Engineering Analysis with Boundary Elements最新文献_第7页

A modified finite particle method with adaptive strategy for solving bilateral obstacle problems 基于自适应策略的修正有限粒子法求解双边障碍问题

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-02 DOI: 10.1016/j.enganabound.2025.106561

Dianjian Ruan , Zhanheng Chen , Daming Yuan

Bilateral obstacle problems are fundamental in the study of partial differential equations (PDEs) and variational inequalities, with significant applications in optimal control, elasticity, and material deformation under constraints. However, numerically solving these problems is challenging due to the inherent nonlinearities and the presence of free boundaries that evolve with complex contact dynamics. Conventional discretization methods, including finite element and finite difference approaches, often struggle to balance accuracy with computational efficiency, especially when dealing with irregular geometries or the need for adaptive resolution. In the present work we introduce a meshless method that overcomes these challenges by combining the modified finite-particle method (MFPM) for discretization with the Picard iteration technique for solving the result piecewise linear system. The proposed technique employs adaptive stencil selection to guarantee a result linear system with a moderate condition number. An adaptive meshless refinement method enhances the free boundary resolution, particularly in capturing the unknown free boundary a priori. Numerical experiments confirm the method’s flexibility and robustness across a range of node layouts – including Cartesian grids, PNP nodes, and Halton points – demonstrating its potential as an effective tool for solving bilateral obstacle problems and broadening the applicability of PDE and variational inequality models.

双边障碍问题是研究偏微分方程（PDEs）和变分不等式的基础，在最优控制、弹性和约束下的材料变形方面有着重要的应用。然而，由于固有的非线性和自由边界的存在，随着复杂接触动力学的发展，数值解决这些问题是具有挑战性的。传统的离散化方法，包括有限元和有限差分方法，常常难以平衡精度和计算效率，特别是在处理不规则几何形状或需要自适应分辨率时。在目前的工作中，我们介绍了一种无网格方法，该方法通过将用于离散化的改进有限粒子方法（MFPM）与用于求解结果分段线性系统的皮卡德迭代技术相结合来克服这些挑战。该方法采用自适应模板选择方法，保证了条件数适中的结果线性系统。一种自适应无网格细化方法提高了自由边界的分辨率，特别是在先验捕获未知自由边界方面。数值实验证实了该方法在一系列节点布局（包括笛卡尔网格、PNP节点和Halton点）上的灵活性和鲁棒性，证明了它作为解决双边障碍问题的有效工具的潜力，并扩大了PDE和变分不等式模型的适用性。

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引用次数: 0

A high-order meshless method for the Allen-Cahn phase-field model Allen-Cahn相场模型的一种高阶无网格方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-01 DOI: 10.1016/j.enganabound.2025.106559

Yuqian Xu, Wentao Ma

Accurately capturing interface dynamics in phase-field models remains a significant challenge, especially in the presence of narrow interfacial layers and geometrically complex domains. In this work, we propose a high-order meshless method based on the Generalized Finite Difference Method (GFDM) to efficiently solve the Allen-Cahn (AC) equation. The spatial discretization is constructed via Taylor expansions combined with moving least-squares approximations, achieving arbitrary-order accuracy without requiring mesh generation. Moreover, the method supports localized node refinement near interfaces and direct boundary treatment in irregular geometries, significantly enhancing computational efficiency and geometric adaptability. A Crank-Nicolson (CN) scheme is employed for time discretization to preserve the energy dissipation property of the model. Extensive numerical experiments, including mean curvature flow and phase separation in both regular and irregular domains, demonstrate the proposed method’s accuracy, energy stability, and geometric adaptability.

