Computers & Mathematics with Applications最新文献_第2页

Time-space fractional anisotropic diffusion equations for multiplicative noise removal

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-19 DOI: 10.1016/j.camwa.2025.02.006

Kexin Sun, Minfu Feng

{"title":"Time-space fractional anisotropic diffusion equations for multiplicative noise removal","authors":"Kexin Sun, Minfu Feng","doi":"10.1016/j.camwa.2025.02.006","DOIUrl":"10.1016/j.camwa.2025.02.006","url":null,"abstract":"<div><div>In this paper, we propose a nonlinear time-space fractional diffusion model to remove the multiplicative gamma noise. This model incorporates Caputo time-fractional derivative into the existing space-fractional diffusion models. It leverages the memory effect of time-fractional derivatives to control the diffusion process, achieving a balance between edge preservation, texture retention and denoising effects. To establish the solvability of the proposed model, an auxiliary time-space fractional diffusion problem is first constructed, and the existence and uniqueness of its weak solution are proven using the Faedo-Galerkin method. Based on this, the existence and uniqueness of the weak solution for the proposed model are further confirmed via the Schauder fixed point theorem. Next, an explicit-implicit semi-discretization scheme is designed using Caputo fractional derivative with an order of <span><math><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></math></span> in time, and the stability of the semi-implicit scheme (<span><math><mi>λ</mi><mo>=</mo><mn>1</mn></math></span>) is proven, ensuring that <span><math><msub><mrow><mo>‖</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span>. For the fully discrete scheme, the more stable shifted Grünwald-Letnikov fractional derivative is used in space with an order of <span><math><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></math></span>. Finally, to verify the effectiveness of the model, numerical experiments are conducted on images with different noise levels and features, and compared with the existing diffusion equation models. The results demonstrate that the proposed model exhibits superior denoising performance while preserving edges and textures.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 1-28"},"PeriodicalIF":2.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444523","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

Analysis and simulation of sparse optimal control of the monodomain model

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-19 DOI: 10.1016/j.camwa.2025.02.008

Maria Robert , Suresh Kumar Nadupuri , Nagaiah Chamakuri

引用次数: 0

Conformal transformation solutions of the extended Motz problem

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-17 DOI: 10.1016/j.camwa.2025.02.007

Neville I. Robinson

引用次数: 0

Collocation-based numerical simulation of multi-dimensional nonlinear time-fractional Schrödinger equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-17 DOI: 10.1016/j.camwa.2025.02.002

Rong Huang , Zhifeng Weng , Jianhua Yuan

{"title":"Collocation-based numerical simulation of multi-dimensional nonlinear time-fractional Schrödinger equations","authors":"Rong Huang , Zhifeng Weng , Jianhua Yuan","doi":"10.1016/j.camwa.2025.02.002","DOIUrl":"10.1016/j.camwa.2025.02.002","url":null,"abstract":"<div><div>This paper introduces meshless and high-precision barycentric interpolation collocation methods, grounded in two well-established difference formulas, for solving the nonlinear time-fractional Schrödinger equation. This equation is characterized by complexity arising from power-law nonlinearity and multi-scale time dependence. To enhance spatial accuracy, we utilize two meshless barycentric interpolation collocation methods that exhibit exponential convergence in the spatial domain. After discretizing the spatial variables, we discretize the Caputo derivative using both the classical L1 formula and a related fast algorithm that incorporates the sum-of-exponentials technique. The nonlinear term is addressed through an explicit scheme augmented with a second-order stabilization term. Consequently, we derive fully discrete schemes capable of numerically solving the equation. Furthermore, we undertake comprehensive consistency analyses of the semi-discretized schemes in the spatial dimension, along with analyses of the nonlinear fully discretized schemes, leveraging the approximation properties of the collocation methods. Our numerical simulations, encompassing one, two, and three dimensions, conclusively demonstrate the remarkable accuracy and efficiency of the proposed collocation methods. Moreover, by comparing the error with that of a traditional finite difference method, we showcase that our schemes offer superior accuracy while requiring fewer nodes, thereby emphasizing their advantageous characteristics.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 214-233"},"PeriodicalIF":2.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428908","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

