Journal of Computational Science最新文献_第9页

Corrosion-induced multiscale damage behavior of ultrahigh strength steel: An integrated simulation and experiment study 超高强度钢腐蚀致多尺度损伤行为：模拟与试验相结合的研究

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-07-13 DOI: 10.1016/j.jocs.2025.102676

Weizheng Lu , Zouxueyin Wang , Libo Yu , Shaohua Xing , Andong Wang , Yong Zhang , Jia Li , Qihong Fang

Corrosion is an aggravating problem to cause the premature failure of structure materials, ultimately impacting the safety and operational expenses of equipment. However, the corrosion-induced multiscale damage evolution in the ultrahigh-strength steel is not clearly revealed from atomic scale to macroscopic scale. Here, corrosion-induced multiscale damage mechanism of ultrahigh strength steel plate is investigated using the experiments combined with multiscale simulation, including molecular dynamic simulation, cellular automaton simulation, and phase field finite element method. The experiment shows that the high angle grain boundaries are particularly vulnerable to corrosion, grain refinement takes place during the process of corrosion, and the exposed surface displays significant cracks in the surface of plate. From molecular dynamic simulation, the thickness of the passivation film and the corrosion rate go up with the increasing temperature, which accelerates the early passivation. The corrosion-induced cracks promote the local healing of surface roughness, leading to low strain softening at the nanoscale. By cellular automaton simulation, the passivation film, formed by the corrosion products, serves to hinder the anodic dissolution of the matrix, thereby reducing the average depth of the corrosion pits. Through phase field finite element simulation, the concentration of local strain plays a crucial role in accelerating the rupture rate of the passive film and increasing the corrosion rate at the tip of a pit. Additionally, strong local strains have a significant impact on the longitudinal advancement of corrosion, leading to the progression from a corrosion pit to a crack. These findings not only give a deep understanding of the corrosion-induced cracking behavior, but also provide valuable insights for the development of steel plate with enhanced mechanical properties.

腐蚀是导致结构材料过早失效的一个日益严重的问题，最终影响设备的安全性和运行费用。然而，从原子尺度到宏观尺度，腐蚀引起的超高强度钢的多尺度损伤演化并没有得到清晰的揭示。采用分子动力学模拟、元胞自动机模拟、相场有限元等多尺度模拟相结合的方法，对超高强度钢板的腐蚀多尺度损伤机理进行了研究。实验表明，高角度晶界特别容易受到腐蚀，在腐蚀过程中晶粒发生细化，暴露表面出现明显裂纹。分子动力学模拟表明，随着温度的升高，钝化膜的厚度和腐蚀速率均呈上升趋势，加速了早期钝化过程。腐蚀引起的裂纹促进表面粗糙度的局部愈合，导致纳米尺度的低应变软化。通过元胞自动机模拟，腐蚀产物形成的钝化膜阻碍了基体的阳极溶解，从而降低了腐蚀坑的平均深度。通过相场有限元模拟，发现局部应变的集中对加速钝化膜的破裂速率和增大坑尖处的腐蚀速率起着至关重要的作用。此外，强的局部应变对腐蚀的纵向进展有显著影响，导致腐蚀坑向裂纹的进展。这些发现不仅对腐蚀致裂行为有了深入的了解，而且为提高钢板的力学性能提供了有价值的见解。

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引用次数: 0

Deep Link Strength Prediction: Leveraging line graph transformations and neural networks 深度链接强度预测：利用线图转换和神经网络

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-07-12 DOI: 10.1016/j.jocs.2025.102661

Zhixin Ming , Jie Li , Jing Wang

Predicting link strengths in complex networks is a fundamental challenge, crucial for understanding network dynamics and optimizing real-world applications. Traditional approaches often rely on shallow structural features, limiting their ability to model intricate dependencies. To address these limitations, we propose Deep Link Strength Prediction (DLSP), a novel framework that integrates line graph transformations with graph convolutional networks (GCNs) to enhance the predictive capability of link weight estimation. DLSP redefines the task by transforming edge-centric information into node-level representations, facilitating effective learning of complex structural patterns. DLSP follows a multi-phase approach: first, a localized subgraph around the target link is extracted and encoded using a weighted node labeling scheme, preserving local structural and attribute-driven properties. Next, the labeled subgraph undergoes a line graph transformation, mapping link dependencies into node representations, thereby enabling a structured embedding space. A GCN is then employed to extract rich hierarchical representations, capturing both micro and macro-level graph structures. Finally, these learned embeddings are passed through a dense neural network to estimate the target link strength, framing the problem as a continuous-valued regression task. Unlike existing methods that rely on handcrafted features or isolated node embeddings, DLSP explicitly models link dependencies through graph-aware transformations, leading to superior predictive performance. Extensive experiments conducted on six diverse network datasets demonstrate that DLSP consistently outperforms state-of-the-art methods, showcasing its robustness, scalability, and potential for real-world applications.

