Computers & Mathematics with Applications最新文献

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Unconditionally energy-stable and accurate schemes based on hyperbolic tangent scalar auxiliary variable approach for gradient flows 基于双曲正切标量辅助变量方法的梯度流无条件能量稳定精确格式

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.camwa.2025.12.031

Haihong Zhou , Huan Zhang , Xiaomin Pan

In this paper, we extend the selection of auxiliary variables by proposing a hyperbolic tangent scalar auxiliary variable (tanh-SAV) approach for solving gradient flows. The proposed tanh-SAV schemes introduce an auxiliary variable based on the hyperbolic tangent function, providing a well-defined formulation that enables the construction of decoupled, linear, and efficient numerical schemes. We demonstrate the construction of first-order, second-order, and higher-order unconditionally energy-stable schemes, utilizing either the Crank–Nicolson method or a k-step backward differentiation formula for time discretization. Only one constant-coefficient equation needs to be solved per time step, and we prove that all resulting tanh-SAV schemes are uniquely solvable at each time level. Furthermore, the theoretical analysis demonstrates the discrete energy stability of the proposed numerical schemes and proves the positivity property of the auxiliary variable. For the tanh-SAV/BDFk schemes (

k = 2, 3, 4

) combined with a Fourier pseudo-spectral spatial discretization, we further establish fully discrete optimal-order error estimates. In addition, we provide numerical simulations of one- and two-dimensional Cahn–Hilliard, Allen–Cahn, and phase-field crystal models. The results demonstrate that, consistent with the theoretical analysis, the proposed schemes preserve the positivity of the auxiliary variable, maintain excellent stability, and achieve the desired temporal accuracy.

本文通过提出求解梯度流的双曲正切标量辅助变量法（tanh-SAV），扩展了辅助变量的选择。提出的tanh-SAV方案引入了一个基于双曲正切函数的辅助变量，提供了一个定义良好的公式，可以构建解耦、线性和高效的数值方案。我们利用Crank-Nicolson方法或k步后向微分公式进行时间离散，证明了一阶、二阶和高阶无条件能量稳定格式的构造。每个时间步只需要求解一个常系数方程，并证明了所有的tanh-SAV格式在每个时间水平上都是唯一可解的。理论分析进一步证明了所提数值格式的离散能量稳定性，并证明了辅助变量的正性。对于tanh-SAV/BDFk格式（k=2,3,4），结合傅里叶伪谱空间离散，我们进一步建立了完全离散的最优阶误差估计。此外，我们还提供了一维和二维Cahn-Hilliard， Allen-Cahn和相场晶体模型的数值模拟。结果表明，与理论分析一致，所提出的方案保留了辅助变量的正性，保持了良好的稳定性，并达到了期望的时间精度。

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引用次数: 0

Numerical methods and analysis for magnetohydrodynamics slip flow and heat transfer of Jeffrey nanofluid with tempered fractional constitutive relationship 具有回火分数本构关系的Jeffrey纳米流体磁流体力学、滑移流动和传热的数值方法与分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.camwa.2025.12.030

Wenxin Zheng , Fawang Liu , Shujuan Lü , Ian Turner , Libo Feng

In this work, the magnetohydrodynamic (MHD) flow and heat transfer for a Jeffrey nanofluid flowing over a semi-infinite plate subjected to slip effects is considered. Firstly, the standard constitutive equation of a Jeffrey fluid is generalized to incorporate the tempered fractional derivative to describe the nonlocal but finite relaxation process, which leads to a novel tempered momentum equation. Combined with a tempered energy equation, the coupled momentum and energy system of a Jeffrey nanofluid is formulated. Secondly, the Legendre spectral method is employed to the tempered fractional coupled model, in which the modified shifted Grünwald superconvergence formula is proposed to discretize the tempered fractional derivative. To enhance computational efficiency, a fast algorithm is further developed, for which the stability and convergence analysis are rigorously established. Finally, some numerical examples are performed to confirm the efficiency of the proposed numerical schemes and to investigate the impacts of important model parameters on the variations of fluid movement and thermal transfer.

