Computers & Mathematics with Applications最新文献_第7页

Artificial Neural Network-Based Parameter Estimation in Lattice Boltzmann Simulations of MHD Nanofluid Natural Convection with Oscillating Wall Temperature 基于人工神经网络的MHD纳米流体自然对流振荡壁温晶格Boltzmann模拟参数估计

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-27 DOI: 10.1016/j.camwa.2025.12.020

C Venkata Lakshmi , Anuradha Aravapalli , K Venkatadri , Hakan F. Öztop

This study investigates magnetohydrodynamic natural convection of nanofluids in a square cavity subjected to sinusoidally varying thermal boundary conditions along the bottom wall. Understanding such flows is important for applications in thermal management, energy systems, and materials processing. The problem is solved using the lattice Boltzmann method coupled with an artificial neural network model to accelerate prediction of heat transfer responses. A comprehensive parametric analysis is performed for Rayleigh numbers up to

10^{6}

, Hartmann numbers up to 40, nanoparticle concentrations up to 4%, and a range of thermal wavelength parameters. The results show that the oscillatory thermal boundary significantly modifies flow structures and heat transfer characteristics: for example, at

R a = 10^{6}

and τ=0.5, the average Nusselt number is enhanced by nearly 28% compared with uniform heating, while strong magnetic damping (Ha=40) reduces it by about 35%. The neural network model reproduces LBM results with prediction errors below 2%, offering rapid estimation of Nusselt numbers across the studied parameter space. The novelty of this work lies in combining a high-fidelity lattice Boltzmann solver with data-driven prediction to study magnetically controlled nanofluid convection under oscillatory heating, an area not previously addressed in the literature. These findings provide new insights into the manipulation of convective transport in multiphysics thermal systems.

本文研究了沿底壁沿正弦变化的热边界条件下方形腔内纳米流体的磁流体力学自然对流。了解这种流动对于热管理、能源系统和材料加工的应用非常重要。采用晶格玻尔兹曼方法结合人工神经网络模型来加速传热响应的预测。一个全面的参数分析进行瑞利数高达106，哈特曼数高达40，纳米颗粒浓度高达4%，和热波长参数的范围。结果表明，振荡热边界显著改变了流动结构和换热特性：例如，在Ra=106和τ=0.5时，平均努塞尔数比均匀加热时提高了近28%，而强磁阻尼（Ha=40）使努塞尔数降低了约35%。神经网络模型以低于2%的预测误差再现LBM结果，在所研究的参数空间中提供对努塞尔数的快速估计。这项工作的新颖之处在于将高保真晶格玻尔兹曼解算器与数据驱动预测相结合，以研究振荡加热下的磁控纳米流体对流，这是以前文献中未涉及的领域。这些发现为多物理场热系统中对流输运的操纵提供了新的见解。

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引用次数: 0

Low-cost adaptive characteristic finite element method for incompressible natural convection problems 不可压缩自然对流问题的低成本自适应特征有限元方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-26 DOI: 10.1016/j.camwa.2025.12.008

Bowen Ren , Jilian Wu , Ning Li , Leilei Wei

This paper firstly adopt a novel low-complexity finite element method for incompressible natural convection problems, which is based on the characteristic finite element method (CFEM) and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method effectively addresses inherent limitations of the characteristic finite element method while retaining its essential advantages. By applying the TF to postprocess solutions obtained from the first-order characteristic finite element method (CFEM-1), we achieve a non-intrusive enhancement to existing code frameworks, boosting temporal accuracy by one order. Secondly, this paper constructs two error operators without increasing complexity, thus facilitating the construction of a new adaptive algorithm conveniently. Additionally, we consturct adaptive CFEM and adaptive CFEM plus TF. Subsequently, this paper proves the unconditional stability of the constant time stepsize CFEM plus TF. Lastly, numerical experiments presented to validate the theoretical analysis and substantiate the aforementioned propositions.

