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

Convexification for a coefficient inverse problem for a system of two coupled nonlinear parabolic equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-09 DOI: 10.1016/j.camwa.2024.12.004

Michael V. Klibanov, Jingzhi Li, Zhipeng Yang

引用次数: 0

The mechanism analysis of the oscillatory flow of Oldroyd-B fluid in a tube with a right triangular cross-section

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-06 DOI: 10.1016/j.camwa.2024.12.001

Lin Liu, Sen Zhang, Lang Liu, Chiyu Xie, Lixiu Wang, Yijia Liu, Jing Zhu, Libo Feng

{"title":"The mechanism analysis of the oscillatory flow of Oldroyd-B fluid in a tube with a right triangular cross-section","authors":"Lin Liu, Sen Zhang, Lang Liu, Chiyu Xie, Lixiu Wang, Yijia Liu, Jing Zhu, Libo Feng","doi":"10.1016/j.camwa.2024.12.001","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.001","url":null,"abstract":"This paper considers the oscillatory flow of the Oldroyd-B fluid in a tube with a right triangular cross-section. The partial differential equation for describing the unidirectional flow of Oldroyd-B fluid is derived. For treating the triangular region, the unstructured mesh finite element method is applied. For verifying the accuracy of the finite element method, the source term is introduced and the exact solution is constructed. We obtain an analytical solution for the isosceles triangular cross-section tube and analyze the effects of different parameters on the velocity amplitude and phase difference of the Oldroyd-B fluid flow. In addition, the dynamic characteristics for the unsteady-state Oldroyd-B fluid flow are discussed and the influence of the involved parameters, such as the pressure gradient, the relaxation and retardation time parameters on the velocity distribution are also investigated and the flow mechanism is analyzed graphically. At the same condition, we find that only the tube with an isosceles right triangle cross-section can produce the oscillatory flow. Finally, the fluid mechanism between the Newtonian fluid and the Oldroyd-B fluid for special cases is analyzed and discussed in detail.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"21 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804451","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

Sparse tensor product finite elements for two scale elliptic and parabolic equations with discontinuous coefficients

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-06 DOI: 10.1016/j.camwa.2024.11.018

Chen Hui Pang, Viet Ha Hoang

{"title":"Sparse tensor product finite elements for two scale elliptic and parabolic equations with discontinuous coefficients","authors":"Chen Hui Pang, Viet Ha Hoang","doi":"10.1016/j.camwa.2024.11.018","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.11.018","url":null,"abstract":"The paper develops the essentially optimal sparse tensor product finite element method for solving two scale elliptic and parabolic problems in a domain <mml:math altimg=\"si1.svg\"><mml:mi>D</mml:mi><mml:mo>⊂</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math>, <mml:math altimg=\"si2.svg\"><mml:mi>d</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:math>, which is embedded with a periodic array of inclusions of microscopic sizes and spacing. The two scale coefficient is thus discontinuous in the fast variable. We obtain approximations for the solution of the homogenized equation and the scale interaction term, i.e. all the macroscopic and microscopic information, within a prescribed level of accuracy, using only an essentially optimal number of degrees of freedom, which is equal (apart from a possible logarithmic factor) to that required to solve one macroscopic scale problem in <ce:italic>D</ce:italic>. This is achieved by solving the two scale homogenized problem, and utilizing the regularity of the scale interaction term in all the slow and fast variables at the same time. However, unlike problems considered in the literature (e.g. Hoang and Schwab, 2004/05 <ce:cross-ref ref>[16]</ce:cross-ref>), the scale interaction term is only piecewise regular in the fast variable. We employ the discretization schemes developed for interface problems (Chen and Zou, 1998 <ce:cross-ref ref>[6]</ce:cross-ref>, and Li et al., 2010 <ce:cross-ref ref>[20]</ce:cross-ref>) for the fast variable. Numerical correctors are developed from the finite element solutions with errors in terms of the finite element mesh size and the microscopic scale. Numerical examples that verify the theoretical convergence rates of the sparse tensor product finite elements are presented.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"2 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804452","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

Partitioned time stepping method for time-fractional Stokes-Darcy model with the Beavers-Joseph-Saffman interface conditions

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-05 DOI: 10.1016/j.camwa.2024.11.033