在相场模型中准确捕获界面动力学仍然是一个重大挑战，特别是在存在窄界面层和几何复杂区域的情况下。在本文中，我们提出了一种基于广义有限差分法（GFDM）的高阶无网格方法来有效地求解Allen-Cahn （AC）方程。空间离散化是通过泰勒展开结合移动最小二乘逼近，实现任意阶精度而不需要网格生成。此外，该方法支持界面附近的局部节点细化和不规则几何的直接边界处理，显著提高了计算效率和几何适应性。采用Crank-Nicolson （CN）格式进行时间离散，以保持模型的能量耗散特性。大量的数值实验，包括规则和不规则域的平均曲率流动和相分离，证明了该方法的准确性、能量稳定性和几何适应性。

引用次数: 0

An improved Tchebychev-radial point interpolation method for large deformation analysis of hyperelastic model 一种用于超弹性模型大变形分析的改进tchebychevv -径向点插值方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-01 DOI: 10.1016/j.enganabound.2025.106566

Nha Thanh Nguyen, Thai Van Vu, Pham Toan Thang

In this study, an improvement for the Tchebychev-radial point interpolation method (TRPIM) is proposed for the finite deformation analysis of the hyperelastic structure. The TRPIM shape function is developed by integrating the radial basis function with the Tchebychev polynomial basis function instead of traditional polynomial basis functions, and this combination produces a more accurate interpolation. Both the first and second kinds of Tchebychev polynomial are tested and evaluated for the proposed method. The modification revolves around integrating the Cartesian transformation method into the TRPIM approach to make it a truly meshfree method that does not use background cells system for numerical integration. The nonlinear behavior of hyperelastic models (Neo-Hookean, Mooney–Rivlin, and Ogden) under a finite deformation state is simulated with the total Lagrange formulation and standard Newton–Raphson algorithm. To assess the large deformation behavior of two-dimensional hyperelastic problems, a series of numerical tests are carried out. The reliability and performance of the proposed method is confirmed by comparing its results with those of available solutions.

本文提出了一种改进的tchebychevv -radial点插值法（TRPIM），用于超弹性结构的有限变形分析。将径向基函数与Tchebychev多项式基函数相结合，取代了传统的多项式基函数，得到了TRPIM形状函数，这种组合可以实现更精确的插值。对所提出的方法进行了第一类和第二类切比切夫多项式的检验和评价。改进的核心是将笛卡尔变换方法与TRPIM方法相结合，使其成为一种真正的无网格方法，不使用背景单元系统进行数值积分。采用全拉格朗日公式和标准Newton-Raphson算法模拟了有限变形状态下的超弹性模型（Neo-Hookean、Mooney-Rivlin和Ogden）的非线性行为。为了评估二维超弹性问题的大变形行为，进行了一系列数值试验。通过与已有解的结果比较，验证了所提方法的可靠性和性能。

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引用次数: 0

A meshfree RBF-PUM method for solving variable-order time-fractional transport equations with an illustrative case in intelligent transportation systems 求解智能交通系统中变阶时分数阶输运方程的无网格RBF-PUM方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-30 DOI: 10.1016/j.enganabound.2025.106570

Marzieh Raei, Seyyed-Mahdi Hosseini-Motlagh, Mohammad Reza Gholamian

This paper develops a robust meshfree numerical framework based on the Radial Basis Function Partition of Unity Method (RBF-PUM) for solving two- and three-dimensional variable-order time-fractional transport equations. The temporal derivative is approximated using the Weighted and Shifted Grünwald–Letnikov (WSGD) scheme, which ensures second-order accuracy and unconditional stability, while spatial discretization is handled by localized RBF-PUM collocation for improved conditioning and flexibility on irregular domains. Extensive numerical experiments confirm second-order convergence, stability, and robustness against geometric perturbations and noise. Benchmark tests with different variable-order profiles and a representative transport scenario in intelligent mobility systems demonstrate that the proposed framework accurately captures heterogeneous memory effects and spatio-temporal transport dynamics beyond classical diffusion. The results highlight the method’s effectiveness for modeling anomalous transport and its potential use in engineering analyses of complex multi-dimensional systems, including applications in intelligent transportation networks.

