</mo><mn>2</mn><mo>−</mo><mi>α</mi><mo>}</mo></mrow></msup><mo>+</mo><msubsup><mi>h</mi><mrow><mi>x</mi></mrow><mn>4</mn></msubsup><mo>+</mo><msubsup><mi>h</mi><mrow><mi>y</mi></mrow><mn>4</mn></msubsup><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span> is constructed where <em>θ<sub>l</sub>, γ<sub>s</sub></em> and <em>α</em> are orders of the Caputo fractional derivatives, <em>τ, h<sub>x</sub></em> and <em>h<sub>y</sub></em> are the time and space step sizes, respectively. The convergence analysis of the proposed fast compact ADI method is rigorously elaborated by the energy method. The temporal and spatial convergence orders are tested through two numerical examples, and the comparisons of the convergence orders and CPU time with the previous results are also listed in tabular forms. The numerical experimental results demonstrate the effectiveness of the proposed fast compact ADI method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 1-18"},"PeriodicalIF":2.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822953","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 : 2025-12-24DOI: 10.1016/j.camwa.2025.12.014
Jiaxing Chen, Lei Wang, Jiawei Xiang
In research on the integration of computer-aided design (CAD) and numerical simulations of boundary types, commonly used methods for constructing approximate functions include non-uniform rational B-splines (NURBS) interpolation and moving least-squares (MLS) interpolation. These methods struggle to precisely enforce boundary conditions due to the lack of Kronecker delta properties in their shape functions. To address this limitation, this paper proposes a geometry-independent spline boundary element method (GISBEM) that introduces a transformation matrix to construct a spline interpolation function as the shape function, enabling direct application of boundary conditions akin to the boundary element method (BEM). First, the concept of geometry-independent field approximation (GIFT) is introduced, where the geometry is accurately described by NURBS, and the field variables of the elements are approximated using B-spline interpolation and transformation matrices. Second, the computation formats for the 3D potential and elasticity problems are derived using parameter mapping. Third, the calculation of variables at the boundary points is performed on the element using the relationship between the variables, with subsequent processing similar to that of BEM. Finally, the effectiveness and accuracy of the proposed method are verified through numerical examples.
{"title":"Geometry-independent spline boundary element method to analyze three-dimensional potential and elasticity problems","authors":"Jiaxing Chen, Lei Wang, Jiawei Xiang","doi":"10.1016/j.camwa.2025.12.014","DOIUrl":"10.1016/j.camwa.2025.12.014","url":null,"abstract":"<div><div>In research on the integration of computer-aided design (CAD) and numerical simulations of boundary types, commonly used methods for constructing approximate functions include non-uniform rational B-splines (NURBS) interpolation and moving least-squares (MLS) interpolation. These methods struggle to precisely enforce boundary conditions due to the lack of Kronecker delta properties in their shape functions. To address this limitation, this paper proposes a geometry-independent spline boundary element method (GISBEM) that introduces a transformation matrix to construct a spline interpolation function as the shape function, enabling direct application of boundary conditions akin to the boundary element method (BEM). First, the concept of geometry-independent field approximation (GIFT) is introduced, where the geometry is accurately described by NURBS, and the field variables of the elements are approximated using B-spline interpolation and transformation matrices. Second, the computation formats for the 3D potential and elasticity problems are derived using parameter mapping. Third, the calculation of variables at the boundary points is performed on the element using the relationship between the variables, with subsequent processing similar to that of BEM. Finally, the effectiveness and accuracy of the proposed method are verified through numerical examples.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"203 ","pages":"Pages 192-208"},"PeriodicalIF":2.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822951","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 : 2025-12-24DOI: 10.1016/j.camwa.2025.12.012
Sitao Zhang , Lin Liu , Yu Liu , Hongqing Song , Libo Feng
The paper contributes to investigating the quantum transport on a comb structure, whose feature of quantum motion is geometrically constrained such that the quantum motion is exclusively restricted to the backbone along the -direction. Instead of substituting with the fractional derivative directly, the one-dimensional (1D) time fractional Schrödinger equation (TFSE) is formulated, which is derived by mathematical derivation from the 2D Schrödinger equation with the wave operator (SEWO). The infinite boundaries are replaced with the absorbing boundary conditions (ABCs). The finite difference method (FDM) is formulated, followed by theoretical analysis to establish stability and convergence. A fast scheme is employed to enhance computational efficiency. The contrast of the numerical and exact solutions is analyzed by innovating a source term. In addition, the contrast of the distributions for the ABCs and zero boundary conditions is analyzed. Results show that ABCs provide a more accurate numerical solution compared to zero boundary conditions. Finally, the evolutions of the modules and the phasic pictures with different parameters are given.
