A new multiscale algorithm for solving the heat conduction equation

Zhang, Yingchao; Jia, Yuntao; Yingzhen, Lin

doi:10.1016/j.aej.2023.06.066

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…To date, the optimization research on cloud service load balancing has not fully explored the possibility and potential advantages of integrating physical models, such as the heat conduction equation, with machine learning algorithms [9,10].…”

Section: Introductionmentioning

confidence: 99%

Optimizing Cloud Service Load Balancing Through Heat Conduction Equation Applications

He,

Wang,

Liu

et al. 2024

IJHT

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With the rapid development of cloud computing, load balancing technology in cloud services has become a critical component in ensuring service quality and system stability. Traditional load balancing methods, often relying on static parameters and preset rules, face challenges in flexibly responding to the dynamic changes in cloud service demands. Recent studies have begun to explore the application of machine learning algorithms to optimize load balancing, aiming to enhance the system's adaptive adjustment capabilities. This study proposes an innovative approach, applying the solution of the heat conduction equation to the optimization of cloud service load balancing issues. It simulates and analyzes the dynamic changes in load distribution, proposing corresponding optimization strategies. The first part of this research focuses on designing a model that integrates genetic algorithms and neural networks to solve the inverse problem of the twodimensional nonlinear heat conduction equation, namely, the accurate prediction of thermal physical parameters. By simulating the heat conduction process, this model can reflect the dynamic distribution characteristics of server loads and guide the adjustment strategy of weights. Furthermore, an adaptive dynamic load balancing strategy algorithm is proposed. By optimizing the existing engine x (Nginx) weighted least connections algorithm, an efficient adaptive algorithm is designed and implemented. This algorithm adjusts server weights dynamically based on real-time load data, enabling cloud services to respond more flexibly and efficiently to different service requests. The findings of this research not only enhance the processing capability and resource utilization rate of cloud services but also provide more scientific and precise theoretical support for load balancing through the introduction of new algorithmic models. Additionally, the proposed adaptive dynamic load balancing strategy algorithm has demonstrated good performance in practical deployment, offering new perspectives and technical paths for the research and practice of cloud service load balancing.

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Section: Introductionmentioning

confidence: 99%

Optimizing Cloud Service Load Balancing Through Heat Conduction Equation Applications

He,

Wang,

Liu

et al. 2024

IJHT

View full text Add to dashboard Cite

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An innovative subdivision collocation algorithm for heat conduction equation with non-uniform thermal diffusivity

Ejaz,

Malik,

Younis

et al. 2024

Sci Rep

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This paper presents a subdivision collocation algorithm for numerically solving the heat conduction equation with non-uniform thermal diffusivity, considering both initial and boundary conditions. The algorithm involves transforming the differential form of the heat conduction equation into a system of equations and discretizing the time variable using the finite difference formula. The numerical solution of the system of heat conduction equations is then obtained. The feasibility of the algorithm is verified through theoretical and numerical analyses. Additionally, numerical and graphical representations of the obtained numerical solutions are provided, along with a comparison to existing methods. The results demonstrate that our proposed method outperforms the existing methods in terms of accuracy.

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Similarity wave solutions of Whitham–Broer–Kaup equations in the oceanic shallow water

Fan,

Bao

2024

Physics of Fluids

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Water waves, which are essentially complex waves controlled by gravity fields and surface movements, have been studied actively. In this article, first, the Bäcklund transformation of Whitham–Broer–Kaup (WBK) equations is studied using the homogeneous balance method. Second, the solitary wave solutions and similar wave solutions of WBK equations are constructed using the obtained Bäcklund transformation, and the conclusions obtained from the homogeneous balance method and the Painlevé analysis method are compared. Then, based on the auxiliary equation method and the Bäcklund transformation obtained previously, the Weierstrass elliptic function solutions and degenerate solutions of WBK equations are attained. Finally, using the symbolic calculation system Mathematica, the dynamic characteristics of solutions are analyzed through images, which helps us increase the diversity of solutions and get more new phenomena. It is worth mentioning that by comparing the Bäcklund transformation and soliton solutions obtained by the two methods, we obtain the same and different contents, respectively. The waves in the ocean are complex and diverse. By studying the dynamic characteristics of waves, theoretical basis is provided for the motion of ships in the ocean. Furthermore, the results derived from this work have not been presented before.

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A new multiscale algorithm for solving the heat conduction equation

Cited by 3 publications

References 26 publications

Optimizing Cloud Service Load Balancing Through Heat Conduction Equation Applications

Optimizing Cloud Service Load Balancing Through Heat Conduction Equation Applications

An innovative subdivision collocation algorithm for heat conduction equation with non-uniform thermal diffusivity

Similarity wave solutions of Whitham–Broer–Kaup equations in the oceanic shallow water

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