预测复杂网络中的链路强度是一项基本挑战，对于理解网络动态和优化实际应用至关重要。传统方法通常依赖于浅层结构特征，限制了它们对复杂依赖关系建模的能力。为了解决这些限制，我们提出了深度链路强度预测（DLSP），这是一种将线形图变换与图卷积网络（GCNs）相结合的新框架，以增强链路权重估计的预测能力。dllsp通过将以边缘为中心的信息转换为节点级表示来重新定义任务，从而促进对复杂结构模式的有效学习。dlp采用多阶段方法：首先，使用加权节点标记方案提取目标链路周围的局部子图并对其进行编码，保留局部结构和属性驱动属性。接下来，标记的子图进行线形图转换，将链接依赖关系映射到节点表示，从而实现结构化嵌入空间。然后使用GCN提取丰富的层次表示，捕获微观和宏观级别的图结构。最后，这些学习到的嵌入通过一个密集的神经网络来估计目标链路的强度，将问题作为一个连续值回归任务。与现有依赖手工特征或孤立节点嵌入的方法不同，dlp通过图形感知转换显式地对链接依赖关系建模，从而获得卓越的预测性能。在六个不同的网络数据集上进行的广泛实验表明，dllsp始终优于最先进的方法，展示了其鲁棒性、可扩展性和现实应用的潜力。

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引用次数: 0

Fractional order malaria epidemic model: Qualitative and computational study to determine the dynamics for sensitivity prevalence 分数阶疟疾流行模型：确定敏感性流行动态的定性和计算研究

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-07-04 DOI: 10.1016/j.jocs.2025.102656

Muhammad Farman , Nezihal Gokbulut , Aamir Shehzad , Kottakkaran Sooppy Nisar , Evren Hincal , Aceng Sambas

In this study, we created a nonlinear mathematical model with eight compartments to understand the dynamics of malaria transmission in North Cyprus region using the Caputo fractional operator. Because of their memory and genetic features, fractional-order models are regarded to be more adaptable than integer-order models. To explore the malaria compartmental model, we use the stability theory of fractional-order differential equations with the Caputo operator. A full explanation of the proposed model’s qualitative and quantitative analysis is offered, as well as a brief overview of its essential aspects and a theoretical evaluation. The Lipschitz criterion and well-known fixed point theorems are used to prove the existence and uniqueness of solutions. In addition to establishing equilibrium points, sensitivity analysis of reproductive number parameters is carried out. The proposed system has been validated in terms of Ulam–Hyers–Rassias. To deal with chaotic circumstances a linear feedback control strategy directs system dynamics near equilibrium points. To verify the existence of bifurcation, we apply bifurcation principles. The study uses numerical methodology based on Newton polynomial interpolation method to graphically model the solutions. The study analyzes system behavior by investigating parameter alterations at various fractional orders while retaining model stability. The long-term memory effect, represented by the Caputo fractional order derivative, has no influence on steady point stability, but solutions get closer to equilibrium faster at higher fractional-orders.