本文研究了杰弗里纳米流体在受滑移效应影响的半无限平板上的磁流体动力学流动和传热问题。首先，将Jeffrey流体的标准本构方程进行推广，引入回火分数阶导数来描述非局部有限松弛过程，得到了新的回火动量方程；结合调质能量方程，建立了Jeffrey纳米流体的动量-能量耦合系统。其次，将Legendre谱法应用于回火分数阶耦合模型，提出了修正位移grengwald超收敛公式对回火分数阶导数进行离散化；为了提高计算效率，进一步开发了一种快速算法，并严格建立了算法的稳定性和收敛性分析。最后，通过数值算例验证了所提数值格式的有效性，并探讨了重要模型参数对流体运动和传热变化的影响。

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引用次数: 0

A FE-MIFVE method for three-dimensional (3D) elliptic interface problems 三维椭圆界面问题的FE-MIFVE方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.camwa.2026.01.003

Quanxiang Wang , Jianqiang Xie , Yu Zheng , Liqun Wang

In this paper, we propose a FE-MIFVE method for the solution of the three-dimensional elliptic interface problems on structured grids. The method uses the standard finite element discretization on regular elements, and uses the modified immersed finite volume element discretization on interface elements. By designing a suitable function which has the same jumps as the solution, we turn the original elliptic interface problem with nonhomogeneous jump conditions to be an elliptic interface problem with homogeneous jump conditions. Numerical experiments for various problems show the new proposed FE-MIFVE method can serve as an efficient field solver in a simulation on structured grids, such as predicting the electrostatics of solvated biomolecules.

本文提出了一种求解结构网格上三维椭圆界面问题的FE-MIFVE方法。该方法对规则单元采用标准有限元离散，对界面单元采用改进的浸入式有限体积单元离散。通过设计一个与解具有相同跳变的合适函数，将原具有非齐次跳变条件的椭圆界面问题转化为具有齐次跳变条件的椭圆界面问题。各种问题的数值实验表明，新提出的FE-MIFVE方法可以作为一种有效的现场求解器，用于结构化网格的模拟，如预测溶剂化生物分子的静电。

引用次数: 0

A generic framework for solving three-dimensional gas dynamics equations 求解三维气体动力学方程的通用框架

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.camwa.2026.01.005

Min Xiao , Xihua Xu

The aim of this study is to develop a generic framework to construct three-dimensional nodal solvers for Lagrangian cell-centered hydrodynamics. By utilizing the specific volume as a medium, a new relationship between pressure and velocity is derived to figure out the nodal velocity. The nodal control volume adheres to Newton’s first law, resulting in the compatible equation. This generic framework ensures conservation of total mass, total momentum, and total energy, and satisfies an entropy inequality. Furthermore, it can be reduced to well-known schemes such as GLACE (Godunov-type LAgrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian HYDrodynamics), demonstrating its versatility and ability to generate various multi-point schemes.

本研究的目的是开发一个通用框架来构建拉格朗日细胞中心流体动力学的三维节点求解器。利用比容作为介质，导出了压力与速度的新关系，求出了节点速度。节点控制体积遵循牛顿第一定律，得到相容方程。这个通用框架保证了总质量、总动量和总能量的守恒，并满足熵不等式。此外，它可以简化为众所周知的格式，如GLACE（对总能量保守的godunov型拉格朗日格式）和EUCCLHYD（显式非结构化细胞中心拉格朗日流体动力学），显示了它的多功能性和生成各种多点格式的能力。

引用次数: 0

An alternating approach for reconstructing the initial value and source term in a time-fractional diffusion-wave equation 一种交替重建时间分数扩散波方程初值和源项的方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-10 DOI: 10.1016/j.camwa.2026.01.004

Yun Zhang , Xiaoli Feng , Xiongbin Yan

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem by leveraging the asymptotic expansion of Mittag-Leffler functions. Subsequently, we decompose the inverse problem into two subproblems and introduce an alternating iteration reconstruction method, complemented by a regularization strategy. Additionally, a comprehensive convergence analysis for this method is provided. To solve the inverse problem numerically, we introduce two semidiscrete schemes based on standard Galerkin method and lumped mass method, respectively. Furthermore, we establish error estimates that are associated with the noise level, iteration step, regularization parameter, and spatial discretization parameter. Finally, we present several numerical experiments in both one-dimensional and two-dimensional cases to validate the theoretical results and demonstrate the effectiveness of our proposed method.

