Computers & Mathematics with Applications最新文献_第9页

The two-grid decoupled method for hybrid-dimensional fracture models based on the discontinuous Galerkin method 基于不连续Galerkin方法的混合维裂缝模型双网格解耦方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.029

Shuangshuang Chen, Yuna Xu, Longchao Jin

{"title":"The two-grid decoupled method for hybrid-dimensional fracture models based on the discontinuous Galerkin method","authors":"Shuangshuang Chen, Yuna Xu, Longchao Jin","doi":"10.1016/j.camwa.2025.07.029","DOIUrl":"10.1016/j.camwa.2025.07.029","url":null,"abstract":"<div><div>In this paper, we consider a kind of hybrid-dimensional fracture models, in which fractures are treated as <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional objects in a <em>n</em>-dimensional porous medium, and the interaction between fractures and surrounding domain is taken into account. For the model with one single fracture, the discontinuous Galerkin (DG) method is firstly proposed, and the optimal order error estimate in the discrete <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm for the pressure is derived. Moreover, a two-grid decoupled method is considered, which uses a coarse grid rough approximations of the interface variables to decouple the mixed domain problem on a fine grid, and the optimal error estimate is also analyzed. The proposed DG method and two-grid decoupled method are then extended to a model with complex intersecting fractures, as well as the corresponding theoretical analysis. Numerical examples with both one single fracture and intersecting fractures are all presented to verity the accuracy of the considered methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 296-321"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A posteriori error estimates for the DD+L2 jumps method on the neutron diffusion equations 中子扩散方程DD+L2跳变方法的后验误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-28 DOI: 10.1016/j.camwa.2025.07.026

Patrick Ciarlet , Minh Hieu Do , Mario Gervais , François Madiot

引用次数: 0

Equilibrated flux a posteriori error estimates and adaptivity for nonlinear and doubly degenerate elliptic problems 非线性和双退化椭圆型问题的平衡通量、后验误差估计和自适应

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-25 DOI: 10.1016/j.camwa.2025.07.019

Elyes Ahmed , Saber Amdouni

{"title":"Equilibrated flux a posteriori error estimates and adaptivity for nonlinear and doubly degenerate elliptic problems","authors":"Elyes Ahmed , Saber Amdouni","doi":"10.1016/j.camwa.2025.07.019","DOIUrl":"10.1016/j.camwa.2025.07.019","url":null,"abstract":"<div><div>In this work, we establish a posteriori error analysis for a class of nonlinear and doubly degenerate elliptic equations, including the Stefan problem and both fast and slow diffusion in porous media. Our analysis leverages equilibrated flux reconstructions, yielding guaranteed and fully computable upper bounds on an energy-type error norm with local efficiency. These bounds are fully computable and robust, remaining unaffected by the degree of nonlinearity and degeneracy. The proposed estimators steer an adaptive solver that dynamically switches between nonlinear solvers to optimize iterations. The adaptive algorithm addresses discretization, regularization, and linearization errors. When Newton's method encounters convergence failures, the algorithm adaptively switches to the L-scheme solver. This solver precomputes the stabilization parameter <span><math><mi>L</mi><mo>></mo><mn>0</mn></math></span> in an offline phase to approximate the Jacobian. The efficiency of the adaptive algorithm is demonstrated through four prototypical examples, showcasing its effective error control and significant computational savings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 239-264"},"PeriodicalIF":2.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703834","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

Solving the second kind Volterra-Fredholm type of two-dimensional integral equations on non-rectangular domains via radial basis functions 利用径向基函数求解非矩形域上第二类Volterra-Fredholm型二维积分方程

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-25 DOI: 10.1016/j.camwa.2025.07.027

Mohsen Jalalian , Manochehr Kazemi , Mohammad Esmael Samei

引用次数: 0

Performance of a vertex-centred block-coupled finite volume methodology for small-strain static elastoplasticity 点心块耦合有限体积方法的小应变静态弹塑性性能

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-24 DOI: 10.1016/j.camwa.2025.07.020