在这项研究中，我们创建了一个非线性数学模型，有八个隔间，以了解疟疾传播的动态在北塞浦路斯地区使用卡普托分数算子。分数阶模型由于具有记忆和遗传特性，被认为比整数阶模型具有更强的适应性。为了探索疟疾区室模型，我们使用了分数阶微分方程的稳定性理论和Caputo算子。对所提出的模型的定性和定量分析进行了充分的解释，并简要概述了其基本方面和理论评价。利用Lipschitz准则和著名的不动点定理证明了解的存在唯一性。在建立平衡点的基础上，对繁殖数参数进行了敏感性分析。所提出的系统已根据Ulam-Hyers-Rassias进行了验证。为了处理混沌环境，采用线性反馈控制策略指导平衡点附近的系统动力学。为了验证分岔的存在性，我们应用了分岔原理。本研究采用基于牛顿多项式插值法的数值方法对解进行图形化建模。该研究在保持模型稳定性的同时，通过研究不同分数阶的参数变化来分析系统行为。以Caputo分数阶导数为代表的长时记忆效应对稳态点稳定性没有影响，但高分数阶解更快接近平衡。

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引用次数: 0

Data classification with dynamically growing and shrinking neural networks 动态增长和收缩神经网络的数据分类

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-07-01 DOI: 10.1016/j.jocs.2025.102660

Szymon Świderski , Agnieszka Jastrzębska

The issue of data-driven neural network model construction is one of the core problems in the domain of Artificial Intelligence. A standard approach assumes a fixed architecture with trainable weights. A conceptually more advanced assumption is that we not only train the weights but also find out the optimal model architecture. We present a new method that realizes just that. This article is an extended version of our conference paper titled “Dynamic Growing and Shrinking of Neural Networks with Monte Carlo Tree Search (Świderski and Jastrzebska, 2024). In the paper, we show in detail how to create a neural network with a procedure that allows dynamic shrinking and growing of the model while it is being trained. The decision-making mechanism for the architectural design is governed by the Monte Carlo tree search procedure, which simulates network behavior and allows comparing several candidate architecture changes to choose the best one. The proposed method was validated using both visual and time series datasets, demonstrating its particular effectiveness in multivariate time series classification. This is attributed to the architecture’s ability to adapt dynamically, allowing independent modifications for each time series. To enhance the reproducibility of our method, we publish open-source code of the proposed method. It was prepared in Python. Experimental evaluations in visual pattern and multivariate time series classification tasks revealed highly promising performance, underscoring the method’s robustness and adaptability.

数据驱动的神经网络模型构建问题是人工智能领域的核心问题之一。标准方法假定具有可训练权重的固定体系结构。一个概念上更高级的假设是，我们不仅要训练权值，还要找出最优的模型架构。我们提出了一种实现这一目标的新方法。本文是我们题为“神经网络与蒙特卡罗树搜索的动态增长和收缩”的会议论文的扩展版本（Świderski和Jastrzebska， 2024）。在本文中，我们详细展示了如何用一个过程创建一个神经网络，该过程允许模型在训练时动态收缩和增长。体系结构设计的决策机制由蒙特卡罗树搜索过程控制，该过程模拟网络行为，并允许比较几种候选体系结构变化以选择最佳方案。采用视觉和时间序列数据集对该方法进行了验证，证明了该方法在多变量时间序列分类中的特殊有效性。这归因于体系结构动态适应的能力，允许对每个时间序列进行独立修改。为了提高方法的可重复性，我们发布了该方法的开源代码。它是用Python编写的。在视觉模式和多变量时间序列分类任务中的实验评价表明，该方法具有良好的鲁棒性和适应性。

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引用次数: 0

Fast and power efficient GPU-based explicit elastic wave propagation analysis by low-ordered orthogonal voxel finite element with INT8 Tensor Cores 基于INT8张量核低阶正交体素有限元的快速高效gpu显式弹性波传播分析

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-07-01 DOI: 10.1016/j.jocs.2025.102659

Tsuyoshi Ichimura , Kohei Fujita , Muneo Hori , Maddegedara Lalith

There is a strong need for faster and more power-efficient explicit elastic wavefield simulations for large and complex three-dimensional media using a structured finite element method. Such wavefield simulations are suitable for GPUs, which have been improving their computational performance in recent years, and the use of GPUs is expected to speed up such simulations. However, there is still room for speedup and improving energy efficiency of such simulations using GPUs, since the performance of GPUs is not fully exploited just by its simple use, and the conventional method involves some numerical dispersion. In this paper, we propose a method for fast and efficient explicit structured-mesh wavefield simulation on GPUs by utilizing INT8 Tensor Cores and reducing numerical dispersion. We implemented the proposed method on GPUs and evaluated its performance in detail using an application example that simulates a real problem, and showed that it is faster and more efficient than conventional methods on many-node CPU-based systems and multiple GPU-based systems. This paper is the extended version of Ichimura et al. (2024).[1]