本文提出了一种基于统一方法径向基函数划分（RBF-PUM）的鲁棒无网格数值框架，用于求解二维和三维变阶时间分数输运方程。时间导数的近似采用加权移位格 nwald - letnikov （WSGD）格式，保证了二阶精度和无条件稳定性；空间离散化采用局部RBF-PUM配置，提高了不规则域上的调节和灵活性。广泛的数值实验证实二阶收敛性，稳定性和抗几何扰动和噪声的鲁棒性。在智能移动系统中，基于不同变序特征和典型传输场景的基准测试表明，所提出的框架准确地捕捉了超越经典扩散的异构记忆效应和时空传输动态。研究结果强调了该方法对异常运输建模的有效性及其在复杂多维系统的工程分析中的潜在应用，包括在智能交通网络中的应用。

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引用次数: 0

A Feature-Enhanced Physics Informed Neural Network for trajectory simulation of charged particles 用于带电粒子轨迹模拟的特征增强物理信息神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-29 DOI: 10.1016/j.enganabound.2025.106562

Fan Yang, Xuan Liu, Pengbo Wang, Xinheng Li

Trajectory simulation of charged particles is a complex multiphysics problem with dynamic field involved. With the mesh-free essence, Physics-Informed Neural Networks (PINNs) offers high capability in conformal modeling and dynamic field mapping. By integrating governing physical laws with real-time or experimental data, PINNs can accurately capture dynamic field variation and system response, demonstrating substantial potential for field–particle coupling simulations. However, conventional PINNs still face challenges caused by space charge effect and multi-scale field variations. This paper proposes a Feature-Enhanced PINN (FE-PINN) framework for the simulation of charged particle dynamics. For electromagnetic fields with evolving internal sources and complex geometries, Feature-Enhanced PINN eliminates the need for network retraining under varying space charge distributions, and applies targeted enhancement in collocation strategies and network structure to improve convergence and accuracy in domains of localized high-gradient. Built upon FE-PINN electromagnetic field solutions, particle trajectory simulation is achieved by iteratively solving the Poisson’s equation and particle motion equation under a fixed magnetic field. The proposed method is validated using the magnetron injection gun (MIG) of an 800 GHz gyrotron with results compared with that of CST Studio Suite.

带电粒子的轨迹模拟是一个涉及动力学场的复杂多物理场问题。物理信息神经网络（PINNs）具有无网格的本质，在保形建模和动态场映射方面具有很高的能力。通过将控制物理定律与实时或实验数据相结合，pinn可以准确地捕获动态场变化和系统响应，显示出场-粒子耦合模拟的巨大潜力。然而，传统的pin - ns仍然面临着空间电荷效应和多尺度场变化带来的挑战。本文提出了一种特征增强的pin - n （fe - pin）框架，用于模拟带电粒子动力学。对于具有演化的内源和复杂几何形状的电磁场，Feature-Enhanced PINN消除了在不同空间电荷分布下对网络进行再训练的需要，并对配置策略和网络结构进行了有针对性的增强，以提高局部高梯度域的收敛性和准确性。在FE-PINN电磁场解的基础上，通过迭代求解固定磁场下的泊松方程和粒子运动方程实现粒子轨迹仿真。利用800 GHz回旋管的磁控管注射枪（MIG）对该方法进行了验证，并与CST Studio Suite的结果进行了比较。

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引用次数: 0

Coupled role of mineral heterogeneity and cross fractures in the macro–meso mechanical behavior of granite: Insights from image-informed numerical modeling 矿物非均质性和交叉裂缝在花岗岩宏观细观力学行为中的耦合作用：来自图像信息数值模拟的见解

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-29 DOI: 10.1016/j.enganabound.2025.106564