本文首先在特征有限元法（CFEM）的基础上，采用一种新的低复杂度有限元方法求解不可压缩自然对流问题，并通过引入时间滤波器（TF）技术实现了高阶精度。新方法有效地解决了特征有限元法固有的局限性，同时保留了特征有限元法的本质优势。通过将TF应用于从一阶特征有限元法（cfm -1）获得的后处理解，我们实现了对现有代码框架的非侵入性增强，将时间精度提高了一个阶。其次，本文在不增加复杂度的情况下构造了两个误差算子，方便了新的自适应算法的构造。此外，构造了自适应CFEM和自适应CFEM + TF。随后，证明了等时间步长CFEM + TF的无条件稳定性。最后，通过数值实验验证了理论分析，证实了上述结论。

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引用次数: 0

Linear high-order energy-conserving Hermite spectral schemes for three-dimensional Klein-Gordon-Schrödinger equations 三维Klein-Gordon-Schrödinger方程的线性高阶节能埃尔米特谱格式

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-25 DOI: 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.

在这项工作中，开发了一类新的线性化高阶能量守恒格式来模拟三维无界域中的耦合Klein-Gordon-Schrödinger方程。我们首先采用指数标量辅助变量（ESAV）方法将原始系统重新表述为等效系统。然后，我们构造了外推高斯配置方法对重构系统进行离散化，得到了一类具有高阶时间精度的半离散格式。利用厄米特-伽辽金谱法进行空间逼近。证明了完全离散格式满足原始能量的无条件保持。同时，该方法在每个时间步长只需要求解解耦的常系数线性系统，易于实现。为了在不牺牲精度的前提下进一步提高效率，提出了一种自适应时间步进策略。通过大量的数值试验证明了所提方案的精度、效率和保守性。此外，还对三维矢量孤子的非线性动力学进行了仿真，加深了对非线性KGS系统的理解。

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引用次数: 0

A fast compact ADI method for the generalized two-dimensional fractional Oldroyd-B type fluid model 广义二维分数阶Oldroyd-B型流体模型的快速紧凑ADI方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-24 DOI: 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

O (τ^{\min {3 - θ_{l}, 2 - γ_{s}, 2 - α}} + h_{x}^{4} + h_{y}^{4} + ϵ)

is constructed where θ_l, γ_s and α are orders of the Caputo fractional derivatives, τ, h_x and h_y 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.

本文提出了一种快速紧凑交替方向隐式（ADI）方法，用于求解涉及多项分数扩散和扩散波行为的广义二维分数阶Oldroyd-B型流体模型。利用快速L1方法和变量替换技术近似（0,1）和（1,2）的时间分数阶导数，以及空间四阶紧化格式近似空间导数和耦合时间分数阶空间导数，构造了收敛精度为O（τmin{3−θl,2−γs,2−α}+hx4+hy4+ λ）的快速紧化ADI方法，其中θl， γs和α为Caputo分数阶导数的阶数，τ， hx和hy为时间和空间步长。分别。用能量法对所提出的快速紧凑ADI方法进行了收敛性分析。通过两个算例验证了算法的时空收敛阶数，并以表格形式将收敛阶数和CPU时间与前人的结果进行了比较。数值实验结果验证了该方法的有效性。

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引用次数: 0

Geometry-independent spline boundary element method to analyze three-dimensional potential and elasticity problems 几何无关样条边界元法分析三维位势和弹性问题

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-24 DOI: 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.

在计算机辅助设计（CAD）与边界类型数值模拟相结合的研究中，常用的近似函数构造方法有非均匀有理b样条（NURBS）插值法和移动最小二乘（MLS）插值法。这些方法很难精确地执行边界条件，因为在它们的形状函数中缺乏Kronecker delta特性。为了解决这一限制，本文提出了一种与几何无关的样条边界元方法（GISBEM），该方法引入了一个变换矩阵来构造样条插值函数作为形状函数，从而可以直接应用类似于边界元方法（BEM）的边界条件。首先，引入了与几何无关的场近似（GIFT）概念，利用NURBS精确描述几何形状，利用b样条插值和变换矩阵逼近单元的场变量；其次，利用参数映射法推导了三维位势和弹性问题的计算格式。第三，利用变量之间的关系对单元进行边界点处变量的计算，后续处理类似于边界元法。最后，通过数值算例验证了所提方法的有效性和准确性。

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引用次数: 0

The mechanism analysis for the fractional quantum dynamics on a comb structure with the absorbing boundary conditions 具有吸收边界条件的梳状结构分数阶量子动力学机理分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-24 DOI: 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

x

-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.