研究了时间分数阶扩散波方程中包含初始值和空间相关源项的同时反演问题。首先，利用Mittag-Leffler函数的渐近展开式，建立了逆问题的唯一性。随后，我们将反问题分解为两个子问题，并引入交替迭代重建方法，并辅以正则化策略。并对该方法进行了全面的收敛性分析。为了在数值上解决反问题，我们分别引入了基于标准伽辽金法和集总质量法的两种半离散格式。此外，我们建立了与噪声水平、迭代步长、正则化参数和空间离散化参数相关的误差估计。最后，我们在一维和二维情况下进行了数值实验来验证理论结果并证明了我们所提出方法的有效性。

引用次数: 0

Two-stage selective segmentation method based on exponential weighted geodesic distance driven model and thresholding method 基于指数加权测地线距离驱动模型和阈值法的两阶段选择性分割方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-10 DOI: 10.1016/j.camwa.2025.12.029

Zhi-Feng Pang , Xiaojie Peng , Bing Li , Hong Ge

Selective segmentation represents a pivotal image processing technique within the domain of computer vision. Its objective is to facilitate the precise identification and extraction of a region of interest (ROI) within an image, while excluding background regions that are irrelevant to the task at hand. Nevertheless, the challenge of segmentation for images with noise, particularly those with grayscale inhomogeneity, still exists in many state-of-the-art segmentation models. In order to address this challenge, this paper proposes a novel two-step selective segmentation method based on an exponential weighted geodesic distance-driven scheme and a thresholding method inspired by the K-means method. In particular, the exponential weighted geodesic distance is first leveraged to enhance the contrast between the ROI and the background. Subsequently, the segmentation of the ROI is obtained through thresholding on the enhanced image generated in the initial stage. The experimental results demonstrate the efficacy of the proposed method in suppressing the influence of noise and grayscale inhomogeneity to a certain extent. Furthermore, the results show that the proposed method yields a higher segmentation accuracy than several existing state-of-the-art variation-based selective segmentation models and two classical deep learning segmentation models.

选择性分割是计算机视觉领域的一项关键图像处理技术。它的目标是促进图像中感兴趣区域（ROI）的精确识别和提取，同时排除与手头任务无关的背景区域。然而，在许多最先进的分割模型中，对带有噪声的图像，特别是那些灰度不均匀的图像的分割仍然存在挑战。为了解决这一问题，本文提出了一种基于指数加权测地线距离驱动方案和受K-means方法启发的阈值分割方法的两步选择性分割方法。特别是，首先利用指数加权测地线距离来增强ROI和背景之间的对比度。随后，对初始阶段生成的增强图像进行阈值分割，得到ROI的分割。实验结果表明，该方法在一定程度上抑制了噪声和灰度不均匀性的影响。此外，研究结果表明，该方法比几种现有的基于变量的选择性分割模型和两种经典深度学习分割模型具有更高的分割精度。

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引用次数: 0

Mathematical relationships and novel extensions of MLPG variants MLPG变体的数学关系和新扩展

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-10 DOI: 10.1016/j.camwa.2026.01.001

Elham Gholamipour , Ahmad Shirzadi , Hossein Hosseinzadeh , Vladimir Sladek , Jan Sladek