Tingting Liu , Shenghao Yang , Luyang Ding , Xiaohan Xie , Hui Shen , Xinping Li

Tectonic evolution induces discontinuities and mineral heterogeneity in rock masses, complicating mechanical behavior. This study examines how mineral composition affects the response of granite with cross fractures, a key issue for underground engineering stability. The discrete element method (DEM) was implemented using the particle flow code in two dimensions (PFC2D). Parameters were calibrated through a digital image processing grain-based model (DIP–GBM), on which a random distribution properties grain-based model (RDP–GBM) was established to simulate mechanical response, fracture evolution, and energy characteristics under varied mineral compositions. Results show that fracture connectivity (ω) is the primary control: uniaxial compressive strength (UCS) decreases with increasing connectivity, while the elastic modulus (E) increases slightly at ω = 0.141 before declining. Mineral composition exerts a secondary influence, with higher biotite content and feldspar-to-quartz (λ) ratios reducing strength. In intact granite, failure is governed by mineral heterogeneity, whereas in cross-fractured granite, fracture geometry dominates. Low-stress region exists in granite with cross fractures and is linked to crack evolution. With increasing connectivity, total and elastic strain energy decrease, while biotite-rich rocks show reduced total energy. These findings highlight the coupled effects of fractures and minerals and provide a basis for stability evaluation in underground engineering.

构造演化导致岩体中的不连续和矿物非均质性，使力学行为复杂化。本文研究了矿物成分如何影响具有交叉裂缝的花岗岩的响应，这是地下工程稳定性的一个关键问题。采用二维粒子流代码（PFC2D）实现离散元法（DEM）。通过数字图像处理颗粒模型（DIP-GBM）标定参数，在此基础上建立随机分布属性颗粒模型（RDP-GBM），模拟不同矿物成分下的力学响应、裂缝演化和能量特征。结果表明，裂缝连通性（ω）是主要控制因素，单轴抗压强度（UCS）随连通性的增加而降低，而弹性模量(E)在ω = 0.141时略有增加，然后下降。矿物组成是次要影响，较高的黑云母含量和长石与石英（λ）比降低了强度。在完整的花岗岩中，破坏是由矿物非均质性决定的，而在交叉断裂的花岗岩中，裂缝几何形状占主导地位。低应力区存在于具有交叉裂缝的花岗岩中，与裂缝演化有关。随着连通性的增加，总应变能和弹性应变能降低，而富含黑云母的岩石总应变能降低。这些发现突出了裂缝与矿物的耦合作用，为地下工程稳定性评价提供了依据。

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引用次数: 0

A 2.5D BEM-based approach in the Bézier–Bernstein space for railway noise prediction and acoustic barrier assessment 基于bsamier - bernstein空间的铁路噪声预测和声障评价的2.5D bem方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-27 DOI: 10.1016/j.enganabound.2025.106568

R. Velázquez-Mata , C. Knuth , A. Romero , G. Squicciarini , A. Tadeu , D.J. Thompson , P. Galvín

Noise pollution from railway traffic, primarily caused by rolling noise resulting from the vibrations of the track and wheels, is a major public health concern. While traditional acoustic barriers are effective, they are often visually intrusive, particularly in urban settings. This has led to growing interest in more integrated solutions, such as low, close barriers, which require accurate noise prediction tools. This paper presents a two-and-a-half-dimensional BEM for predicting and mitigating railway noise. The method uses Bézier–Bernstein space to accurately model complex geometries, enhancing noise prediction across different rail profiles. Several rail configurations are compared to evaluate their impact on noise emissions and to support the design of more effective and adaptable barrier solutions. The method is then applied to evaluate the performance of a specific low-height barrier configuration, considering the presence of the vehicle to assess its impact on noise reduction. Numerical predictions are validated through comparison with experimental data and other numerical approaches. Results highlight the importance of accurate source modelling for barrier design and demonstrate the potential of the proposed method as a flexible tool for developing noise mitigation solutions that utilize the barrier’s geometry to improve acoustic performance and support visual integration in urban environments.