对于大型复杂的三维介质，迫切需要采用结构有限元法进行更快、更节能的显式弹性波场模拟。这种波场模拟适合gpu，近年来gpu的计算性能一直在提高，gpu的使用有望加快这种模拟。然而，由于gpu的简单使用并不能充分发挥其性能，并且传统方法涉及到一些数值色散，因此使用gpu进行此类模拟仍有加速和提高能效的空间。本文提出了一种利用INT8张量核和减少数值色散的方法，在gpu上实现快速高效的显式结构网格波场模拟。我们在gpu上实现了该方法，并通过一个模拟实际问题的应用实例对其性能进行了详细的评估，结果表明，该方法在基于多节点cpu的系统和基于多gpu的系统上比传统方法更快、更高效。本文是Ichimura et al. (2024). b[1]的扩展版

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引用次数: 0

TECNN: Identification of key nodes in complex networks based on transformer encoder and Convolutional Neural Network 基于变压器编码器和卷积神经网络的复杂网络关键节点识别

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-06-28 DOI: 10.1016/j.jocs.2025.102632

Lihui Sun, Pengli Lu

In complex networks, identifying key nodes is crucial for controlling information dissemination, optimizing resource allocation, and enhancing network robustness. Although many methods for identifying key nodes have been proposed, most deep learning-based approaches lack in-depth study of multi-hop neighbor relationships when constructing node features, often ignoring critical information and thus affecting identification accuracy. To address this issue, we propose a hybrid model based on the Transformer encoder and Convolutional Neural Network (TECNN) to better capture comprehensive information of nodes and predict their diffusion influence. Firstly, we use the neighborhood aggregation module to aggregate the 7-hop neighbor features of the nodes, obtaining a neighborhood matrix for the nodes. Next, the neighborhood matrix is fed into the Transformer encoder to capture the long-range dependencies between nodes, producing new node feature representations. These new node representations are then input into the Convolutional Neural Network, and the structural information of the nodes is further extracted through multilayer convolutional operations. Finally, a fully connected layer is used to predict the influence of the nodes. We perform comparative experiments by comparing the TECNN algorithm with four classical centrality algorithms and three state-of-the-art deep learning-based algorithms on 12 networks. The experimental results show that TECNN performs well in terms of ranking accuracy, discriminative ability, and top-10 node identification precision.

在复杂网络中，关键节点识别对于控制信息传播、优化资源配置、增强网络鲁棒性至关重要。尽管已经提出了许多识别关键节点的方法，但大多数基于深度学习的方法在构建节点特征时缺乏对多跳邻居关系的深入研究，往往忽略了关键信息，从而影响了识别的准确性。为了解决这一问题，我们提出了一种基于Transformer编码器和卷积神经网络（TECNN）的混合模型，以更好地捕获节点的综合信息并预测其扩散影响。首先，利用邻域聚合模块对节点的7跳邻居特征进行聚合，得到节点的邻域矩阵；接下来，将邻域矩阵馈送到Transformer编码器中以捕获节点之间的远程依赖关系，从而产生新的节点特征表示。然后将这些新的节点表示输入到卷积神经网络中，并通过多层卷积操作进一步提取节点的结构信息。最后，利用全连通层来预测节点的影响。我们将TECNN算法与四种经典的中心性算法和三种最先进的基于深度学习的算法在12个网络上进行了对比实验。实验结果表明，TECNN在排序精度、判别能力和top-10节点识别精度方面都有较好的表现。

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引用次数: 0

A surrogate model for studying random field energy release rates in 2D brittle fractures 研究二维脆性裂缝随机场能释放率的替代模型

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-06-28 DOI: 10.1016/j.jocs.2025.102635

Luis Blanco-Cocom , Marcos A. Capistrán , Jaroslaw Knap , J. Andrés Christen

This article proposes a weighted-variational model as an approximated surrogate model to lessen numerical complexity and lower the execution times of brittle fracture simulations. Consequently, Monte Carlo studies of brittle fractures become possible when energy release rates are modeled as a random field. In the weighed-variational model, we propose applying a Gaussian random field with a Matérn covariance function to simulate a non-homogeneous energy release rate (

G_{c}

) of a material. Numerical solutions to the weighed-variational model, along with the more standard but computationally demanding hybrid phase-field models, are obtained using the FEniCS open-source software. The results have indicated that the weighted-variational model is a competitive surrogate model of the hybrid phase-field method to mimic brittle fractures in real structures. This method reduces execution times by 90%. We conducted a similar study and compared our results with an actual brittle fracture laboratory experiment. We present an example where a Monte Carlo study is carried out, modeling

G_{c}

as a Gaussian Process, obtaining a distribution of possible fractures, and load–displacement curves.