本文研究了量子运动特征受几何约束的梳状结构上的量子输运，这种结构的量子运动只局限于沿x方向的主干上。本文不直接代入分数阶导数，而是利用波浪算子（SEWO）对二维Schrödinger方程进行数学推导，得到一维时间分数阶Schrödinger方程。用吸收边界条件（abc）代替了无限边界。建立了有限差分法，并进行了理论分析，证明了算法的稳定性和收敛性。为了提高计算效率，采用了快速方案。通过对源项进行创新，分析了数值解与精确解的对比。此外，还对abc和零边界条件下的分布进行了对比分析。结果表明，与零边界条件相比，abc提供了更精确的数值解。最后给出了模块的演化过程和不同参数下的相位图。

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引用次数: 0

Image restoration strategy stimulated level set model for segmenting images with strongly disturbance information 图像恢复策略刺激水平集模型对具有强干扰信息的图像进行分割

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-24 DOI: 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.

为了解决传统水平集方法在处理具有强干扰信息的图像时遇到的像素误分类、边界泄漏和分割模型不稳定等问题，本文在变分水平集框架中引入了一种基于类全局拟合项和变分去噪项的能量泛函。不仅显著提高了对严重强度非均匀图像的分割效果，而且有效地实现了图像的去噪和去模糊处理。具体而言，我们利用全局和类全局信息构建的拟合项来降低传统水平集方法对强度非均匀性的敏感性。同时，引入有界Hessian变分恢复项，有效抑制强噪声、阶梯伪影和模糊对分割的不良影响。此外，设计了一种新的边缘指示函数，增强了模型对图像弱边界的鲁棒性。在经典数据集上的实验结果表明，与现有的水平集方法相比，我们的模型在噪声抑制和边缘保存方面具有显著的优势。该模型的鲁棒性和可扩展性使其适用于广泛的图像分割场景。

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引用次数: 0

Hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis of functionally graded piezoelectric structures under hygrothermal environment 湿热环境下功能梯度压电结构的水热机电耦合非均匀等几何分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-22 DOI: 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.

功能梯度压电结构（FGPS）具有优异的压电效应和梯度分布特性，是设计和开发新型智能元件的核心结构之一。由于FGPS结构复杂，工作环境复杂，因此有必要提出一种有效的算法来解决FGPS的多物理场耦合问题。基于FGPS的结构特点，引入NURBS基函数，结合FGPS的本构方程和边界条件，提出了湿热机电耦合非齐次等几何分析（HTMEI-IGA），推导了HTMEI-IGA的控制方程和运动方程。采用子空间迭代法和Newmark法求解了FGPS在湿热场中的自由振动、瞬态响应和谐波响应。通过多个数值算例验证了HTMEI-IGA算法的收敛性和精度。研究了指数因子、水分和热量对FGPS结构的影响，为FGPS的设计和开发提供了新的手段。

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引用次数: 0

Analytic regularity of strong solutions for the complexified stochastic nonlinear Poisson-Boltzmann equation 复变随机非线性泊松-玻尔兹曼方程强解的解析正则性

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-22 DOI: 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.

非线性泊松-玻尔兹曼方程（nPBE）是静电学中的一个基本偏微分方程，广泛用于计算生物学和化学中溶剂或等离子体中的势场模型。本文研究了nPBE随机解在其系数随机变化下的统计不确定性的量化问题。由于实值nPBE的常规凸优化技术不能自然地扩展到复杂设置，我们使用收缩映射论证建立了复化nPBE解的存在唯一性。利用存在唯一性结果，我们证明了解在复超平面上的一个定义良好的区域上允许解析扩展。解析性使得对感兴趣的实值量的统计计算适用于稀疏网格等数值技术。稀疏网格被应用于统一近似解析函数，与结点数量相关的代数到次指数误差，从而允许高维积分的有效近似。我们的数值实验证实了预测的误差行为。

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引用次数: 0

A linear, unconditionally stable, second order decoupled method for the Ericksen-Leslie model with SAV approach 基于SAV方法的Ericksen-Leslie模型线性、无条件稳定、二阶解耦方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-12-21 DOI: 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.

本文给出了求解Erickson-Leslie模型的一种二阶、线性、完全解耦、无条件能量稳定格式。该方法将压力校正方法与标量辅助变量技术相结合。我们严格地证明了所提出方案的无条件能量稳定性。通过数值实验验证了该算法的收敛顺序、稳定性和计算效率。

引用次数: 0