Federico Mazzanti , Philip Cardiff

引用次数: 0

Nonlinear PDE model for pricing European options with transaction costs under the 3/2 non-affine stochastic volatility model 3/2非仿射随机波动率模型下具有交易费用的欧式期权定价的非线性PDE模型

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI: 10.1016/j.camwa.2025.07.014

Jianguo Tan , Jiling Cao

引用次数: 0

Denoising algorithm of the modified Gray-Scott model on non-uniform grids 改进Gray-Scott模型在非均匀网格上的去噪算法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI: 10.1016/j.camwa.2025.07.016

Shanshan Ge , Jian Wang

{"title":"Denoising algorithm of the modified Gray-Scott model on non-uniform grids","authors":"Shanshan Ge , Jian Wang","doi":"10.1016/j.camwa.2025.07.016","DOIUrl":"10.1016/j.camwa.2025.07.016","url":null,"abstract":"<div><div>This paper introduces an denoising algorithm based on the Gray-Scott (GS) model, which adopts non-uniform grids and highly adaptive numerical strategy to achieve effective denoising for two-dimensional (2D) and three-dimensional (3D) models. This method adjusts the grid density based on regional characteristics: dense grids are used in the area of interest to improve local accuracy, and sparse grids are used in non-critical areas to enhance the overall computational efficiency. In order to enhance the robustness and shape preserving ability, we modify the original GS model by replacing <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mi>v</mi></math></span> with <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>v</mi><mo>−</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, which effectively relives the volume shrinkage and shape distortion problems, and achieves the retention of structural details and effective suppression of noise. Numerical experiments show that our algorithm can maintain key geometric features while improving the smoothness, and has excellent denoising performance and extensive applicability.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 191-211"},"PeriodicalIF":2.9,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686130","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 energy gradient stable numerical scheme for Cahn–Hilliard equation with high-order degenerate mobility 具有高阶退化迁移率的Cahn-Hilliard方程的无条件能量梯度稳定数值格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI: 10.1016/j.camwa.2025.07.012

Gyeonggyu Lee , Seunggyu Lee

引用次数: 0

NURBS-Divergence-Meshless (NDM) method nurbs -发散-无网格（NDM）方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.011

N. Rasin , H. Hirol , A.R. Zainal Abidin , M.H. Mokhtaram , M.A. Mohd Noor , A.Y. Mohd Yassin

{"title":"NURBS-Divergence-Meshless (NDM) method","authors":"N. Rasin , H. Hirol , A.R. Zainal Abidin , M.H. Mokhtaram , M.A. Mohd Noor , A.Y. Mohd Yassin","doi":"10.1016/j.camwa.2025.07.011","DOIUrl":"10.1016/j.camwa.2025.07.011","url":null,"abstract":"<div><div>In this study, we present a new formulation that applies the divergence theorem within the NURBS parameter space to discretize governing equations using meshless techniques. We refer to this method as the NURBS-Divergence-Meshless (NDM) method. In this method, NURBS not only represents the domain exactly but also simplifies both the expression and the process of line integration, benefiting from the rectangular structure of the parameter space.</div><div>The primary advantage of NDM lies in its use of the divergence theorem, which simplifies the discretization of governing equations by ensuring that the line integral yields the required number of equations. It also enables the direct imposition of boundary conditions in interpolation schemes lacking the Kronecker delta property, such as moving least squares (MLS).</div><div>To illustrate the foundational concept, the discretization and solution of a simple scalar problem are presented. The equation is discretized using either the MLS or radial basis function (RBF) interpolation, with the divergence theorem providing the resulting algebraic equations. Convergence studies show that the non-overlapping NDM-MLS performs best, exhibiting all the anticipated favorable characteristics.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"196 ","pages":"Pages 151-171"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679050","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 adaptive conforming mixed method with high-order elements for clustered eigenvalues of the Helmholtz transmission problem with index of refraction n(x)=1 折射率为n(x)=1的亥姆霍兹传输问题聚类特征值的高阶元自适应协调混合方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-22 DOI: 10.1016/j.camwa.2025.07.017

Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang

引用次数: 0