While various Meshless Local Petrov-Galerkin (MLPG) method variants exist, primarily distinguished by their choice of test functions in local subdomains, the mathematical relationships among these approaches remain unexplored. This paper establishes rigorous connections between existing MLPG formulations and proposes novel extensions based on an analysis of test function smoothness. It is shown that MLPG5, which employs Heaviside step test functions, corresponds to the mean value of MLPG2 (the collocation method), while MLPG4, using logarithmic test functions, is proven equivalent to the mean value of MLPG5 over the radius of local subdomains. Building on these insights, a systematic framework for generating new MLPG variants is introduced by leveraging the smoothness properties of test functions. All existing and newly proposed MLPG variants are demonstrated to have local weak forms equivalent to the original strong-form equations. This equivalence establishes the unique solvability of the methods, addressing long-standing questions regarding their consistency. Comprehensive numerical experiments validate the theoretical findings, confirming both the inter-variant relationships and the robustness of the newly extended MLPG variants.

虽然存在各种无网格局部Petrov-Galerkin （MLPG）方法变体，主要通过在局部子域中选择测试函数来区分，但这些方法之间的数学关系仍未被探索。本文建立了现有MLPG公式之间的严格联系，并在分析测试函数平滑性的基础上提出了新的扩展。结果表明，采用Heaviside步长测试函数的MLPG5与配置法的MLPG2均值相对应，而采用对数测试函数的MLPG4与局部子域半径上的MLPG5均值相对应。在这些见解的基础上，通过利用测试函数的平滑特性，引入了一个用于生成新的MLPG变体的系统框架。所有现有的和新提出的MLPG变体都证明具有与原始强形式方程等效的局部弱形式。这种等价建立了方法的唯一可解性，解决了关于其一致性的长期问题。综合数值实验验证了理论发现，证实了新扩展的MLPG变体之间的关系和鲁棒性。

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引用次数: 0

Mathematical modeling of myocardial perfusion using lattice Boltzmann method 用晶格玻尔兹曼方法建立心肌灌注的数学模型

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-08 DOI: 10.1016/j.camwa.2025.12.005

Jan Kovář , Radek Fučík , Tarique Hussain , Munes Fares , Radomír Chabiniok

We propose a two-compartment mathematical model of myocardial perfusion, representing myocardial tissue at the arteriolar level. The model comprises a simplified two-dimensional geometrical analog of the complex three-dimensional myocardial vasculature. In the advective compartment, consisting of a 2D vasculature analog, fluid flow and contrast agent transport are governed by Navier-Stokes and system of advection-diffusion equations, respectively. The surrounding myocardium, included in porous capillary compartment and modeled as a porous medium, assumes purely diffusive transport without fluid flow. Contrast agent exchange occurs through the interface between the two compartments. The model is numerically solved using the lattice Boltzmann method, with GPU implementation enabling massive parallelization. Sample contrast agent profiles are analyzed for both healthy and defective tissues. The model’s capability to interpret actual MRI perfusion curves is evaluated using mathematical optimization techniques. Furthermore, the model is employed for a binary classification test to evaluate its agreement with the expert opinion of a qualified clinician. Myocardial blood flow approximations from the proposed model compare favorably to results from established medical software utilizing signal-deconvolution methods. Despite its simplifications, the 2D model accurately represents essential perfusion dynamics, matching or exceeding clinical software in agreement with expert evaluations. Although tested on a small number of patients, this proof of concept shows potential for direct application during perfusion exams or generating synthetic data for machine learning.

我们提出了心肌灌注的两室数学模型，代表心肌组织在小动脉水平。该模型包含复杂的三维心肌血管系统的简化二维几何模拟。在由二维脉管系统模拟组成的平流室中，流体流动和造影剂运输分别由Navier-Stokes方程和平流-扩散方程系统控制。周围的心肌，包括在多孔毛细血管室中，并模拟为多孔介质，假设纯扩散运输，没有流体流动。造影剂的交换通过两个隔室之间的界面进行。该模型采用晶格玻尔兹曼方法进行数值求解，GPU实现实现了大规模并行化。样本造影剂配置文件分析为健康和缺陷组织。该模型解释实际MRI灌注曲线的能力使用数学优化技术进行评估。此外，将该模型用于二元分类检验，以评估其与合格临床医生的专家意见的一致性。所提出的模型的心肌血流量近似与利用信号反卷积方法建立的医疗软件的结果相比较有利。尽管其简化，二维模型准确地表示基本灌注动力学，匹配或超过临床软件与专家的评估一致。尽管在少数患者身上进行了测试，但这一概念证明显示了在灌注检查或为机器学习生成合成数据时直接应用的潜力。