Yuting Xiang, Haibiao Zheng

引用次数: 0

Finding minimal cubature rules for finite elements passing the patch test

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-05 DOI: 10.1016/j.camwa.2024.11.030

Weizhu Wang, Stefanos-Aldo Papanicolopulos

引用次数: 0

In-plane vibration analysis of elastically restrained FGM skew plates using variational differential quadrature method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-03 DOI: 10.1016/j.camwa.2024.11.026

C. Li, S. Li, Y.M. Zhang, J.W. Cai, S.K. Lai

{"title":"In-plane vibration analysis of elastically restrained FGM skew plates using variational differential quadrature method","authors":"C. Li, S. Li, Y.M. Zhang, J.W. Cai, S.K. Lai","doi":"10.1016/j.camwa.2024.11.026","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.11.026","url":null,"abstract":"This work presents an accurate in-plane vibration analysis of functionally graded material (FGM) skew plates with elastically restrained boundaries using the variational differential quadrature method (VDQM). The weak form of the governing equations is derived by integrating two-dimensional elasticity theory with Hamilton's principle. The differential and integral operators are directly converted into matrix forms, thereby removing the necessity for higher-order derivative approximations in the displacement field. Transformation matrices are then developed for both interior and boundary nodes to link the governing equations with the boundary conditions, leading to the formulation of the vibration eigenvalue equations for FGM skew plates. Various factors, including aspect ratios, skew angles, boundary restraints, and gradient indices, are considered to investigate the in-plane vibration mode characteristics of FGM skew plates. Detailed solution procedures are provided, and numerical examples using the proposed solutions indicate that the VDQM exhibits superior numerical convergence and stability compared to other existing methods. The study also investigates the influence of highly skewed plates (75°), where stress singularities arise at the corners. This aspect is crucial for in-plane vibration analysis and has garnered limited attention in the existing literature. Furthermore, the dynamic analysis of FGM skew plates reveals a coupling between normal and tangential vibration modes.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"24 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762994","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

Meshfree methods for nonlinear equilibrium radiation diffusion equation with interface and discontinuous coefficient

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-03 DOI: 10.1016/j.camwa.2024.11.029

Haowei Liu, Zhiyong Liu, Qiuyan Xu, Jiye Yang

{"title":"Meshfree methods for nonlinear equilibrium radiation diffusion equation with interface and discontinuous coefficient","authors":"Haowei Liu, Zhiyong Liu, Qiuyan Xu, Jiye Yang","doi":"10.1016/j.camwa.2024.11.029","DOIUrl":"10.1016/j.camwa.2024.11.029","url":null,"abstract":"<div><div>The partial differential equation describing equilibrium radiation diffusion is strongly nonlinear, which has been widely utilized in various fields such as astrophysics and others. The equilibrium radiation diffusion equation usually appears over multiple complicated domains, and the material characteristics vary between each domain. The diffusion coefficient near the interface is discontinuous. In this paper, the equilibrium radiation diffusion equation with discontinuous diffusion coefficient will be solved numerically by the unsymmetric radial basis function collocation method. The energy term <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> is linearized by utilizing the Picard-Newton and Richtmyer linearization methods on the basis of the fully implicit scheme discretization. And the successive permutation iteration and direct linearization methods are applied to linearize the diffusion terms. The accuracy of the proposed methods is proved by numerical experiments for regular and irregular domains with different types of interfaces.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"178 ","pages":"Pages 108-135"},"PeriodicalIF":2.9,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758959","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 graded mesh technique for numerical approximation of a multi-term Caputo time-fractional Fokker-Planck equation in 2D space

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-02 DOI: 10.1016/j.camwa.2024.11.031

Pradip Roul, Trishna Kumari, Sameer N. Khandagale

引用次数: 0

A semi-analytic collocation technique for solving 3D anomalous non-linear thermal conduction problem associated with the Caputo fractional derivative

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-30 DOI: 10.1016/j.camwa.2024.11.032

Farzaneh Safari , Yanjun Duan

引用次数: 0

Quasi-Newton iterative solution approaches for nonsmooth elliptic operators with applications to elasto-plasticity 非光滑椭圆算子的准牛顿迭代求解方法及其在弹塑性中的应用