本文提出一种加权变分模型作为近似替代模型，以降低脆性断裂模拟的数值复杂度和执行次数。因此，当能量释放率作为随机场建模时，脆性断裂的蒙特卡罗研究成为可能。在加权变分模型中，我们提出了一个带mat协方差函数的高斯随机场来模拟材料的非均匀能量释放率（Gc）。利用FEniCS开源软件获得了加权变分模型的数值解，以及更标准但计算要求较高的混合相场模型。结果表明，加权变分模型是混合相场法模拟实际结构脆性断裂的一个有竞争力的替代模型。这种方法减少了90%的执行时间。我们进行了类似的研究，并将我们的结果与实际的脆性断裂实验室实验进行了比较。我们提出了一个蒙特卡罗研究的例子，将Gc建模为高斯过程，获得可能断裂的分布和负载-位移曲线。

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引用次数: 0

Path planning of complex environment based on hyper view ant colony algorithm 基于超视场蚁群算法的复杂环境路径规划

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-06-26 DOI: 10.1016/j.jocs.2025.102658

Junqi Yang, Feiyang Liu, Hongwei Zhang

A hyper view ant colony algorithm is developed to deal with the issues of sluggish convergence and poor search ability of traditional ant colony algorithms in complex environments. The concept of hyper view ant and view selection mechanism are first introduced in the enhanced ant colony algorithm. Dijkstra algorithm is used to determine the optimal path for the reachable node set of hyper view ants, where the state transition is accomplished using the designed pheromone calculation method. In addition, this paper creates an ant knowledge database and introduces it into the state transition type, which makes the information communication between ants more adequate. The knowledge database will be updated via historical path, and its value will be adaptively loaded. Then, an ant view atrophy mechanism is developed to balance the time efficiency of the proposed algorithm, and a pheromone compensation method is given to ensure the adsorption of algorithm to optimal path. Finally, by the experiments in various complex environments, the statistics of different performance parameters show that the results of the proposed algorithm in this paper are better than the ones of the existing algorithms including traditional ant colony algorithm.

针对传统蚁群算法在复杂环境下收敛速度慢、搜索能力差的问题，提出了一种超视点蚁群算法。在增强型蚁群算法中，首次引入了超视图蚁的概念和视图选择机制。采用Dijkstra算法确定超视图蚂蚁可达节点集的最优路径，并利用所设计的信息素计算方法完成状态转移。此外，本文还建立了蚂蚁知识库，并将其引入状态转换类型，使蚂蚁之间的信息通信更加充分。通过历史路径更新知识库，并自适应加载知识库的值。然后，建立了蚁视萎缩机制来平衡算法的时间效率，并给出了信息素补偿方法来保证算法对最优路径的吸附。最后，通过在各种复杂环境下的实验，对不同性能参数的统计表明，本文算法的结果优于包括传统蚁群算法在内的现有算法。

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引用次数: 0

A pseudospectral method for time-fractional PDEs with shifted Chebyshev and Lagrange interpolating polynomials on overlapping decomposed domains 在重叠分解域上具有移位切比雪夫和拉格朗日插值多项式的时间分数阶偏微分方程的伪谱方法

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-06-25 DOI: 10.1016/j.jocs.2025.102654