{"title":"The mechanism analysis for the fractional quantum dynamics on a comb structure with the absorbing boundary conditions","authors":"Sitao Zhang , Lin Liu , Yu Liu , Hongqing Song , Libo Feng","doi":"10.1016/j.camwa.2025.12.012","DOIUrl":"10.1016/j.camwa.2025.12.012","url":null,"abstract":"<div><div>The paper contributes to investigating the quantum transport on a comb structure, whose feature of quantum motion is geometrically constrained such that the quantum motion is exclusively restricted to the backbone along the <span><math><mi>x</mi></math></span>-direction. Instead of substituting with the fractional derivative directly, the one-dimensional (1D) time fractional Schrödinger equation (TFSE) is formulated, which is derived by mathematical derivation from the 2D Schrödinger equation with the wave operator (SEWO). The infinite boundaries are replaced with the absorbing boundary conditions (ABCs). The finite difference method (FDM) is formulated, followed by theoretical analysis to establish stability and convergence. A fast scheme is employed to enhance computational efficiency. The contrast of the numerical and exact solutions is analyzed by innovating a source term. In addition, the contrast of the distributions for the ABCs and zero boundary conditions is analyzed. Results show that ABCs provide a more accurate numerical solution compared to zero boundary conditions. Finally, the evolutions of the modules and the phasic pictures with different parameters are given.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"203 ","pages":"Pages 209-229"},"PeriodicalIF":2.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822952","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 : 2025-12-24DOI: 10.1016/j.camwa.2025.11.023
Yanjun Ren , Dong Li , Liming Tang
In order to solve the problems of pixel misclassification, boundary leakage and unstable segmentation model encountered by the traditional level set method when dealing with images with strong disturbance information, this paper introduces a new energy functional based on a global-like global fitting term and a variational denoising term into variational level set framework, which not only significantly improves the segmentation of severe intensity inhomogeneous images and effectively realizes the denoising and deblurring process of images. Specifically, we utilize fitting term constructed with global and global-like information to reduce the sensitivity of the traditional level set method to intensity inhomogeneity. At the same time, we introduce a bounded Hessian variational restoration term to effectively suppressing the undesirable effects of strong noise, staircase artifacts, and blurring on segmentation. Moreover, a new edge indicator function was designed to enhance the model’s robustness to weak boundaries of the images. Experimental results on classical datasets demonstrate that our model exhibits significant advantages in noise suppression and edge preservation compared to existing state-of-the-art level set methods. The robustness and scalability of the model make it suitable for a wide range of image segmentation scenarios.
{"title":"Image restoration strategy stimulated level set model for segmenting images with strongly disturbance information","authors":"Yanjun Ren , Dong Li , Liming Tang","doi":"10.1016/j.camwa.2025.11.023","DOIUrl":"10.1016/j.camwa.2025.11.023","url":null,"abstract":"<div><div>In order to solve the problems of pixel misclassification, boundary leakage and unstable segmentation model encountered by the traditional level set method when dealing with images with strong disturbance information, this paper introduces a new energy functional based on a global-like global fitting term and a variational denoising term into variational level set framework, which not only significantly improves the segmentation of severe intensity inhomogeneous images and effectively realizes the denoising and deblurring process of images. Specifically, we utilize fitting term constructed with global and global-like information to reduce the sensitivity of the traditional level set method to intensity inhomogeneity. At the same time, we introduce a bounded Hessian variational restoration term to effectively suppressing the undesirable effects of strong noise, staircase artifacts, and blurring on segmentation. Moreover, a new edge indicator function was designed to enhance the model’s robustness to weak boundaries of the images. Experimental results on classical datasets demonstrate that our model exhibits significant advantages in noise suppression and edge preservation compared to existing state-of-the-art level set methods. The robustness and scalability of the model make it suitable for a wide range of image segmentation scenarios.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 123-139"},"PeriodicalIF":2.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822950","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 : 2025-12-22DOI: 10.1016/j.camwa.2025.12.002
Zhong Zhang, Bo Cui, Pengxu Chen, Liming Zhou, Yue Wu
The functionally graded piezoelectric structure (FGPS) is one of the core structures for the design and development of new intelligent components, and has excellent piezoelectric effect and gradient distribution characteristics. Since FGPS has a complex structure and often operates in complex environments, it is essential to propose an efficient algorithm for solving the multi-physics coupling problem of FGPS. Based on the structural characteristics of FGPS, this study introduces NURBS basis functions, proposes hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis (HTMEI-IGA) combining the constitutive equations and boundary conditions of FGPS, and derives the control equations and motion equations of HTMEI-IGA. The free vibration, transient response and harmonic response of FGPS in the hygrothermal field are solved using the subspace iteration method and the Newmark method. The convergence and accuracy of HTMEI-IGA are verified through multiple numerical examples. The influence of exponential factors, moisture and thermal on the FGPS structure is also studied, providing a new means for design and development of FGPS.