铁路交通的噪音污染是一个重大的公共卫生问题，主要是由轨道和车轮振动产生的滚动噪音造成的。虽然传统的隔音屏障是有效的，但它们往往是视觉上的干扰，特别是在城市环境中。这导致人们对更集成的解决方案越来越感兴趣，例如需要精确噪声预测工具的低、封闭屏障。本文提出了一种用于铁路噪声预测和抑制的二维半边界元法。该方法使用bsamzier - bernstein空间来精确模拟复杂的几何形状，增强了不同轨道轮廓的噪声预测。对几种轨道配置进行比较，以评估其对噪声排放的影响，并支持设计更有效和适应性更强的屏障解决方案。然后将该方法应用于评估特定低高度屏障配置的性能，考虑车辆的存在以评估其对降噪的影响。通过与实验数据和其他数值方法的比较，验证了数值预测的正确性。结果强调了准确的声源建模对屏障设计的重要性，并证明了所提出的方法作为开发噪声缓解解决方案的灵活工具的潜力，这些解决方案利用屏障的几何形状来改善声学性能并支持城市环境中的视觉整合。

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引用次数: 0

Dual integral formulation for acoustic resonances of a two-dimensional damped cavity with a thinpartition 具有薄隔板的二维阻尼腔的声学共振的对偶积分公式

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-27 DOI: 10.1016/j.enganabound.2025.106560

Kue-Hong Chen , Yi-Kui Liu , Jeng-Hong Kao , Jeng-Tzong Chen

This paper derives a dual integral formulation for the Helmholtz equation used to analyze the problem of the acoustic resonances for a damped cavity with a thin, incomplete partition. The presence of damping in the medium results in the incorporation of complex wave numbers in the Helmholtz equation within mathematical models. To address the singular and hypersingular integrals of the four complex-valued wave number kernel functions, the addition theorem is employed to expand them into series representations involving only real wave number. After then, the singular and hypersingular integrals are successfully transformed into a summation of regular integrals in an infinite series using the proposed regularization technique. This study investigates the acoustic resonances of a cavity with a thin partition, focusing on the effect of damping on these resonances. A case with an exact solution is given as a standard benchmark to evaluate the convergence and accuracy of the proposed dual integral equation. Finally, two numerical examples, involving rectangular and submarine-shaped cavities with a thin, incomplete partition, are presented. The acoustic frequencies and modes are determined using the developed program.

本文导出了用于分析具有薄不完全隔板的阻尼腔的声学共振问题的亥姆霍兹方程的对偶积分公式。介质中阻尼的存在导致在数学模型中亥姆霍兹方程中加入复波数。为了求解四个复值波数核函数的奇异积分和超奇异积分，利用加法定理将它们展开为只涉及实波数的级数表示。然后，利用所提出的正则化技术，将奇异积分和超奇异积分成功地转化为无穷级数上的正则积分和。本文研究了具有薄隔板的腔体的声学共振，重点研究了阻尼对这些共振的影响。给出了一个精确解的例子，作为评价对偶积分方程收敛性和准确性的标准基准。最后，给出了矩形腔和不完全薄隔板的潜艇形腔的两个数值算例。使用所开发的程序确定声频率和模态。

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引用次数: 0

Semi-analytical Discrete Green’s Function Method for cathodic protection problems 阴极保护问题的半解析离散格林函数法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-26 DOI: 10.1016/j.enganabound.2025.106544

Kevin D. Cole , Barış Çetin , Barbaros Çetin

Cathodic protection (CP) is a vital technique to prevent corrosion in submerged or intermittently exposed metallic structures. While numerical methods such as finite element and boundary element methods are commonly used to model CP systems, they often involve high computational costs, especially under nonlinear boundary conditions. This paper introduces a semi-analytical approach based on the Discrete Green’s Function Method (DGFM) for solving cathodic protection problems with both linear and nonlinear boundary conditions. The DGFM combines the accuracy of analytical methods with the flexibility of numerical techniques, enabling efficient and precise solutions. A graph theory-based framework is employed to generate the discrete Green’s functions from the Laplacian matrix, allowing the electric potential distribution to be calculated through matrix multiplications. The method is verified against analytical solutions for a linear test problem and verified through comparison with COMSOL Multiphysics simulations for a nonlinear CP model involving realistic polarization curves for zinc and steel. Results demonstrate that DGFM significantly reduces computational time while maintaining high accuracy, making it a promising tool for CP design and optimization.