Nancy Mukwevho , Olumuyiwa Otegbeye , Shina Daniel Oloniiju

Time-fractional partial differential equations (TFPDEs) are powerful mathematical tools for modeling a wide range of physical and biological phenomena that exhibit memory effects, anomalous diffusion and non-local behavior. These classes of equations are crucial in capturing dynamics where the influence of past states affects future evolution, making them essential in many areas of applied science, such as heat transfer, viscoelasticity and anomalous diffusion. This study proposes a pseudospectral method that combines the weighted sums of the Chebyshev and Lagrange polynomials to numerically approximate the solutions of TFPDEs. The spatial domain is partitioned into uniform, overlapping subdomains, where the solution in each subdomain is represented as a weighted sum of the Lagrange interpolating polynomials. On the other hand, the time domain is treated as a whole without decomposition, and the solution in the temporal dimension is expanded using the first-kind shifted Chebyshev polynomials. We validate the accuracy and performance of the method through a series of test cases, covering both linear and nonlinear TFPDEs in one and multiple spatial dimensions. These examples showcase the method’s capability to handle the computational challenges associated with TFPDEs and underline its potential for broader applications in problems involving fractional dynamics. Specifically, the proposed technique is applied to resolve TFPDE, which models heat transfer on a disk, a problem relevant to modeling heat conduction in circular plates and semiconductor wafers. A time-dependent Gaussian heat source concentrated in a specific region of the disk is introduced to accurately simulate practical thermal diffusion dynamics. The gradual increase of the source term over time offers a more realistic representation of the evolving thermal diffusion process.

时间分数阶偏微分方程（TFPDEs）是一种强大的数学工具，用于模拟各种表现出记忆效应、异常扩散和非局部行为的物理和生物现象。这些类型的方程对于捕捉过去状态影响未来演变的动力学至关重要，使它们在许多应用科学领域至关重要，例如传热，粘弹性和异常扩散。本文提出了一种结合切比雪夫多项式和拉格朗日多项式加权和的伪谱方法来数值逼近TFPDEs的解。空间域被划分为一致的，重叠的子域，其中每个子域的解被表示为拉格朗日插值多项式的加权和。另一方面，将时域视为一个整体而不进行分解，并利用第一类移位的切比雪夫多项式展开时间维的解。我们通过一系列测试用例验证了该方法的准确性和性能，这些测试用例涵盖了一维和多维空间的线性和非线性tfpde。这些例子展示了该方法处理与tfpde相关的计算挑战的能力，并强调了其在涉及分数动力学的问题中更广泛应用的潜力。具体来说，所提出的技术被应用于解决TFPDE，它模拟磁盘上的传热，一个与模拟圆形板和半导体晶圆中的热传导有关的问题。为了准确地模拟实际的热扩散动力学，引入了集中在圆盘特定区域的时变高斯热源。随着时间的推移，源项逐渐增加，可以更真实地反映热扩散过程的演变。

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引用次数: 0

Pell wavelet-optimization procedure for two classes of fractional partial differential equations with nonlocal boundary conditions 两类具有非局部边界条件的分数阶偏微分方程的Pell小波优化方法

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science

Pub Date : 2025-06-25 DOI: 10.1016/j.jocs.2025.102655

Sedigheh Sabermahani , Parisa Rahimkhani , Yadollah Ordokhani

Studying initial value problems with nonlocal conditions is important because they have applications in physics and other areas of applied mathematics. This manuscript presents a hybrid scheme for solving two classes of fractional partial differential equations with nonlocal boundary conditions (N-BCs), namely fractional-order reaction–diffusion equations (F-RDEs), and fractional-order hyperbolic partial differential equations (FH-PDEs). We develop a new computational technique that employs Pell wavelet functions. To this end, we present a derivative pseudo-operational matrix and an extra pseudo-operational matrix for integral and Riemann–Liouville fractional integration and design the desired method with the help of optimization and collocation methods. The systems resulting from this technique are solved using the FindRoot package in Mathematica software. We also perform several numerical experiments to validate the accuracy and superiority of the suggested strategy.

研究具有非定域条件的初值问题是很重要的，因为它们在物理学和其他应用数学领域都有应用。本文提出了求解两类具有非局部边界条件的分数阶偏微分方程的混合格式，即分数阶反应扩散方程（F-RDEs）和分数阶双曲型偏微分方程（FH-PDEs）。我们开发了一种新的利用Pell小波函数的计算技术。为此，我们给出了积分和Riemann-Liouville分数阶积分的一个导数伪操作矩阵和一个额外的伪操作矩阵，并借助优化和配置方法设计了所需的方法。使用Mathematica软件中的FindRoot包解决了由该技术产生的系统。我们还进行了几个数值实验来验证所建议策略的准确性和优越性。

引用次数: 0