{"title":"Hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis of functionally graded piezoelectric structures under hygrothermal environment","authors":"Zhong Zhang, Bo Cui, Pengxu Chen, Liming Zhou, Yue Wu","doi":"10.1016/j.camwa.2025.12.002","DOIUrl":"10.1016/j.camwa.2025.12.002","url":null,"abstract":"<div><div>The functionally graded piezoelectric structure (FGPS) is one of the core structures for the design and development of new intelligent components, and has excellent piezoelectric effect and gradient distribution characteristics. Since FGPS has a complex structure and often operates in complex environments, it is essential to propose an efficient algorithm for solving the multi-physics coupling problem of FGPS. Based on the structural characteristics of FGPS, this study introduces NURBS basis functions, proposes hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis (HTMEI-IGA) combining the constitutive equations and boundary conditions of FGPS, and derives the control equations and motion equations of HTMEI-IGA. The free vibration, transient response and harmonic response of FGPS in the hygrothermal field are solved using the subspace iteration method and the Newmark method. The convergence and accuracy of HTMEI-IGA are verified through multiple numerical examples. The influence of exponential factors, moisture and thermal on the FGPS structure is also studied, providing a new means for design and development of FGPS.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 71-96"},"PeriodicalIF":2.5,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813853","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 : 2025-12-22DOI: 10.1016/j.camwa.2025.12.003
Brian Choi, Jie Xu, Trevor Norton, Mark Kon, Julio E. Castrillón-Candás
The nonlinear Poisson-Boltzmann equation (nPBE) is a fundamental partial differential equation (PDE) in electrostatics, widely used in computational biology and chemistry to model potential fields in solvents or plasmas. In this paper, we consider the problem of quantifying the statistical uncertainty of the stochastic nPBE solution under random variations in its coefficients. We establish the existence and uniqueness of solutions of the complexified nPBE using a contraction mapping argument, as conventional convex optimization techniques for the real-valued nPBE do not naturally extend to the complex setting. Using the existence and uniqueness result, we demonstrate that the solutions admit analytic extensions over a well-defined region in the complex hyperplane The analyticity makes the computation for statistics of real-valued quantities of interest amenable to numerical techniques such as sparse grids. Sparse grids are applied to uniformly approximate analytic functions with algebraic to sub-exponential error with respect to the number of knots, thus allowing for efficient approximations of high-dimensional integrals. Our numerical experiments confirm the predicted error behavior.
{"title":"Analytic regularity of strong solutions for the complexified stochastic nonlinear Poisson-Boltzmann equation","authors":"Brian Choi, Jie Xu, Trevor Norton, Mark Kon, Julio E. Castrillón-Candás","doi":"10.1016/j.camwa.2025.12.003","DOIUrl":"10.1016/j.camwa.2025.12.003","url":null,"abstract":"<div><div>The nonlinear Poisson-Boltzmann equation (nPBE) is a fundamental partial differential equation (PDE) in electrostatics, widely used in computational biology and chemistry to model potential fields in solvents or plasmas. In this paper, we consider the problem of quantifying the statistical uncertainty of the stochastic nPBE solution under random variations in its coefficients. We establish the existence and uniqueness of solutions of the complexified nPBE using a contraction mapping argument, as conventional convex optimization techniques for the real-valued nPBE do not naturally extend to the complex setting. Using the existence and uniqueness result, we demonstrate that the solutions admit analytic extensions over a well-defined region in the complex hyperplane The analyticity makes the computation for statistics of real-valued quantities of interest amenable to numerical techniques such as sparse grids. Sparse grids are applied to uniformly approximate analytic functions with algebraic to sub-exponential error with respect to the number of knots, thus allowing for efficient approximations of high-dimensional integrals. Our numerical experiments confirm the predicted error behavior.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 97-122"},"PeriodicalIF":2.5,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822955","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 : 2025-12-21DOI: 10.1016/j.camwa.2025.11.018
Ruonan Cao , Nianyu Yi
In this paper, we present a second order, linear, fully decoupled, and unconditionally energy stable scheme for solving the Erickson-Leslie model. This approach integrates the pressure correction method with a scalar auxiliary variable technique. We rigorously demonstrate the unconditional energy stability of the proposed scheme. Furthermore, we present several numerical experiments to validate its convergence order, stability, and computational efficiency.