Unconditionally stable numerical scheme for the 2D transport equation 二维输运方程的无条件稳定数值方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-14 DOI: 10.1016/j.camwa.2025.02.003

Bérénice Grec , Davor Kumozec , Yohan Penel

{"title":"Unconditionally stable numerical scheme for the 2D transport equation","authors":"Bérénice Grec , Davor Kumozec , Yohan Penel","doi":"10.1016/j.camwa.2025.02.003","DOIUrl":"10.1016/j.camwa.2025.02.003","url":null,"abstract":"<div><div>The main goal of this paper is to extend the numerical scheme for the transport equation described in previous works [Penel, 2012; Bernard et al., 2014] from one to two dimensional problems. It is based on the method of characteristics, which consists in solving two ordinary differential equations rather than a partial differential equation. Our scheme uses an adaptive 6-point stencil in order to reach second-order accuracy whenever it is possible, and preserves some essential physical properties of the equation, such as the maximum principle. The resulting scheme is proved to be unconditionally stable and to reach second-order accuracy. We show numerical examples with comparisons to the well known Essentially Non-Oscillatory (ENO) scheme [Shu, 1998], in order to illustrate the good properties of our scheme (order of convergence, unconditional stability, accuracy). Using a Gaussian initial condition, several test cases are considered, using a constant or a rotating velocity field, taking into account or not variable source terms. Also, a test is given that shows the possibility of applying the scheme in more realistic fluid mechanics case.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 275-290"},"PeriodicalIF":2.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422126","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

An ensemble-based efficient iterative method for uncertainty quantification of partial differential equations with random inputs 基于集合的高效迭代法，用于随机输入偏微分方程的不确定性量化

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-13 DOI: 10.1016/j.camwa.2025.02.001

Yuming Ba , Qiuqi Li , Zehua Li , Lingling Ma

{"title":"An ensemble-based efficient iterative method for uncertainty quantification of partial differential equations with random inputs","authors":"Yuming Ba , Qiuqi Li , Zehua Li , Lingling Ma","doi":"10.1016/j.camwa.2025.02.001","DOIUrl":"10.1016/j.camwa.2025.02.001","url":null,"abstract":"<div><div>In this paper, an ensemble-based efficient iterative method is used to solve the partial differential equations (PDEs) with random inputs. The aim of the efficient iterative method is to get a good approximation of the Galerkin solution for PDEs with random inputs. An essential ingredient of the proposed method is to construct the decomposition of stochastic functions, involving parameter-independent and parameter-dependent. The parameter-dependent term can affect the computation efficiency and approximation accuracy. In order to decrease the computation cost, the efficient iterative method by the decomposition is performed by a fixed-point iterative manner. The computation of the efficient iterative method decomposes into offline phase and online phase. The parameter-independent matrices can be precomputed and stored in offline stage. At online stage, a group of numerical simulations is simultaneously calculated in each iterative step. For the parameter identification, the proposed inversion method combines the advantages of the ensemble-based efficient iterative method and ensemble filtering. Then four models with random inputs are considered to formulate the details and methodologies of the proposed method. To illustrate the computation efficiency and approximation accuracy, the results of the efficient iterative method are compared with the model order reduction methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 256-274"},"PeriodicalIF":2.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394583","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

Analysis on the force evaluation by the momentum exchange method and a localized refilling scheme for the lattice Boltzmann method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-12 DOI: 10.1016/j.camwa.2025.01.029

