Computers & Mathematics with Applications最新文献_第10页

Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networks 通过基于有限差分的无监督小型线性卷积神经网络解决椭圆和抛物问题

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-26 DOI: 10.1016/j.camwa.2024.08.013

Adrian Celaya , Keegan Kirk , David Fuentes , Beatrice Riviere

引用次数: 0

Discontinuous Galerkin methods for magnetic advection-diffusion problems 磁平流扩散问题的非连续伽勒金方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-26 DOI: 10.1016/j.camwa.2024.08.022

Jindong Wang, Shuonan Wu

引用次数: 0

A difference finite element method based on the conforming P1(x,y)×Q1(z,s) element for the 4D Poisson equation 基于符合 P1(x,y)×Q1(z,s)元素的差分有限元法，用于四维泊松方程

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-23 DOI: 10.1016/j.camwa.2024.08.016

Yaru Liu , Yinnian He , Dongwoo Sheen , Xinlong Feng

{"title":"A difference finite element method based on the conforming P1(x,y)×Q1(z,s) element for the 4D Poisson equation","authors":"Yaru Liu , Yinnian He , Dongwoo Sheen , Xinlong Feng","doi":"10.1016/j.camwa.2024.08.016","DOIUrl":"10.1016/j.camwa.2024.08.016","url":null,"abstract":"<div><p>This paper proposes a difference finite element method (DFEM) for solving the Poisson equation in the four-dimensional (4D) domain Ω. The method combines finite difference discretization based on the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-element in the third and fourth directions with finite element discretization based on the <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-element in the other directions. In this way, the numerical solution of the 4D Poisson equation can be transformed into a series of finite element solutions of the 2D Poisson equation. Moreover, we prove that the DFE solution <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> satisfies <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-stability, and the error function <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>−</mo><mi>u</mi></math></span> achieves first-order convergence under the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-error. Finally, we provide three numerical examples to verify the accuracy and efficiency of the method.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142047822","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 novel family of Q1-finite volume element schemes on quadrilateral meshes 四边形网格上的新型 Q1 有限体积元素方案系列

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-23 DOI: 10.1016/j.camwa.2024.08.019

Yanhui Zhou , Shuai Su

{"title":"A novel family of Q1-finite volume element schemes on quadrilateral meshes","authors":"Yanhui Zhou , Shuai Su","doi":"10.1016/j.camwa.2024.08.019","DOIUrl":"10.1016/j.camwa.2024.08.019","url":null,"abstract":"<div><p>A novel family of isoparametric bilinear finite volume element schemes are constructed and analyzed to solve the anisotropic diffusion problems on general convex quadrilateral meshes. These new schemes are obtained by employing a special quadrature rule to approximate the line integrals in classical <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-finite volume element method. The new quadrature rule is a linear combination of trapezoidal and midpoint rules, and the weights depend on a parameter <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span>. The novelty of this work is that, for any fully anisotropic diffusion tensor, we provide some specific <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> to ensure the coercivity result of the proposed schemes on arbitrary parallelogram, quasi-parallelogram, trapezoidal and some general convex quadrilateral meshes. More interesting is that, the parameter <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> can only involves the anisotropic diffusion tensor and the geometry of quadrilateral cell. An optimal <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> error estimate is also proved on quasi-parallelogram meshes. Finally, the theoretical findings are validated by several numerical examples.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049751","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

Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility 具有退化流动性的 Navier-Stokes-Cahn-Hilliard 系统的结构保持有限元方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-22 DOI: 10.1016/j.camwa.2024.08.003

Francisco Guillén-González , Giordano Tierra

引用次数: 0

Application of MUSIC-type imaging for anomaly detection without background information 应用 MUSIC 型成像技术进行无背景信息的异常检测

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-22 DOI: 10.1016/j.camwa.2024.08.015

Won-Kwang Park

{"title":"Application of MUSIC-type imaging for anomaly detection without background information","authors":"Won-Kwang Park","doi":"10.1016/j.camwa.2024.08.015","DOIUrl":"10.1016/j.camwa.2024.08.015","url":null,"abstract":"<div><p>It has been demonstrated that the MUltiple SIgnal Classification (MUSIC) algorithm is fast, stable, and effective for localizing small anomalies in microwave imaging. For the successful application of MUSIC, exact values of permittivity, conductivity, and permeability of the background must be known. If one of these values is unknown, it will fail to identify the location of an anomaly. However, to the best of our knowledge, no explanation of this failure has been provided yet. In this paper, we consider the application of MUSIC to the localization of a small anomaly from scattering parameter data when complete information of the background is not available. Thanks to the framework of the integral equation formulation for the scattering parameter data, an analytical expression of the MUSIC-type imaging function in terms of the infinite series of Bessel functions of integer order is derived. Based on the theoretical result, we confirm that the identification of a small anomaly is significantly affected by the applied values of permittivity and conductivity. However, fortunately, it is possible to recognize the anomaly if the applied value of conductivity is small. Simulation results with synthetic data are reported to demonstrate the theoretical result.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040155","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

Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation 非线性耦合构成关系模型的多重解及其在非平衡流动计算中的矫正

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-21 DOI: 10.1016/j.camwa.2024.08.017

Junzhe Cao , Sha Liu , Chengwen Zhong , Congshan Zhuo , Kun Xu

{"title":"Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation","authors":"Junzhe Cao , Sha Liu , Chengwen Zhong , Congshan Zhuo , Kun Xu","doi":"10.1016/j.camwa.2024.08.017","DOIUrl":"10.1016/j.camwa.2024.08.017","url":null,"abstract":"<div><p>In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the generalized hydrodynamic equations of Eu, and aims to describe rarefied flows. In the non-equilibrium regime, the NCCR equations are more reliable than the Navier-Stokes equations. And the NCCR equations have an advantage of efficiency over the discrete velocity methods and stochastic particle methods. However, the NCCR model is a complicated nonlinear system. Many assumptions have been used in the schemes for solving the NCCR equations. The corresponding numerical methods may be associated with unphysical solution and instability. At the same time, it is hard to analyze the physical accuracy and stability of NCCR model due to the uncertainties in the numerical discretization. In this study, a new numerical method for solving NCCR equations is proposed and used to analyze the properties of NCCR equations. More specifically, the nonlinear equations are converted into the solutions of an objective function of a single variable. Under this formulation, the multiple solutions of the NCCR system are identified and the criteria for picking up the physical solution are proposed. Therefore, a numerical scheme for solving NCCR equations is constructed. A series of flow problems in the near continuum and low transition regimes with a large variation of Mach numbers are conducted to validate the numerical performance of proposed method and the physical accuracy of NCCR model.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142044614","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

Linear stability analysis of a Couette-Poiseuille flow: A fluid layer overlying an anisotropic and inhomogeneous porous layer Couette-Poiseuille 流动的线性稳定性分析：各向异性和不均匀多孔层上的流体层

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-21 DOI: 10.1016/j.camwa.2024.08.006

Monisha Roy , Sukhendu Ghosh , G.P. Raja Sekhar

{"title":"Linear stability analysis of a Couette-Poiseuille flow: A fluid layer overlying an anisotropic and inhomogeneous porous layer","authors":"Monisha Roy , Sukhendu Ghosh , G.P. Raja Sekhar","doi":"10.1016/j.camwa.2024.08.006","DOIUrl":"10.1016/j.camwa.2024.08.006","url":null,"abstract":"<div><p>We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011466","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 symmetric multigrid-preconditioned Krylov subspace solver for Stokes equations 斯托克斯方程的对称多网格预处理克雷洛夫子空间求解器

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-21 DOI: 10.1016/j.camwa.2024.08.018

Yutian Tao, Eftychios Sifakis

{"title":"A symmetric multigrid-preconditioned Krylov subspace solver for Stokes equations","authors":"Yutian Tao, Eftychios Sifakis","doi":"10.1016/j.camwa.2024.08.018","DOIUrl":"10.1016/j.camwa.2024.08.018","url":null,"abstract":"<div><p>Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of the multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme <span><span>[1]</span></span>, and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020721","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

Approximation of one and two dimensional nonlinear generalized Benjamin-Bona-Mahony Burgers' equation with local fractional derivative 具有局部分数导数的一维和二维非线性广义本杰明-博纳-马霍尼布尔格斯方程的近似值

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-08-20 DOI: 10.1016/j.camwa.2024.07.032

Abdul Ghafoor , Manzoor Hussain , Danyal Ahmad , Shams Ul Arifeen

{"title":"Approximation of one and two dimensional nonlinear generalized Benjamin-Bona-Mahony Burgers' equation with local fractional derivative","authors":"Abdul Ghafoor , Manzoor Hussain , Danyal Ahmad , Shams Ul Arifeen","doi":"10.1016/j.camwa.2024.07.032","DOIUrl":"10.1016/j.camwa.2024.07.032","url":null,"abstract":"<div><p>This study presents, a numerical method for the solutions of the generalized nonlinear Benjamin-Bona-Mahony-Burgers' equation, with variable order local time fractional derivative. This derivative is expressed as a product of two functions, the usual integer order time derivative, and a function of time having a fractional exponent. Then, forward difference approximation is used for time derivative. The unknown solution of the differential problem and corresponding derivatives are estimated using Haar wavelet approximations (HWA). The collocation procedure is then implemented in HWA, to transform the given model to the system of linear algebraic equations for the determination of unknown constant coefficient of the Haar wavelet series, which update the derivatives and the numerical solutions. The sufficient condition is established for the stability of the proposed technique, and then verified computationally. To check the performance of the scheme, few illustrative examples in one and two dimensions along with <span><math><msub><mrow><mi>l</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> and <span><math><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> error norms are also given. Besides this, the computational convergence rate is calculated for both type equations. Additionally, computed solutions are compared with available results in literature. Simulations and graphical data discloses, that suggested scheme works well for such complex problems.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142013053","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