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引用次数: 0

On the numerical solution of high-dimensional PDEs arising in multi-asset options via a kernel-type solver 基于核解的多资产期权高维偏微分方程数值解

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-08 DOI: 10.1016/j.camwa.2025.12.027

Yanlai Song

In this study, we present a numerical framework founded on a specialized version of radial basis function-produced finite difference solvers, designed for application in both interpolation tasks and the computational solution of higher-dimensional PDEs arising in multi-asset options. The distinguishing feature of the proposed method lies in its utilization of integrated forms of a special power of the multiquadric kernel to construct novel derivative weights, thereby enhancing solution accuracy and robustness. The derivative approximations are obtained through the derivation of analytical expressions, which are then evaluated on stencils comprising both uniformly spaced and non-uniformly distributed nodes. These formulations are constructed to offer greater flexibility in handling a wide spectrum of discretization patterns. Numerical results are provided to support the theoretical discussions.

在这项研究中，我们提出了一个基于径向基函数生成的有限差分解的专门版本的数值框架，该框架旨在应用于插值任务和多资产选项中出现的高维偏微分方程的计算解决方案。该方法的显著特点在于利用多次二次核的特殊幂的积分形式来构造新的导数权值，从而提高了解的精度和鲁棒性。通过解析表达式的推导得到导数近似，然后在包含均匀分布和非均匀分布节点的模板上求值。这些公式的构造是为了在处理广泛的离散化模式时提供更大的灵活性。数值结果支持了理论讨论。

引用次数: 0

An hp-adaptive Galerkin least squares intrinsic finite element method for the convection-dominated problem on surfaces 曲面上对流占优问题的自适应Galerkin最小二乘内禀有限元法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-08 DOI: 10.1016/j.camwa.2025.12.026

Longyuan Wu , Xinlong Feng

We propose an hp-adaptive Galerkin least squares intrinsic finite element method for the stationary convection-reaction-diffusion equation on closed surfaces. The discrete variational formulation is intrinsic to the interpolated surface, incorporating the contribution of the local parametrization. This eliminates the reliance on pre-established surface parametrization and circumvents the challenge of high-order numerical integration in the space where the surface is embedded. The Galerkin least squares method, a variant of the streamline-upwind/Petrov-Galerkin method, is employed to enhance the stability of the numerical scheme. Unique solvability of the discrete variational problem is shown. To generate appropriate anisotropic mesh, an hp-adaptive refinement strategy is designed by combining the Galerkin least squares method with the quadratic intrinsic finite element method. The recovery function, based on centroid weights, yields more accurate estimates compared to area-weighted counterparts. Finally, numerical experiments show the effectiveness of the proposed method.

提出了一种求解闭表面上稳态对流-反应-扩散方程的自适应Galerkin最小二乘内禀有限元方法。离散变分公式是插值曲面固有的，包含了局部参数化的贡献。这消除了对预先建立的表面参数化的依赖，并规避了在表面嵌入的空间中进行高阶数值积分的挑战。采用流线迎风/Petrov-Galerkin方法的一种变体Galerkin最小二乘法来提高数值格式的稳定性。证明了离散变分问题的唯一可解性。为了生成合适的各向异性网格，将伽辽金最小二乘法与二次内禀有限元法相结合，设计了一种自适应优化策略。与面积加权函数相比，基于质心权重的恢复函数产生更准确的估计。最后，通过数值实验验证了该方法的有效性。

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