Shuai Wang , Xinnan Wu , Cheng Peng , Songying Chen , Hao Liu

{"title":"Analysis on the force evaluation by the momentum exchange method and a localized refilling scheme for the lattice Boltzmann method","authors":"Shuai Wang , Xinnan Wu , Cheng Peng , Songying Chen , Hao Liu","doi":"10.1016/j.camwa.2025.01.029","DOIUrl":"10.1016/j.camwa.2025.01.029","url":null,"abstract":"<div><div>The momentum exchange method (MEM) is widely used to calculate hydrodynamic forces on solid particles in the lattice Boltzmann method. Although MEM achieves second-order accurate force computation on particles with appropriate bounce-back schemes, significant numerical fluctuations can occur when particle moves relative to the mesh lines. In this work, we extend the recent analysis of Dong et al. <span><span>[1]</span></span> from static flat walls to moving curved walls to examine the forces computed using MEM with different bounce-back schemes. This analysis reveals Galilean variance errors in the conventional MEM and identifies a primary source of force fluctuations due to the time-dependent distance between boundary nodes and the solid surface. Inspired by these findings, we propose a localized “refilling” scheme to initialize distribution functions on newly uncovered fluid nodes as solid objects move. Unlike existing refilling schemes, this local scheme requires no information from neighboring nodes, making it easier to implement and reducing data communication load in parallel computing. The force fluctuations with this new scheme are also significantly lower than those with existing alternatives.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 180-199"},"PeriodicalIF":2.9,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387700","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

Non-conforming generalized mixed element methods based on the volume coordinate system

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-10 DOI: 10.1016/j.camwa.2025.01.028

Jintao Zhou, Guanghui Qing

{"title":"Non-conforming generalized mixed element methods based on the volume coordinate system","authors":"Jintao Zhou, Guanghui Qing","doi":"10.1016/j.camwa.2025.01.028","DOIUrl":"10.1016/j.camwa.2025.01.028","url":null,"abstract":"<div><div>The computation accuracy of non-conforming isoparametric elements in the displacement finite element method remains suboptimal when confronted with serious mesh distortion. To improve this issue, the area coordinate system and the volume coordinate system method based on displacement were proposed in the last century. By adopting volume coordinates as local coordinates and integrating the advantages of the non-conforming mixed finite element method, which simultaneously handles displacement and stress boundary conditions, this paper proposes the Non-conforming Generalized Mixed Element Method based on the Volume Coordinate System (NGMVC). The local natural coordinates of the NGMVC maintain a linear relationship with the Cartesian coordinate system, ensuring insensitivity to mesh distortion. Moreover, the proposed method addresses the limitation that lacks stress analysis of the conventional univariate method. Consequently, it enhances the rationality of the finite element model and the accuracy of numerical results. In theory, the model is more rational and objective. The numerical results show that the NGMVC series elements have excellent stability and much superior accuracy compared to the conventional non-conforming displacement isoparametric elements when the mesh distortion is severe.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 236-255"},"PeriodicalIF":2.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378401","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 the Schrödinger eigenvalue problem

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-06 DOI: 10.1016/j.camwa.2025.01.035

Dibyendu Adak , Gianmarco Manzini , Jesus Vellojin

{"title":"Nonconforming virtual element method for the Schrödinger eigenvalue problem","authors":"Dibyendu Adak , Gianmarco Manzini , Jesus Vellojin","doi":"10.1016/j.camwa.2025.01.035","DOIUrl":"10.1016/j.camwa.2025.01.035","url":null,"abstract":"<div><div>This study presents an in-depth analysis of the nonconforming virtual element method (VEM) as a novel approach for approximating the eigenvalues of the Schrödinger equation. Central to the strategy is deploying the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> projection operator to discretize potential terms within the model problem. Through compact operator theory, we rigorously establish the methodology's capability to achieve double-order convergence rates for the eigenvalue spectrum. Addressing the challenge posed by the nonconformity of the discrete space, we redefine the solution operator on a weaker space, which aligns with the Babuška-Osborn compactness framework. A comprehensive set of numerical experiments confirms the theoretical findings, showing the approximation qualities and computational efficiency of the method. A series of potential functions are used to illustrate the various challenges behind the choice of a potential for the simulation of the Schrödinger eigenvalue problem. These results confirm the potential of the nonconforming VEM as a robust and accurate tool for quantum mechanical eigenvalue problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 213-235"},"PeriodicalIF":2.9,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143275616","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 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