{"title":"A linear, unconditionally stable, second order decoupled method for the Ericksen-Leslie model with SAV approach","authors":"Ruonan Cao , Nianyu Yi","doi":"10.1016/j.camwa.2025.11.018","DOIUrl":"10.1016/j.camwa.2025.11.018","url":null,"abstract":"<div><div>In this paper, we present a second order, linear, fully decoupled, and unconditionally energy stable scheme for solving the Erickson-Leslie model. This approach integrates the pressure correction method with a scalar auxiliary variable technique. We rigorously demonstrate the unconditional energy stability of the proposed scheme. Furthermore, we present several numerical experiments to validate its convergence order, stability, and computational efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 52-70"},"PeriodicalIF":2.5,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796144","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 : 2025-12-16DOI: 10.1016/j.camwa.2025.12.001
Jinhua Lu , Nikolaus A. Adams
The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-based macroscopic equations of LBM-IF are derived. Numerical investigations demonstrate that discretized equations can achieve even better numerical stability than the single-relaxation-time LBM-IF. It is concluded that the good numerical stability of LBM-IF can be roughly interpreted as the entropy increase of the collision step and the diffusion process of the streaming step. However, the discretized non-equilibrium-moments-based macroscopic equations are found to have significant numerical errors at a fixed Reynolds number and very small kinematic viscosities. By combining the non-equilibrium-moments-based and equilibrium-moments-based macroscopic equations, the paper proposes a hybrid model that achieves good numerical stability and accuracy for both small and large kinematic viscosities, even for inviscid flow. The deviation term in the recovered momentum equation of LBM-IF can be easily removed in the hybrid model. Compared with LBM-IF, finite difference/volume solvers based on the hybrid model exhibit better numerical stability and accuracy, as well as superior efficiency in simulations using nonuniform meshes.
{"title":"Macroscopic reconstruction of the lattice Boltzmann model for incompressible flows","authors":"Jinhua Lu , Nikolaus A. Adams","doi":"10.1016/j.camwa.2025.12.001","DOIUrl":"10.1016/j.camwa.2025.12.001","url":null,"abstract":"<div><div>The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-based macroscopic equations of LBM-IF are derived. Numerical investigations demonstrate that discretized equations can achieve even better numerical stability than the single-relaxation-time LBM-IF. It is concluded that the good numerical stability of LBM-IF can be roughly interpreted as the entropy increase of the collision step and the diffusion process of the streaming step. However, the discretized non-equilibrium-moments-based macroscopic equations are found to have significant numerical errors at a fixed Reynolds number and very small kinematic viscosities. By combining the non-equilibrium-moments-based and equilibrium-moments-based macroscopic equations, the paper proposes a hybrid model that achieves good numerical stability and accuracy for both small and large kinematic viscosities, even for inviscid flow. The deviation term in the recovered momentum equation of LBM-IF can be easily removed in the hybrid model. Compared with LBM-IF, finite difference/volume solvers based on the hybrid model exhibit better numerical stability and accuracy, as well as superior efficiency in simulations using nonuniform meshes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 24-51"},"PeriodicalIF":2.5,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784756","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 : 2025-12-15DOI: 10.1016/j.camwa.2025.11.024
El Hadji S. Diop
In this work we propose multiplicative image denoising methods that are based on variational methods and topological shape optimization techniques. First, we extend a total variation-based multiplicative denoising approach to the W1,p Sobolev space using the p-Dirichlet integral as a regularizer. We then formulate the new denoising problem as a topological shape optimization problem, which is solved using a generalized adjoint method. We propose a nonlocal denoising method that works on patch-by-patch basis thanks to the useful information given by the topological sensitivity, which is explicitly provided. Obtained numerical experiments on speckled and SAR images show neat qualitative and quantitative improvements of the proposed methods, especially in very noisy environments. Results show that the nonlocal method performs better than other denoising approaches in comparison.
{"title":"Nonlocal multiplicative denoising method based on variational approach and topological shape optimization","authors":"El Hadji S. Diop","doi":"10.1016/j.camwa.2025.11.024","DOIUrl":"10.1016/j.camwa.2025.11.024","url":null,"abstract":"<div><div>In this work we propose multiplicative image denoising methods that are based on variational methods and topological shape optimization techniques. First, we extend a total variation-based multiplicative denoising approach to the W<sup>1,<em>p</em></sup> Sobolev space using the p-Dirichlet integral as a regularizer. We then formulate the new denoising problem as a topological shape optimization problem, which is solved using a generalized adjoint method. We propose a nonlocal denoising method that works on patch-by-patch basis thanks to the useful information given by the topological sensitivity, which is explicitly provided. Obtained numerical experiments on speckled and SAR images show neat qualitative and quantitative improvements of the proposed methods, especially in very noisy environments. Results show that the nonlocal method performs better than other denoising approaches in comparison.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 1-23"},"PeriodicalIF":2.5,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753834","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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