阴极保护（CP）是防止水下或间歇暴露金属结构腐蚀的重要技术。虽然有限元和边界元等数值方法通常用于模拟CP系统，但它们往往涉及较高的计算成本，特别是在非线性边界条件下。本文介绍了一种基于离散格林函数法的半解析方法，用于求解具有线性和非线性边界条件的阴极保护问题。DGFM结合了分析方法的准确性和数值技术的灵活性，实现了高效和精确的解决方案。采用基于图论的框架，由拉普拉斯矩阵生成离散格林函数，通过矩阵乘法计算电势分布。通过一个线性测试问题的解析解验证了该方法的有效性，并通过COMSOL Multiphysics仿真对锌和钢的实际极化曲线非线性CP模型进行了验证。结果表明，DGFM显著减少了计算时间，同时保持了较高的精度，使其成为CP设计和优化的一个有前途的工具。

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引用次数: 0

Stability and convergence of a meshless Newmark scheme for nonlinear distributed-order Caputo models on complex domains 复杂域上非线性分布阶Caputo模型的无网格Newmark格式的稳定性和收敛性

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-26 DOI: 10.1016/j.enganabound.2025.106565

MohammadHossein Derakhshan

This paper investigates a class of nonlinear distributed-order fractional models governed by Caputo-type temporal derivatives and Riesz-type spatial operators. The distributed-order framework captures multi-scale memory effects, while the nonlocal Riesz derivatives characterize spatial anomalous diffusion. To approximate the solution, we develop a fully discrete numerical method that combines a second-order accurate Newmark scheme for the distributed-order time discretization with a meshless differentiation technique for the spatial Riesz operators. The proposed method avoids the limitations of structured grids and is particularly well-suited to complex geometrical domains. A rigorous analysis of the scheme is carried out: stability is established using a discrete energy method, and convergence is proven with error bounds of the form

‖ e_{i}^{N_{t}} ‖ \leq C (τ^{2} + h^{2} + Δ α^{2}), i = 1, 2,

demonstrating second-order accuracy in time and optimal spatial consistency. Two numerical experiments are presented to validate the theoretical findings: the first example admits an exact solution and confirms the predicted convergence rates, while the second example, which lacks a closed-form solution, employs a refined reference solution to quantify absolute errors. The results illustrate the robustness, flexibility, and accuracy of the fully discrete meshless scheme, highlighting its potential for modeling complex nonlinear fractional phenomena in science and engineering.

本文研究了一类由caputo型时间导数和riesz型空间算子控制的非线性分布阶分数阶模型。分布阶框架捕获多尺度记忆效应，而非局部Riesz导数表征空间异常扩散。为了近似解，我们开发了一种完全离散的数值方法，该方法结合了用于分布阶时间离散化的二阶精确Newmark格式和用于空间Riesz算子的无网格微分技术。该方法避免了结构网格的局限性，特别适合于复杂的几何域。对该方案进行了严格的分析：使用离散能量法建立了稳定性，并证明了收敛性，误差界为‖eiNt‖≤C(τ2+h2+Δα2),i=1,2，证明了时间上的二阶精度和最优空间一致性。通过两个数值实验验证了理论结论：第一个例子有精确解并证实了预测的收敛速度，而第二个例子没有封闭解，采用了精炼参考解来量化绝对误差。结果说明了完全离散无网格方案的鲁棒性、灵活性和准确性，突出了其在科学和工程中复杂非线性分数现象建模的潜力。

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引用次数: 0